54 | 63 | 0.17 | 0.35 |  33 $\pm$ 28 | Methyldopa | Iron (II) Sulfate | 21.60 | Moderate | Iron decreases the absorption of dopa derivatives
54 | 63 | 0.08 | 0.34 |  110 $\pm$ 118 | Diltiazem | Amlodipine | 1.52 | Moderate | Increases the effect and toxicity of amlodipine
56 | 60 | 0.01 | 0.19 |  49 $\pm$ 95 | Prednisone | Warfarin | 0.76 | Moderate | The corticosteroid alters the anticoagulant effect
56 | 60 | 0.01 | 0.12 |  28 $\pm$ 43 | Amitriptyline | Fenoterol | 2.83 | * | The tricyclic increases the sympathomimetic effect
58 | 59 | 0.01 | 0.15 |  34 $\pm$ 34 | Fluconazole | Carbamazepine | 1.03 | Moderate | Increases the effect of carbamazepine
59 | 58 | 0.05 | 0.03 |  5 $\pm$ 10 | Hydrocortisone | ASA | 1.35 | Moderate | The corticosteroid decreases the effect of salicylates
60 | 57 | 0.01 | 0.15 |  50 $\pm$ 48 | Fluconazole | Imipramine | 7.37 | Moderate | The imidazole increases the effect and toxicity of the tricyclic
60 | 57 | 0.02 | 0.35 |  96 $\pm$ 96 | Glyburide | Carvedilol | 0.73 | Moderate | The beta-blocker decreases the symptoms of hypoglycemia
62 | 52 | 0.08 | 0.49 |  118 $\pm$ 114 | Digoxin | Amiodarone | 0.56 | Major | Amiodarone increases the effect of digoxin
63 | 51 | 0.00 | 0.23 |  93 $\pm$ 90 | Hydrochlorothiazide | Lithium | 2.90 | Major | The thiazide diuretic increases serum levels of lithium
64 | 48 | 0.00 | 0.16 |  65 $\pm$ 74 | Enalapril | Lithium | 1.91 | Moderate | The ACE inhibitor increases serum levels of lithium
65 | 47 | 0.04 | 0.46 |  135 $\pm$ 109 | Allopurinol | Warfarin | 0.19 | Moderate | Allopurinol increases the anticoagulant effect
66 | 44 | 0.03 | 0.16 |  51 $\pm$ 61 | Imipramine | Salbutamol | 3.19 | Moderate | The tricyclic increases the sympathomimetic effect
67 | 43 | 0.08 | 0.40 |  144 $\pm$ 153 | Phenytoin | Diazepam | 0.62 | Moderate | Possible increased levels of the hydantoin, decrease of benzodiazepine
68 | 41 | 0.00 | 0.21 |  82 $\pm$ 74 | Losartan | Lithium | 4.13 | Moderate | Losartan increases serum levels of lithium
69 | 39 | 0.04 | 0.42 |  82 $\pm$ 64 | Gliclazide | Carvedilol | 0.67 | None | The beta-blocker decreases the symptoms of hypoglycemia
69 | 39 | 0.14 | 0.15 |  30 $\pm$ 46 | Timolol | Ibuprofen | 1.42 | None | Risk of inhibition of renal prostaglandins
69 | 39 | 0.06 | 0.42 |  130 $\pm$ 122 | Nortriptyline | Carbamazepine | 1.26 | Moderate | The tricyclic increases the effect of carbamazepine
72 | 36 | 0.05 | 0.05 |  15 $\pm$ 14 | Phenobarbital | Dexamethasone | 1.11 | Moderate | The barbiturate decreases the effect of the corticosteroid
73 | 31 | 0.01 | 0.04 |  9 $\pm$ 8 | Prednisolone | ASA | 2.95 | Moderate | The corticosteroid decreases the effect of salicylates
73 | 31 | 0.01 | 0.20 |  48 $\pm$ 66 | Propranolol | Salbutamol | 6.61 | Major | Antagonism
75 | 30 | 0.00 | 0.09 |  10 $\pm$ 3 | Clavulanate | Ethinyl Estradiol | inf | None | Anti-infectious agent could decrease effect of oral contraceptive
76 | 28 | 0.04 | 0.22 |  83 $\pm$ 86 | Digoxin | Diazepam | 1.09 | Moderate | The benzodiazepine increases the effect of digoxin
77 | 27 | 0.01 | 0.30 |  81 $\pm$ 73 | Propranolol | Gliclazide | 2.02 | None | The beta-blocker decreases the symptoms of hypoglycemia
77 | 27 | 0.03 | 0.19 |  11 $\pm$ 6 | Doxycycline | Ethinyl Estradiol | inf | Moderate | Anti-infectious agent could decrease effect of oral contraceptive
77 | 27 | 0.05 | 0.05 |  10 $\pm$ 6 | Phenytoin | Ciprofloxacin | 0.49 | Moderate | Ciprofloxacin decreases the hydantoin effect
77 | 27 | 0.01 | 0.05 |  7 $\pm$ 3 | Carbamazepine | Metronidazole | 1.68 | Moderate | Metronidazole increases the effect of carbamazepine
77 | 27 | 0.00 | 0.07 |  8 $\pm$ 7 | Prednisone | Estradiol | inf | Moderate | The estrogenic agent increases the effect of corticosteroid
82 | 26 | 0.00 | 0.20 |  44 $\pm$ 70 | Fluconazole | Nortriptyline | 5.43 | Moderate | The imidazole increases the effect and toxicity of the tricyclic
82 | 26 | 0.05 | 0.07 |  14 $\pm$ 12 | Phenytoin | Dexamethasone | 1.13 | Moderate | The enzyme inducer decreases the effect of the corticosteroid
84 | 25 | 0.03 | 0.56 |  157 $\pm$ 136 | Diltiazem | Amiodarone | 1.26 | Major | Increased risk of cardiotoxicity and arrhythmias
85 | 24 | 0.01 | 0.17 |  15 $\pm$ 10 | Propranolol | Fenoterol | 3.54 | * | Antagonism
85 | 24 | 0.01 | 0.29 |  100 $\pm$ 85 | Carbamazepine | Warfarin | 0.99 | Moderate | Decreases the anticoagulant effect
85 | 24 | 0.00 | 0.05 |  3 $\pm$ 2 | Diclofenac | Warfarin | 0.84 | Major | The NSAID increases the anticoagulant effect
85 | 24 | 0.04 | 0.15 |  29 $\pm$ 45 | Phenytoin | Prednisone | 1.72 | Moderate | The enzyme inducer decreases the effect of the corticosteroid
89 | 23 | 0.03 | 0.47 |  152 $\pm$ 143 | Diltiazem | Propranolol | 2.01 | Major | Increased risk of bradycardia
89 | 23 | 0.00 | 0.16 |  36 $\pm$ 44 | Fluconazole | Haloperidol | 1.33 | Major | The imidazole increases the effect and toxicity of haloperidol
91 | 22 | 0.05 | 0.20 |  19 $\pm$ 28 | Estrogens Conj. | Prednisone | inf | Moderate | The estrogenic agent increases the effect of corticosteroid
91 | 22 | 0.00 | 0.07 |  9 $\pm$ 4 | Ciprofloxacin | Warfarin | 1.02 | Major | The quinolone increases the anticoagulant effect
93 | 21 | 0.01 | 0.08 |  10 $\pm$ 6 | Tobramycin | Furosemide | 3.01 | Major | Increased ototoxicity
93 | 21 | 0.02 | 0.33 |  94 $\pm$ 116 | Chlorpromazine | Propranolol | 1.77 | Moderate | Increased effect of both drugs
95 | 19 | 0.00 | 0.07 |  26 $\pm$ 35 | Prednisone | Phenobarbital | 1.53 | Moderate | The barbiturate decreases the effect of the corticosteroid
95 | 19 | 0.00 | 0.07 |  10 $\pm$ 7 | Ciprofloxacin | Aminophylline | 1.21 | Major | The quinolone increases the effect of theophylline
97 | 18 | 0.00 | 0.13 |  33 $\pm$ 44 | Fluconazole | Warfarin | 0.89 | Major | Increases the anticoagulant effect
98 | 17 | 0.03 | 0.24 |  50 $\pm$ 48 | Nortriptyline | Salbutamol | 1.70 | Moderate | The tricyclic increases the sympathomimetic effect
98 | 17 | 0.01 | 0.26 |  107 $\pm$ 85 | Propranolol | Phenobarbital | 1.01 | Moderate | The barbiturate decreases the effect of metabolized beta-blocker
100 | 16 | 0.02 | 0.24 |  46 $\pm$ 29 | Haloperidol | Propranolol | 1.56 | Moderate | Increased effect of both drugs
Supplementary Table 8:  DDI list 51-100. See Supplementary Table 7 for column
description. Continues on Supplementary Table 9.

rankΦ | $|U_{i,j}^{\Phi}|$ | $\gamma_{i,j}^{\Phi}$ | $\tau_{i,j}^{\Phi}$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity | interaction
---|---|---|---|---|---|---|---|---|---
100 | 16 | 0.00 | 0.07 |  6 $\pm$ 3 | Azithromycin | Warfarin | 1.18 | Moderate | Increases the anticoagulant effect
100 | 16 | 0.00 | 0.08 |  16 $\pm$ 21 | Metronidazole | Lithium | 4.96 | Moderate | Metronidazole increases the effect and toxicity of lithium
100 | 16 | 0.03 | 0.31 |  94 $\pm$ 83 | Phenytoin | Furosemide | 0.55 | Minor | The hydantoin decreases the effect of furosemide
104 | 15 | 0.01 | 0.13 |  20 $\pm$ 17 | Carvedilol | Fenoterol | 0.47 | * | Antagonism
105 | 14 | 0.02 | 0.21 |  5 $\pm$ 3 | Doxycycline | Amoxicillin | 0.53 | Moderate | Possible antagonism of action
105 | 14 | 0.00 | 0.12 |  9 $\pm$ 7 | Furosemide | Gentamicin | 0.71 | Major | Increased ototoxicity
105 | 14 | 0.00 | 0.23 |  63 $\pm$ 59 | Fluconazole | Phenytoin | 1.28 | Moderate | Increases the effect of hydantoin
105 | 14 | 0.03 | 0.23 |  88 $\pm$ 71 | Phenytoin | Warfarin | 0.94 | Moderate | Increased hydantoin levels and risk of bleeding
109 | 13 | 0.01 | 0.14 |  35 $\pm$ 26 | Carbamazepine | Ethinyl Estradiol | inf | Major | This product might cause a slight decrease of contraceptive effect
109 | 13 | 0.01 | 0.14 |  35 $\pm$ 26 | Levonorgestrel | Carbamazepine | inf | Major | Carbamazepine decreases the contraceptive effect
109 | 13 | 0.01 | 0.56 |  122 $\pm$ 113 | Propranolol | Methyldopa | 8.50 | Major | Possible hypertensive crisis
109 | 13 | 0.05 | 0.19 |  55 $\pm$ 59 | Timolol | Glyburide | 1.13 | Moderate | The beta-blocker decreases the symptoms of hypoglycemia
113 | 12 | 0.01 | 0.18 |  72 $\pm$ 98 | Captopril | Lithium | 1.42 | Moderate | The ACE inhibitor increases serum levels of lithium
114 | 11 | 0.01 | 0.08 |  33 $\pm$ 63 | Imipramine | Fenoterol | 7.08 | * | The tricyclic increases the sympathomimetic effect
114 | 11 | 0.01 | 0.24 |  57 $\pm$ 46 | Methylphenidate | Carbamazepine | 0.07 | None | Carbamazepine could reduce the effect of methylphendiate
114 | 11 | 0.00 | 0.15 |  14 $\pm$ 21 | Norfloxacin | Aminophylline | 7.08 | Moderate | The quinolone increases the effect of theophylline
117 | 10 | 0.02 | 0.04 |  11 $\pm$ 4 | Erythromycin | Simvastatin | 2.83 | Major | The macrolide possibly increases the statin toxicity
118 | 9 | 0.00 | 0.03 |  7 $\pm$ 1 | Prednisolone | Phenobarbital | 0.89 | Moderate | The barbiturate decreases the effect of the corticosteroid
118 | 9 | 0.00 | 0.29 |  62 $\pm$ 46 | Folic acid | Phenytoin | 1.42 | Moderate | Folic acid decreases the levels of hydantoin
118 | 9 | 0.00 | 0.11 |  16 $\pm$ 9 | Metoclopramide | Levodopa | 5.67 | Moderate | Levodopa decreases the effect of metoclopramide
118 | 9 | 0.00 | 0.29 |  72 $\pm$ 128 | Carbamazepine | Norethisterone | inf | Major | This product may cause a slight decrease of contraceptive effect
118 | 9 | 0.03 | 0.15 |  51 $\pm$ 91 | Timolol | Salbutamol | 0.89 | Major | Antagonism
123 | 8 | 0.01 | 0.22 |  67 $\pm$ 36 | Diltiazem | Carbamazepine | 0.71 | Major | Increases the effect of carbamazepine
123 | 8 | 0.00 | 0.04 |  6 $\pm$ 2 | Metronidazole | Phenobarbital | 1.18 | Moderate | The barbiturate decreases the effect of metronidazole
123 | 8 | 0.02 | 0.33 |  53 $\pm$ 40 | Methyldopa | Salbutamol | 4.96 | Moderate | Increased arterial pressure
123 | 8 | 0.00 | 0.25 |  82 $\pm$ 54 | Carbamazepine | Aminophylline | 0.71 | Moderate | Increases or decreases the effect of theophylline
127 | 7 | 0.01 | 0.16 |  62 $\pm$ 97 | Phenytoin | Trimethoprim | 0.94 | Moderate | Trimethoprim increases the effect of hydantoin
127 | 7 | 0.00 | 0.23 |  122 $\pm$ 123 | Propranolol | Maprotiline | 4.25 | Minor | Propranolol increases the serum levels of cisapride
127 | 7 | 0.01 | 0.11 |  25 $\pm$ 15 | Nortriptyline | Fenoterol | 1.77 | * | The tricyclic increases the sympathomimetic effect
127 | 7 | 0.02 | 0.09 |  13 $\pm$ 8 | Methyldopa | Fenoterol | 4.25 | None | Increased arterial pressure
127 | 7 | 0.01 | 0.20 |  11 $\pm$ 4 | Doxycycline | Iron (II) Sulfate | inf | Moderate | Formation of non-absorbable complexes
132 | 5 | 0.00 | 0.55 |  82 $\pm$ 86 | Propranolol | Aminophylline | 1.06 | Major | Antagonism of action and increased effect of theophylline
132 | 5 | 0.04 | 0.45 |  221 $\pm$ 207 | Propylthiouracil | Warfarin | 1.06 | Moderate | The anti-thyroid agent causes variations in the anticoagulant effect
132 | 5 | 0.01 | 0.09 |  9 $\pm$ 4 | Doxycycline | Carbamazepine | 2.83 | Moderate | The anticonvulsant decreases the effect of doxycycline
132 | 5 | 0.02 | 0.22 |  34 $\pm$ 26 | Timolol | Gliclazide | 1.06 | None | The beta-blocker decreases the symptoms of hypoglycemia
132 | 5 | 0.00 | 0.17 |  10 $\pm$ 6 | Prednisolone | Ethinyl Estradiol | inf | Moderate | The estrogenic agent increases the effect of the corticosteroid
132 | 5 | 0.00 | 0.31 |  162 $\pm$ 120 | Medroxyproges. Ac. | Phenobarbital | inf | Moderate | The enzyme inducer decreases the effect of hormones
132 | 5 | 0.01 | 0.35 |  107 $\pm$ 123 | Phenytoin | Amiodarone | 0.18 | Moderate | Amiodarone increases the effect of hydantoin
132 | 5 | 0.00 | 0.21 |  104 $\pm$ 153 | Folic acid | Phenobarbital | 2.83 | Moderate | Folic acid decreases the effect of anticonvulsant
140 | 4 | 0.00 | 0.16 |  40 $\pm$ 29 | Levonorgestrel | Phenobarbital | inf | Major | Phenobarbital decreases the effect of levonorgestrel
140 | 4 | 0.00 | 0.26 |  72 $\pm$ 61 | Atenolol | Verapamil | 0.00 | Major | Increased effect of both drugs
140 | 4 | 0.01 | 0.14 |  10 $\pm$ 2 | Estrogens Conj. | Prednisolone | inf | Moderate | The estrogenic agent increases the effect of corticosteroid
140 | 4 | 0.00 | 0.14 |  4 $\pm$ 3 | Doxycycline | Clavulanate | 0.71 | None | Possible antagonism of action
140 | 4 | 0.00 | 0.17 |  62 $\pm$ 44 | Phenobarbital | Aminophylline | 0.24 | Moderate | The barbiturate decreases the effect of theophylline
145 | 3 | 0.01 | 0.18 |  97 $\pm$ 94 | Estrogens Conj. | Phenobarbital | inf | Moderate | The enzyme inducer decreases the effect of hormones
145 | 3 | 0.00 | 0.32 |  136 $\pm$ 117 | Ethinyl Estradiol | Aminophylline | inf | Moderate | The contraceptive increases the effect and toxicity of theophylline
145 | 3 | 0.00 | 0.20 |  53 $\pm$ 16 | Ethinyl Estradiol | Phenobarbital | inf | Major | This product may cause a slight decrease of contraceptive effect
145 | 3 | 0.00 | 0.22 |  45 $\pm$ 43 | Medroxyproges. Ac. | Warfarin | inf | None | The agent increases the effect of anticoagulant
145 | 3 | 0.00 | 0.01 |  2 $\pm$ 0 | Hydrocortisone | Phenobarbital | 1.42 | Moderate | The barbiturate decreases the effect of the corticosteroid
145 | 3 | 0.00 | 0.23 |  11 $\pm$ 9 | Doxycycline | Warfarin | 1.42 | Moderate | The tetracycline increases the anticoagulant effect
Supplementary Table 9:  DDI list 101-150. See Supplementary Table 7 for column
description. Continues on Supplementary Table 10.

rankΦ | $|U_{i,j}^{\Phi}|$ | $\gamma_{i,j}^{\Phi}$ | $\tau_{i,j}^{\Phi}$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity | interaction
---|---|---|---|---|---|---|---|---|---
145 | 3 | 0.01 | 0.12 |  23 $\pm$ 13 | Phenytoin | Aminophylline | 1.42 | Moderate | Decreased effect of both products
145 | 3 | 0.01 | 0.43 |  40 $\pm$ 57 | Methyldopa | Levodopa | inf | Minor | Methyldopa increases the effect and toxicity of levodopa
145 | 3 | 0.00 | 0.12 |  40 $\pm$ 19 | Digoxin | Verapamil | inf | Moderate | Verapamil increases the effect of digoxin
145 | 3 | 0.00 | 0.15 |  58 $\pm$ 56 | Aminophylline | Lithium | 1.42 | Moderate | Theophylline decreases serum levels of lithium
145 | 3 | 0.01 | 0.10 |  9 $\pm$ 4 | Phenytoin | Prednisolone | 0.35 | Moderate | The enzyme inducer decreases the effect of the corticosteroid
145 | 3 | 0.01 | 0.43 |  185 $\pm$ 98 | Phenytoin | Levodopa | 0.00 | Moderate | The hydantoin decreases the effect of levodopa
157 | 2 | 0.00 | 0.06 |  6 $\pm$ 1 | Estradiol | Prednisolone | inf | Moderate | The estrogenic agent increases the effect of corticosteroid
157 | 2 | 0.01 | 0.13 |  31 $\pm$ 0 | Timolol | Aminophylline | inf | Major | Antagonism of action and increased effect of theophylline
157 | 2 | 0.00 | 0.24 |  62 $\pm$ 53 | Phenytoin | Estradiol | inf | Moderate | The enzyme inducer decreases the effect of the hormones
157 | 2 | 0.00 | 0.08 |  23 $\pm$ 11 | Doxycycline | Phenobarbital | inf | Moderate | The anticonvulsant decreases the effect of doxycycline
157 | 2 | 0.00 | 0.20 |  79 $\pm$ 30 | Norethisterone | Phenobarbital | inf | Major | This product may cause a slight decrease of contraceptive effect
157 | 2 | 0.00 | 0.20 |  79 $\pm$ 30 | Estradiol | Phenobarbital | inf | Moderate | The enzyme inducer decreases the effect of hormones
157 | 2 | 0.00 | 0.42 |  102 $\pm$ 110 | Propranolol | Verapamil | 0.71 | Major | Increased effect of both drugs
157 | 2 | 0.01 | 0.03 |  2 $\pm$ 0 | Timolol | Fenoterol | inf | * | Antagonism
157 | 2 | 0.00 | 0.02 |  2 $\pm$ 0 | Phenytoin | Hydrocortisone | 0.71 | Moderate | The enzyme inducer decreases the effect of the corticosteroid
157 | 2 | 0.00 | 0.53 |  288 $\pm$ 213 | Phenytoin | Medroxyproges. Ac. | inf | Moderate | The enzyme inducer decreases the effect of the hormones
157 | 2 | 0.00 | 0.24 |  62 $\pm$ 53 | Phenytoin | Norethisterone | inf | Major | This product may cause a slight decrease of contraceptive effect
157 | 2 | 0.00 | 0.42 |  274 $\pm$ 218 | Digoxin | Propylthiouracil | 0.71 | Moderate | The antithyroid agent increases the effect of digoxin
169 | 1 | 0.00 | 0.00 |  2 $\pm$ 0 | Atenolol | Epinephrine | inf | Moderate | Hypertension, then bradycardia
169 | 1 | 0.00 | 0.49 |  179 $\pm$ 0 | Phenytoin | Ethinyl Estradiol | inf | Major | This product may cause a slight decrease of contraceptive effect
169 | 1 | 0.00 | 0.30 |  117 $\pm$ 0 | Haloperidol | Methyldopa | inf | Moderate | Methyldopa increases haloperidol effect or risk of psychosis
169 | 1 | 0.00 | 0.49 |  179 $\pm$ 0 | Phenytoin | Levonorgestrel | inf | Major | Phenytoin decreases the contraceptive effect
169 | 1 | 0.00 | 0.51 |  31 $\pm$ 0 | Phenytoin | Sulfadiazine | 0.00 | Moderate | The sulfonamide increases the effect of hydantoin
169 | 1 | 0.00 | 0.02 |  4 $\pm$ 0 | Erythromycin | Aminophylline | inf | Moderate | The macrolide increases the effect and toxicity of theophylline
169 | 1 | 0.00 | 0.24 |  12 $\pm$ 0 | Timolol | Methyldopa | inf | Major | Possible hypertensive crisis
169 | 1 | 0.00 | 0.05 |  6 $\pm$ 0 | Erythromycin | Carbamazepine | 0.00 | Major | The macrolide increases the effect of carbamazepine
169 | 1 | 0.00 | 0.06 |  2 $\pm$ 0 | Erythromycin | Diazepam | inf | Moderate | The macrolide increases the effect of the benzodiazepine
169 | 1 | 0.00 | 0.03 |  9 $\pm$ 0 | Erythromycin | Fluoxetine | inf | Moderate | Possible serotoninergic syndrome with this combination
169 | 1 | 0.00 | 0.25 |  15 $\pm$ 0 | Phenytoin | Doxycycline | inf | Moderate | The anticonvulsant decreases the effect of doxycycline
169 | 1 | 0.00 | 0.06 |  29 $\pm$ 0 | Phenytoin | Estrogens Conj. | inf | Moderate | The enzyme inducer decreases the effect of the hormones
169 | 1 | 0.00 | 0.31 |  124 $\pm$ 0 | Carbamazepine | Verapamil | 0.00 | Major | Verapamil increases the effect of carbamazepine
Supplementary Table 10:  DDI list 151-181. See Supplementary Table 7 for
column description.

rankΦ | $|U_{i,j}^{\Phi}|$ | $\gamma_{i,j}^{\Phi}$ | $\tau_{i,j}^{\Phi}$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity
---|---|---|---|---|---|---|---|---
2 | 2117 | 0.18 | 0.23 |  53 $\pm$ 74 | ASA | Ibuprofen | 1.42 | Major
5 | 1190 | 0.19 | 0.45 |  127 $\pm$ 127 | Amitriptyline | Fluoxetine | 3.55 | Major
7 | 892 | 0.14 | 0.20 |  56 $\pm$ 61 | Fluconazole | Simvastatin | 2.63 | Major
16 | 470 | 0.63 | 0.55 |  160 $\pm$ 133 | Diltiazem | Simvastatin | 1.27 | Major
23 | 257 | 0.16 | 0.42 |  123 $\pm$ 130 | Imipramine | Fluoxetine | 3.08 | Major
27 | 222 | 0.02 | 0.47 |  148 $\pm$ 139 | Fluoxetine | Lithium | 1.79 | Major
33 | 154 | 0.01 | 0.33 |  94 $\pm$ 92 | Fluoxetine | Nortriptyline | 2.70 | Major
36 | 148 | 0.14 | 0.49 |  168 $\pm$ 160 | Haloperidol | Lithium | 1.31 | Major
47 | 91 | 0.01 | 0.52 |  154 $\pm$ 142 | Atenolol | Diltiazem | 1.19 | Major
62 | 52 | 0.08 | 0.49 |  118 $\pm$ 114 | Digoxin | Amiodarone | 0.56 | Major
63 | 51 | 0.00 | 0.23 |  93 $\pm$ 90 | Hydrochlorothiazide | Lithium | 2.90 | Major
73 | 31 | 0.01 | 0.20 |  48 $\pm$ 66 | Propranolol | Salbutamol | 6.61 | Major
84 | 25 | 0.03 | 0.56 |  157 $\pm$ 136 | Diltiazem | Amiodarone | 1.26 | Major
85 | 24 | 0.00 | 0.05 |  3 $\pm$ 2 | Diclofenac | Warfarin | 0.84 | Major
89 | 23 | 0.03 | 0.47 |  152 $\pm$ 143 | Diltiazem | Propranolol | 2.01 | Major
89 | 23 | 0.00 | 0.16 |  36 $\pm$ 44 | Fluconazole | Haloperidol | 1.33 | Major
91 | 22 | 0.00 | 0.07 |  9 $\pm$ 4 | Ciprofloxacin | Warfarin | 1.02 | Major
93 | 21 | 0.01 | 0.08 |  10 $\pm$ 6 | Tobramycin | Furosemide | 3.01 | Major
95 | 19 | 0.00 | 0.07 |  10 $\pm$ 7 | Ciprofloxacin | Aminophylline | 1.21 | Major
97 | 18 | 0.00 | 0.13 |  33 $\pm$ 44 | Fluconazole | Warfarin | 0.89 | Major
Supplementary Table 11:  Top 20 _major_ DDI pairs $(i,j)$ by rank of $|U_{i,j}^{\Phi}|$, the number of patients affects by the DDI (1st and 2nd columns, respectively). The normalized drug pair footprint in the population ($\gamma_{i,j}^{\Phi}$) as well as the normalized co-administration length ($\tau_{i,j}^{\Phi}$), are shown in columns 3 and 4, respectively. Mean ($\pm$ s.d.) co-administration length, $\langle\lambda^{u}_{i,j}\rangle$, is shown in column 5 (in days) for each DDI pair $(i,j)$ whose English drug names are shown in columns 6 and 7. The relative gender risk of DDI pair co-administration, $RRI^{F}_{i,j}$, is shown in column 8. DDI severity classification, according to Drugs.com, shown in column 9.  rankp($\gamma$) | $\gamma_{i,j}^{\Phi}$ | $\gamma_{j,i}^{\Phi}$ | $|U_{i,j}^{\Phi}|$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity
---|---|---|---|---|---|---|---|---
1 | 0.50 | 0.61 | 524 |  243 $\pm$ 188 | Haloperidol | Biperiden | 0.62 | Moderate
2 | 0.59 | 0.12 | 385 |  155 $\pm$ 125 | Digoxin | Furosemide | 0.61 | Moderate
3 | 0.19 | 0.36 | 5078 |  102 $\pm$ 95 | Omeprazole | Clonazepam | 2.28 | Moderate
4 | 0.10 | 0.50 | 1249 |  141 $\pm$ 124 | ASA | Glyburide | 0.89 | Moderate
5 | 0.42 | 0.14 | 272 |  140 $\pm$ 114 | Digoxin | Spironolactone | 0.58 | Minor
6 | 0.63 | 0.02 | 470 |  160 $\pm$ 133 | Diltiazem | Simvastatin | 1.27 | Major
7 | 0.27 | 0.15 | 173 |  109 $\pm$ 96 | Digoxin | Carvedilol | 0.53 | Moderate
8 | 0.04 | 0.44 | 496 |  103 $\pm$ 87 | ASA | Gliclazide | 0.78 | None
9 | 0.04 | 0.31 | 999 |  87 $\pm$ 86 | Omeprazole | Diazepam | 1.21 | Moderate
9 | 0.19 | 0.09 | 1190 |  127 $\pm$ 127 | Amitriptyline | Fluoxetine | 3.55 | Major
11 | 0.14 | 0.16 | 148 |  168 $\pm$ 160 | Haloperidol | Lithium | 1.31 | Major
12 | 0.07 | 0.22 | 535 |  152 $\pm$ 132 | Atenolol | Glyburide | 1.22 | Moderate
13 | 0.18 | 0.08 | 186 |  142 $\pm$ 156 | Haloperidol | Carbamazepine | 0.62 | Moderate
14 | 0.18 | 0.06 | 2117 |  53 $\pm$ 74 | ASA | Ibuprofen | 1.42 | Major
14 | 0.20 | 0.04 | 1460 |  54 $\pm$ 77 | Atenolol | Ibuprofen | 1.88 | Moderate
16 | 0.02 | 0.24 | 222 |  148 $\pm$ 139 | Fluoxetine | Lithium | 1.79 | Major
17 | 0.03 | 0.18 | 201 |  107 $\pm$ 95 | Atenolol | Gliclazide | 1.09 | None
18 | 0.01 | 0.26 | 154 |  94 $\pm$ 92 | Fluoxetine | Nortriptyline | 2.70 | Major
19 | 0.28 | 0.00 | 149 |  115 $\pm$ 109 | Phenytoin | Omeprazole | 0.80 | Moderate
20 | 0.03 | 0.17 | 377 |  143 $\pm$ 138 | Fluoxetine | Carbamazepine | 0.98 | Moderate
Supplementary Table 12:  Top 20 known DDI pairs $(i,j)$ by rank product (1st column) of the ranks of $\gamma_{i,j}^{\Phi}$ and $\gamma_{j,i}^{\Phi}$, the normalized drug pair footprint in the population (1st, 2nd and 3rd columns, respectively). The number of patients affected by the drug pair, $|U_{i,j}^{\Phi}|$, is shown in column 4. Mean ($\pm$ s.d.) co-administration length, $\langle\lambda^{u}_{i,j}\rangle$, is shown in column 5 (in days) for each DDI pair $(i,j)$ whose English drug names are shown in columns 6 and 7. The relative gender risk of DDI pair co-administration, $RRI^{F}_{i,j}$, is shown in column 8. DDI severity classification, according to Drugs.com, shown in column 9; DDIs or drugs not found in Drugs.com are labeled as None or *, respectively.  rankτ | $\tau_{i,j}^{\Phi}$ | $|U_{i,j}^{\Phi}|$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity
---|---|---|---|---|---|---|---
1 | 0.70 | 524 |  243 $\pm$ 188 | Haloperidol | Biperiden | 0.62 | Moderate
2 | 0.60 | 1249 |  141 $\pm$ 124 | ASA | Glyburide | 0.89 | Moderate
3 | 0.60 | 385 |  155 $\pm$ 125 | Digoxin | Furosemide | 0.61 | Moderate
4 | 0.58 | 535 |  152 $\pm$ 132 | Atenolol | Glyburide | 1.22 | Moderate
5 | 0.57 | 95 |  140 $\pm$ 126 | Propranolol | Glyburide | 1.61 | Moderate
6 | 0.56 | 25 |  157 $\pm$ 136 | Diltiazem | Amiodarone | 1.26 | Major
7 | 0.56 | 13 |  122 $\pm$ 113 | Propranolol | Methyldopa | 8.50 | Major
8 | 0.55 | 470 |  160 $\pm$ 133 | Diltiazem | Simvastatin | 1.27 | Major
9 | 0.55 | 5 |  82 $\pm$ 86 | Propranolol | Aminophylline | 1.06 | Major
10 | 0.55 | 272 |  140 $\pm$ 114 | Digoxin | Spironolactone | 0.58 | Minor
11 | 0.53 | 2 |  288 $\pm$ 213 | Phenytoin | Medroxyproges. Ac. | inf | Moderate
12 | 0.52 | 91 |  154 $\pm$ 142 | Atenolol | Diltiazem | 1.19 | Major
13 | 0.51 | 1 |  31 $\pm$ 0 | Phenytoin | Sulfadiazine | 0.00 | Moderate
14 | 0.50 | 90 |  161 $\pm$ 157 | Imipramine | Carbamazepine | 1.35 | Moderate
15 | 0.50 | 377 |  143 $\pm$ 138 | Fluoxetine | Carbamazepine | 0.98 | Moderate
16 | 0.49 | 226 |  151 $\pm$ 145 | Amitriptyline | Carbamazepine | 0.99 | Moderate
17 | 0.49 | 52 |  118 $\pm$ 114 | Digoxin | Amiodarone | 0.56 | Major
18 | 0.49 | 1 |  179 $\pm$ 0 | Phenytoin | Levonorgestrel | inf | Major
18 | 0.49 | 1 |  179 $\pm$ 0 | Phenytoin | Ethinyl Estradiol | inf | Major
20 | 0.49 | 148 |  168 $\pm$ 160 | Haloperidol | Lithium | 1.31 | Major
Supplementary Table 13:  Top 20 known DDI pairs $(i,j)$ by rank of
$\tau_{i,j}^{\Phi}$, the normalized co-administration length (1st and 2nd
columns, respectively). The number of patients affected by the drug pair,
$|U_{i,j}^{\Phi}|$, is shown in column 3. Mean ($\pm$ s.d.) co-administration
length, $\langle\lambda^{u}_{i,j}\rangle$, is shown in column 4 (in days) for
each DDI pair $(i,j)$ whose English drug names are shown in columns 5 and 6.
The relative gender risk of DDI pair co-administration, $RRI^{F}_{i,j}$, shown
in column 7. DDI severity classification, according to Drugs.com, shown in
column 8; DDIs or drugs not found in Drugs.com are labeled as None or *,
respectively.

###  4.1 Interactions per severity

In this section, Supplementary Table 14 shows the number of individual
interactions and unique users, both per severity of interaction.

Note that some interactions present in DrugBrank were not found in Drugs.com.
These are marked as None. The drug Fenoterol (brand name Berotec in Brazil)
was not found in Drugs.com. These interactions were summed separately and are
shown with an asterisk (*).

severity $s$ | $\Phi_{s}$ | $|U^{\Phi}_{s}|$ | $|U^{\Phi}_{s}|/|U|$ | $|U^{\Phi}_{s}|/|\Omega|$
---|---|---|---|---
Major | 5,968 (22.50%) | 5,224 | 3.94% | 1.54%
Moderate | 18,335 (69.13%) | 12,711 | 9.58% | 3.75%
Minor | 542 (02.04%) | 528 | 0.40% | 0.16%
None | 1,489 (05.61%) | 1,314 | 0.99% | 0.39%
* | 190 (00.72%) | 179 | 0.13% | 0.05%
Total | 26,524 (100%) | 19,956 | -% | -%
Supplementary Table 14:  The 2nd column lists the numbers of interactions,
$\Phi_{s}$, per DDI severity class (1st column); percentages of interactions
per class are shown in parenthesis. Drugs or interactions identified in
_DrugBank_ but not present in Drugs.com are tallied as None. Interactions for
Berotec tallied as *. The 3rd column lists the number of patients affected by
at least one interaction $|U^{\Phi}_{s}|$, per DDI severity. Fourth and fifth
columns lists the proportion of patients in each DDI severity class for the
Pronto system and the entire Blumenau populations, respectively. Notice that
the same patient may have been administered DDI of more than one severity
type.

###  4.2 Interactions per gender

In this section, Supplementary Table 15 shows the number of individual
interactions and unique users per gender.

gender $g$ | $\Phi^{g}$ | $|U^{\Phi,g}|$ | $|U^{\Phi,g}|/|U|$ | $|U^{\Phi,g}|/|\Omega|$
---|---|---|---|---
Male | 8,100 (30.54%) | 4,793 | 3.61% | 1.41%
Female | 18,424 (69.46%) | 10,734 | 8.09% | 3.17%
Total | 26,524 (100%) | 15,527 | 11.70% | 4.58%
Supplementary Table 15:  The 2nd column lists the numbers of interactions,
$\Phi$, per gender (1st column); percentages of interactions per gender shown
in parenthesis. The 3rd column lists the number of patients affected by at
least one interaction per gender, $|U^{\Phi,g}|$. The 4th and 5th columns show
the proportion of patients in each gender for the Pronto system and entire
Blumenau populations, respectively.

###  4.3 Interactions per age

Supplementary Table 16 shows the number of individual interaction and unique
users per age group.

age y | $\Phi^{y}$ | $|U^{\Phi,y}|$ | $|U^{\Phi,y}|/|U|$ | $|U^{\Phi,y}|/|\Omega|$
---|---|---|---|---
00-04 | 23 (0.09%) | 20 | 0.02% | 0.01%
05-09 | 7 (0.03%) | 7 | 0.01% | 0.00%
10-14 | 29 (0.11%) | 25 | 0.02% | 0.01%
15-19 | 172 (0.65%) | 139 | 0.10% | 0.04%
20-24 | 311 (1.17%) | 237 | 0.18% | 0.07%
25-29 | 433 (1.63%) | 301 | 0.23% | 0.09%
30-34 | 771 (2.91%) | 525 | 0.40% | 0.15%
35-39 | 1,097 (4.14%) | 687 | 0.52% | 0.20%
40-44 | 1,581 (5.96%) | 1,023 | 0.77% | 0.30%
45-49 | 2,332 (8.79%) | 1,426 | 1.07% | 0.42%
50-54 | 3,128 (11.79%) | 1,868 | 1.41% | 0.55%
55-59 | 3,447 (13.00%) | 1,956 | 1.47% | 0.58%
60-64 | 3,508 (13.23%) | 2,006 | 1.51% | 0.59%
65-69 | 3,254 (12.27%) | 1,794 | 1.35% | 0.53%
70-74 | 2,417 (9.11%) | 1,311 | 0.99% | 0.39%
75-79 | 1,978 (7.46%) | 1,057 | 0.80% | 0.31%
80-84 | 1,143 (4.31%) | 638 | 0.48% | 0.19%
85-89 | 620 (2.34%) | 349 | 0.26% | 0.10%
90-94 | 205 (0.77%) | 117 | 0.09% | 0.03%
95-99 | 49 (0.18%) | 27 | 0.02% | 0.01%
>99 | 19 (0.07%) | 14 | 0.01% | 0.00%
Total | 26,524 (100%) | 15,527 | 11.70% | 4.58%
Supplementary Table 16:  The 2nd column lists the numbers of interactions,
$\Phi^{y}$, per age range (1st column); percentages of interactions per age
range shown in parenthesis. The 3rd column lists the number of patients
affected by at least one interaction per age range, $|U^{\Phi,y}|$. The 4th
and 5th columns show the proportion of patients in each age range from the
Pronto system and entire Blumenau populations, respectively.

###  4.4 Interaction per age and gender

Supplementary Figure 4:  The joint probability a patient was dispensed at
least one drug $P(U^{\nu>0,y,g})$, had co-administrations $P(U^{\Psi,y,g})$,
or had a DDI $P(U^{\Phi,y,g})$, given age range ($[y_{1},y_{2}]$) and gender
($g$), are shown in blue, orange and red lines, respectively. Values for age
group $y\geq\text{90}$ were aggregated for plotting. Population distribution
for Blumenau $P(\Omega^{y,g})$ is shown as a green fill. A Kolmogorov-Smirnov
test cannot reject the hypothesis that both the female and male distribution
of patients with at least one co-administration known to be DDI
($U^{\Phi,y,g}$) are drawn from the same underlying continuous distribution
($KS=.3810$, $p\text{-value}=.0706$).  Supplementary Figure 5:  Left. Mean
number of drugs dispensed ($\nu^{u}$) to patients in each age group. Middle.
Mean number of drug pairs co-administered ($\Psi^{u}$) by patients in each age
group. Right. Mean number of drug pairs known to be a DDI ($\Phi^{u}$) co-
administered by patients in each age group. Numbers for male and female
patients shown in lighter and darker colors, respectively. In all plots
vertical bars denote the standard deviation.

Supplementary Figure 6:  Left. Absolute number of patients with at least one
co-administration per age group, $|U^{\Psi,[y_{1},y_{2}]}|$. Right. Absolute
number of patients with at least one co-administration per age group and
gender, $|U^{\Psi,[y_{1},y_{2}],g}|$.

## Supplementary Note 5 Risk and Relative Risk measures

Risk and Relative Risk measures are computed based on the number of patients
in specific groups. Here we detail the computation of all measures used
throughout the main manuscript.

The relative risk of co-administration and interaction for women, are computed
as

$RRC^{\text{F}}=\frac{P(\Psi^{u}>0\,|\,u\in
U^{\text{F}})}{P(\Psi^{u}>0\,|\,u\in
U^{\text{M}})}=\frac{|U^{\Psi,\text{F}}\,|\,/|U^{\text{F}}|}{|U^{\Psi,\text{M}}\,|\,/|U^{\text{M}}|};\;RRI^{\text{F}}=\frac{P(\Phi^{u}>0\,|\,u\in
U^{\text{F}})}{P(\Phi^{u}>0\,|\,u\in
U^{\text{M}})}=\frac{|U^{\Phi,\text{F}}\,|\,/|U^{\text{F}}|}{|U^{\Phi,\text{M}}\,|\,/|U^{\text{M}}|}.$
(10)

Similarly, $RRC^{M}=1/RRC^{F}$ and $RRI^{M}=1/RRI^{F}$. In the main manuscript
we mentioned the computation of $RRI^{F}$ without contraceptive drugs. The
drug removed in this computation were Ethinyl Estradiol, Estradiol,
Norethisterone, Levonorgestrel and Estrogens Conjugated.

The relative risk of an interaction at a certain DDI severity level,
$s\in\\{\text{major},\text{moderate},\text{minor},\text{none},\text{*}\\}$,
given gender, is computed as

$RRI^{F}_{s}=\frac{P(\Phi^{u}_{s}>0\,|\,u\in
U^{\text{F}})}{P(\Phi^{u}_{s}>0\,|\,u\in
U^{\text{M}})}=\frac{|U^{\Phi,\text{F}}_{s}|/|U^{\text{F}}|}{|U^{\Phi,\text{M}}_{s}|\
|U^{\text{M}}|}\quad.$ (11)

The relative risk of an interaction between two drugs, given gender, is
computed as

$RRI^{F}_{i,j}=\frac{P(\Phi^{u}_{i,j}>0\,|\,u\in
U^{\text{F}})}{P(\Phi^{u}_{i,j}>0\,|\,u\in
U^{\text{M}})}=\frac{|U^{\Phi,\text{F}}_{i,j}|/|U^{\text{F}}|}{|U^{\Phi,\text{M}}_{i,j}|/|U^{M}|}.$
(12)

The relative risk of co-administration and interaction, given number of
dispensed drugs, are computed as

$RRC^{\nu=x}=\frac{P(\Psi^{u}\,|\,u\in U^{\nu=x})}{P(\Psi^{y}\,|\,u\in
U^{\nu=2})}=\frac{|U^{\Psi,\nu=x}|/|U^{\nu=x}|}{|U^{\Psi,\nu=2}|/|U^{\nu=2}|};\;RRI^{\nu=x}=\frac{P(\Phi^{u}\,|\,u\in
U^{\nu=x})}{P(\Phi^{u}\,|\,u\in
U^{\nu=2})}=\frac{|U^{\Phi,\nu=x}|/|U^{\nu=x}|}{|U^{\Phi,\nu=2}|/|U^{\nu=2}|}.$
(13)

The risk of co-administration and interaction, given age group, are computed
as

$RC^{[y_{1},y_{2}]}=\frac{P(\Psi^{u}>0\,|\,u\in
U^{[y_{1},y_{2}]})}{P(\nu^{u}\geq 2\,|\,u\in
U^{[y_{1},y_{2}]})}=\frac{|U^{\Psi,[y_{1},y_{2}]}|}{|U^{\nu\geq
2,[y_{1},y_{2}]}|};\;RI^{[y_{1},y_{2}]}=\frac{P(\Phi^{u}>0\,|\,u\in
U^{[y_{1},y_{2}]})}{P(\Psi^{u}>0\,|\,u\in
U^{[y_{1},y_{2}]})}=\frac{|U^{\Psi,[y_{1},y_{2}]}|}{|U^{\Phi,[y_{1},y_{2}]}|}.$
(14)

Note $RC^{[y_{1},y_{2}]}$ and $RI^{[y_{1},y_{2}]}$ can be also interpreted as
probabilities. Similarly, we also compute the risk of co-administration and
interaction, per age group and gender as

$RC^{g,[y_{1},y_{2}]}=\frac{P(\Psi^{u}>0\,|\,u\in
U^{g,[y_{1},y_{2}]})}{P(\nu^{u}\geq 2\,|\,u\in
U^{g,[y_{1},y_{2}]})}=\frac{|U^{\Psi,g,[y_{1},y_{2}]}|}{|U^{\nu\geq
2,g,[y_{1},y_{2}]}|};\;RI^{g,[y_{1},y_{2}]}=\frac{P(\Phi^{u}>0\,|\,u\in
U^{g,[y_{1},y_{2}]})}{P(\Psi^{u}>0\,|\,u\in
U^{g,[y_{1},y_{2}]})}=\frac{|U^{\Psi,g,[y_{1},y_{2}]}|}{|U^{\Phi,g,[y_{1},y_{2}]}|}.$
(15)

###  5.1 Relative Risk per gender

$g$ | $|U^{g}|$ | $|U^{\nu\geq 2}|$ | $|U^{\Psi,g}|$ | $|U^{\Phi,g}|$ | $RRC^{F}$ | $RRI^{F}$
---|---|---|---|---|---|---
Male | 55,032 | 41,922 | 39,723 | 4,793 | 1.0000 | 1.0000
Female | 77,690 | 62,889 | 59,738 | 10,734 | 1.0653 | 1.5864
Supplementary Table 17:  Absolute number of patients and relative risk measures per gender ($g$, 1st column). Columns 2 through 5 lists, per gender, absolute numbers of: patients ($|U^{g}|$), patients with at least $2$ administrations ($|U^{\nu\geq 2}|$), patients with at least one co-administration ($|U^{\Psi,g}|$), and patients with at least one known DDI co-administration ($|U^{\Phi,g}|$). Relative Risk for women for both co-administration ($RRC^{F}$) and known DDI co-administration ($RRI^{F}$) are listed in columns 6 and 7, respectively.  rankp($RRI,U^{\text{F}})$ | $|U^{\Phi,M}|$ | $|U^{\Phi,F}|$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{F}_{i,j}$ | severity
---|---|---|---|---|---|---|---
1 (1,49) | 0 | 30 |  10 $\pm$ 3 | Clavulanate | Ethinyl Estradiol | inf | None
2 (1,51) | 0 | 27 |  8 $\pm$ 7 | Prednisone | Estradiol | inf | Moderate
2 (1,51) | 0 | 27 |  11 $\pm$ 6 | Doxycycline | Ethinyl Estradiol | inf | Moderate
4 (1,57) | 0 | 22 |  19 $\pm$ 28 | Estrogens Conj. | Prednisone | inf | Moderate
5 (1,71) | 0 | 13 |  35 $\pm$ 26 | Carbamazepine | Ethinyl Estradiol | inf | Major
5 (1,71) | 0 | 13 |  35 $\pm$ 26 | Levonorgestrel | Carbamazepine | inf | Major
7 (76,1) | 1204 | 3874 |  102 $\pm$ 95 | Omeprazole | Clonazepam | 2.28 | Moderate
8 (1,83) | 0 | 9 |  72 $\pm$ 128 | Carbamazepine | Norethisterone | inf | Major
9 (1,89) | 0 | 7 |  11 $\pm$ 4 | Doxycycline | Iron (II) Sulfate | inf | Moderate
10 (1,94) | 0 | 5 |  162 $\pm$ 120 | Medroxyproges. Ac. | Phenobarbital | inf | Moderate
10 (1,94) | 0 | 5 |  10 $\pm$ 6 | Prednisolone | Ethinyl Estradiol | inf | Moderate
12 (1,98) | 0 | 4 |  40 $\pm$ 29 | Levonorgestrel | Phenobarbital | inf | Major
12 (1,98) | 0 | 4 |  10 $\pm$ 2 | Estrogens Conj. | Prednisolone | inf | Moderate
14 (1,102) | 0 | 3 |  97 $\pm$ 94 | Estrogens Conj. | Phenobarbital | inf | Moderate
14 (1,102) | 0 | 3 |  40 $\pm$ 57 | Methyldopa | Levodopa | inf | Minor
14 (1,102) | 0 | 3 |  45 $\pm$ 43 | Medroxyproges. Ac. | Warfarin | inf | None
14 (1,102) | 0 | 3 |  40 $\pm$ 19 | Digoxin | Verapamil | inf | Moderate
14 (1,102) | 0 | 3 |  53 $\pm$ 16 | Ethinyl Estradiol | Phenobarbital | inf | Major
14 (1,102) | 0 | 3 |  136 $\pm$ 117 | Ethinyl Estradiol | Aminophylline | inf | Moderate
20 (1,111) | 0 | 2 |  23 $\pm$ 11 | Doxycycline | Phenobarbital | inf | Moderate
20 (1,111) | 0 | 2 |  79 $\pm$ 30 | Norethisterone | Phenobarbital | inf | Major
20 (1,111) | 0 | 2 |  288 $\pm$ 213 | Phenytoin | Medroxyproges. Ac. | inf | Moderate
20 (1,111) | 0 | 2 |  62 $\pm$ 53 | Phenytoin | Norethisterone | inf | Major
20 (1,111) | 0 | 2 |  62 $\pm$ 53 | Phenytoin | Estradiol | inf | Moderate
20 (1,111) | 0 | 2 |  79 $\pm$ 30 | Estradiol | Phenobarbital | inf | Moderate
20 (1,111) | 0 | 2 |  2 $\pm$ 0 | Timolol | Fenoterol | inf | *
20 (1,111) | 0 | 2 |  31 $\pm$ 0 | Timolol | Aminophylline | inf | Major
20 (1,111) | 0 | 2 |  6 $\pm$ 1 | Estradiol | Prednisolone | inf | Moderate
29 (1,124) | 0 | 1 |  117 $\pm$ 0 | Haloperidol | Methyldopa | inf | Moderate
29 (1,124) | 0 | 1 |  2 $\pm$ 0 | Atenolol | Epinephrine | inf | Moderate
29 (1,124) | 0 | 1 |  12 $\pm$ 0 | Timolol | Methyldopa | inf | Major
29 (1,124) | 0 | 1 |  29 $\pm$ 0 | Phenytoin | Estrogens Conj. | inf | Moderate
29 (1,124) | 0 | 1 |  2 $\pm$ 0 | Erythromycin | Diazepam | inf | Moderate
29 (1,124) | 0 | 1 |  4 $\pm$ 0 | Erythromycin | Aminophylline | inf | Moderate
29 (1,124) | 0 | 1 |  179 $\pm$ 0 | Phenytoin | Ethinyl Estradiol | inf | Major
29 (1,124) | 0 | 1 |  179 $\pm$ 0 | Phenytoin | Levonorgestrel | inf | Major
29 (1,124) | 0 | 1 |  15 $\pm$ 0 | Phenytoin | Doxycycline | inf | Moderate
29 (1,124) | 0 | 1 |  9 $\pm$ 0 | Erythromycin | Fluoxetine | inf | Moderate
39 (104,2) | 706 | 1411 |  53 $\pm$ 74 | ASA | Ibuprofen | 1.42 | Major
40 (59,4) | 198 | 992 |  127 $\pm$ 127 | Amitriptyline | Fluoxetine | 3.55 | Major
41 (83,3) | 400 | 1060 |  54 $\pm$ 77 | Atenolol | Ibuprofen | 1.88 | Moderate
42 (75,5) | 189 | 703 |  56 $\pm$ 61 | Fluconazole | Simvastatin | 2.63 | Major
43 (62,7) | 108 | 519 |  46 $\pm$ 54 | Fluconazole | Clonazepam | 3.40 | None
44 (61,9) | 86 | 415 |  44 $\pm$ 62 | Propranolol | Ibuprofen | 3.42 | Moderate
45 (52,12) | 46 | 309 |  86 $\pm$ 84 | Fluoxetine | Propranolol | 4.76 | Moderate
46 (38,17) | 1 | 178 |  10 $\pm$ 6 | Ethinyl Estradiol | Amoxicillin | 126.09 | Moderate
47 (117,6) | 369 | 630 |  87 $\pm$ 86 | Omeprazole | Diazepam | 1.21 | Moderate
48 (53,14) | 38 | 246 |  66 $\pm$ 57 | Levothyroxine | Iron (II) Sulfate | 4.59 | Moderate
49 (81,10) | 134 | 366 |  52 $\pm$ 75 | Furosemide | Ibuprofen | 1.93 | Moderate
49 (54,15) | 35 | 210 |  42 $\pm$ 40 | Fluconazole | Amitriptyline | 4.25 | Moderate
51 (110,8) | 265 | 487 |  30 $\pm$ 50 | ASA | Dexamethasone | 1.30 | Moderate
52 (64,16) | 48 | 209 |  123 $\pm$ 130 | Imipramine | Fluoxetine | 3.08 | Major
53 (47,23) | 12 | 104 |  9 $\pm$ 7 | Norfloxacin | Iron (II) Sulfate | 6.14 | Moderate
54 (41,27) | 7 | 95 |  4 $\pm$ 4 | Diclofenac | Alendronate | 9.61 | Moderate
55 (39,29) | 1 | 83 |  15 $\pm$ 26 | Prednisone | Ethinyl Estradiol | 58.79 | Moderate
56 (115,11) | 197 | 338 |  152 $\pm$ 132 | Atenolol | Glyburide | 1.22 | Moderate
57 (40,35) | 2 | 61 |  33 $\pm$ 28 | Methyldopa | Iron (II) Sulfate | 21.60 | Moderate
58 (71,20) | 31 | 124 |  68 $\pm$ 80 | Amitriptyline | Salbutamol | 2.83 | Moderate
59 (112,13) | 168 | 302 |  160 $\pm$ 133 | Diltiazem | Simvastatin | 1.27 | Major
60 (84,18) | 63 | 159 |  148 $\pm$ 139 | Fluoxetine | Lithium | 1.79 | Major
Supplementary Table 18:  Top 60 known DDI pairs $(i,j)$ most imbalanced for _females_ , sorted by rank product (1st column; individual rank in parenthesis) of $RRI^{F}_{i,j}$, the relative gender risk of DDI pair co-administration, and $|U^{\Phi,F}|$, the number of women affected by the DDI (7nd and 3rd columns, respectively). The number of men ($|U^{\Phi,M}|$) affected is shown in column 2. Mean ($\pm$ s.d.) co-administration length, $\langle\lambda^{u}_{i,j}\rangle$, is shown in column 4 (in days) for each DDI pair $(i,j)$ whose English drug names are shown in columns 5 and 6. DDI severity classification, according to Drugs.com, shown in column 8; DDIs or drugs not found in Drugs.com are labeled as None or *, respectively.  rankp$(RRI,U^{\text{M}})$ | $|U^{\Phi,M}|$ | $|U^{\Phi,F}|$ | $\langle\lambda^{u}_{i,j}\rangle$ | $i$ | $j$ | $RRI^{M}_{i,j}$ | severity
---|---|---|---|---|---|---|---
1 (1,32) | 4 | 0 |  72 $\pm$ 61 | Atenolol | Verapamil | inf | Major
2 (1,38) | 3 | 0 |  185 $\pm$ 98 | Phenytoin | Levodopa | inf | Moderate
3 (20,2) | 280 | 244 |  243 $\pm$ 188 | Haloperidol | Biperiden | 1.62 | Moderate
3 (40,1) | 553 | 696 |  141 $\pm$ 124 | ASA | Glyburide | 1.12 | Moderate
5 (1,43) | 1 | 0 |  124 $\pm$ 0 | Carbamazepine | Verapamil | inf | Major
5 (1,43) | 1 | 0 |  6 $\pm$ 0 | Erythromycin | Carbamazepine | inf | Major
5 (1,43) | 1 | 0 |  31 $\pm$ 0 | Phenytoin | Sulfadiazine | inf | Moderate
8 (18,5) | 207 | 178 |  155 $\pm$ 125 | Digoxin | Furosemide | 1.64 | Moderate
9 (13,9) | 99 | 74 |  109 $\pm$ 96 | Digoxin | Carvedilol | 1.89 | Moderate
10 (8,15) | 37 | 10 |  135 $\pm$ 109 | Allopurinol | Warfarin | 5.22 | Moderate
11 (41,3) | 262 | 347 |  48 $\pm$ 93 | Prednisone | ASA | 1.07 | Moderate
12 (33,4) | 236 | 260 |  103 $\pm$ 87 | ASA | Gliclazide | 1.28 | None
13 (17,8) | 149 | 123 |  140 $\pm$ 114 | Digoxin | Spironolactone | 1.71 | Minor
14 (6,24) | 10 | 1 |  57 $\pm$ 46 | Methylphenidate | Carbamazepine | 14.12 | None
15 (21,9) | 99 | 87 |  142 $\pm$ 156 | Haloperidol | Carbamazepine | 1.61 | Moderate
16 (7,32) | 4 | 1 |  107 $\pm$ 123 | Phenytoin | Amiodarone | 5.65 | Moderate
17 (12,22) | 16 | 11 |  10 $\pm$ 6 | Phenytoin | Ciprofloxacin | 2.05 | Moderate
18 (16,17) | 29 | 23 |  118 $\pm$ 114 | Digoxin | Amiodarone | 1.78 | Major
19 (46,6) | 158 | 219 |  143 $\pm$ 138 | Fluoxetine | Carbamazepine | 1.02 | Moderate
20 (11,26) | 9 | 6 |  20 $\pm$ 17 | Carvedilol | Fenoterol | 2.12 | *
21 (42,7) | 156 | 208 |  110 $\pm$ 106 | Carbamazepine | Simvastatin | 1.06 | Moderate
22 (9,38) | 3 | 1 |  62 $\pm$ 44 | Phenobarbital | Aminophylline | 4.24 | Moderate
23 (19,20) | 23 | 20 |  144 $\pm$ 153 | Phenytoin | Diazepam | 1.62 | Moderate
24 (15,26) | 9 | 7 |  94 $\pm$ 83 | Phenytoin | Furosemide | 1.82 | Minor
25 (14,28) | 8 | 6 |  5 $\pm$ 3 | Doxycycline | Amoxicillin | 1.88 | Moderate
26 (34,12) | 70 | 79 |  115 $\pm$ 109 | Phenytoin | Omeprazole | 1.25 | Moderate
27 (10,41) | 2 | 1 |  9 $\pm$ 4 | Phenytoin | Prednisolone | 2.82 | Moderate
28 (22,21) | 20 | 19 |  82 $\pm$ 64 | Gliclazide | Carvedilol | 1.49 | None
29 (36,13) | 55 | 68 |  31 $\pm$ 43 | Ibuprofen | Carvedilol | 1.14 | Moderate
30 (30,16) | 35 | 36 |  169 $\pm$ 151 | Phenytoin | Fluoxetine | 1.37 | Moderate
31 (48,11) | 94 | 132 |  151 $\pm$ 145 | Amitriptyline | Carbamazepine | 1.01 | Moderate
32 (32,17) | 29 | 31 |  49 $\pm$ 95 | Prednisone | Warfarin | 1.32 | Moderate
33 (31,19) | 28 | 29 |  96 $\pm$ 96 | Glyburide | Carvedilol | 1.36 | Moderate
34 (45,14) | 50 | 67 |  126 $\pm$ 127 | Digoxin | Hydrochlorothiazide | 1.05 | Moderate
35 (23,30) | 7 | 7 |  9 $\pm$ 7 | Furosemide | Gentamicin | 1.41 | Major
36 (24,32) | 4 | 4 |  82 $\pm$ 54 | Carbamazepine | Aminophylline | 1.41 | Moderate
36 (24,32) | 4 | 4 |  67 $\pm$ 36 | Diltiazem | Carbamazepine | 1.41 | Major
38 (35,23) | 11 | 13 |  3 $\pm$ 2 | Diclofenac | Warfarin | 1.19 | Major
39 (24,41) | 2 | 2 |  4 $\pm$ 3 | Doxycycline | Clavulanate | 1.41 | None
40 (24,43) | 1 | 1 |  102 $\pm$ 110 | Propranolol | Verapamil | 1.41 | Major
40 (24,43) | 1 | 1 |  274 $\pm$ 218 | Digoxin | Propylthiouracil | 1.41 | Moderate
40 (24,43) | 1 | 1 |  2 $\pm$ 0 | Phenytoin | Hydrocortisone | 1.41 | Moderate
43 (37,28) | 8 | 10 |  33 $\pm$ 44 | Fluconazole | Warfarin | 1.13 | Major
44 (47,24) | 10 | 14 |  100 $\pm$ 85 | Carbamazepine | Warfarin | 1.01 | Moderate
45 (37,32) | 4 | 5 |  51 $\pm$ 91 | Timolol | Salbutamol | 1.13 | Major
45 (37,32) | 4 | 5 |  7 $\pm$ 1 | Prednisolone | Phenobarbital | 1.13 | Moderate
47 (42,31) | 6 | 8 |  88 $\pm$ 71 | Phenytoin | Warfarin | 1.06 | Moderate
48 (42,38) | 3 | 4 |  62 $\pm$ 97 | Phenytoin | Trimethoprim | 1.06 | Moderate
Supplementary Table 19:  All 48 known DDI pairs $(i,j)$ most imbalaced for _males_ , sorted by rank product (1st column; individual rank in parenthesis) of $RRI^{M}_{i,j}$, the relative gender risk of DDI pair co-administration, and $|U^{\Phi,M}|$, the number of men affected by the DDI (7nd and 2rd columns, respectively). The number of women ($|U^{\Phi,F}|$) affected is shown in column 3. Mean ($\pm$ s.d.) co-administration length, $\langle\lambda^{u}_{i,j}\rangle$, is shown in column 4 (in days) for each DDI pair $(i,j)$ whose English drug names are shown in columns 5 and 6. DDI severity classification, according to Drugs.com, shown in column 8; DDIs or drugs not found in Drugs.com are labeled as None or *, respectively.  $RRI^{g}_{i,j}\geq x$ | $|D^{\Phi,F}|$ | $|D^{\Phi,M}|$ | $\Phi^{F}$ | $\Phi^{M}$ | $\Phi^{F}_{major}$ | $\Phi^{M}_{major}$
---|---|---|---|---|---|---
1 | 68 | 46 | 133 | 48 | 31 | 10
2 | 56 | 17 | 80 | 12 | 21 | 3
3 | 49 | 13 | 65 | 9 | 16 | 3
4 | 45 | 13 | 58 | 9 | 13 | 3
5 | 38 | 11 | 49 | 8 | 13 | 3
6 | 36 | 8 | 47 | 6 | 13 | 3
7 | 35 | 8 | 45 | 6 | 12 | 3
8 | 32 | 8 | 42 | 6 | 12 | 3
9 | 31 | 8 | 41 | 6 | 11 | 3
10 | 29 | 8 | 40 | 6 | 11 | 3
Supplementary Table 20:  Number and proportions of drugs and interactions at increasing level of relative gender risk of DDI pair co-administration, $RRI^{g}_{i,j}>x$ (1st column). Number of drugs by gender, is shown in columns 2 and 3. Number of drug pairs known to be a DDI, by gender, is shown in columns 4 and 5. Number of drug pairs, known to be a _major_ DDI, by gender, is shown in columns 6 and 7. See also Supplementary Table 21.  $RRI^{g}_{i,j}\geq x$ | $|U^{\Phi,F}|$ | $|U^{\Phi,M}|$ | $|U^{\Phi,F}_{major}|$ | $|U^{\Phi,M}_{major}|$ | $\frac{|U^{\Phi,F}|}{|U^{F}|}$ | $\frac{|U^{\Phi,M}|}{|U^{M}|}$ | $\frac{|U^{\Phi,F}_{major}|}{|U^{F}|}$ | $\frac{|U^{\Phi,M}_{major}|}{|U^{M}|}$
---|---|---|---|---|---|---|---|---
1 | 9,836 | 2,010 | 3,747 | 69 | 12.66% | 03.65% | 04.82% | 00.13%
2 | 7,089 | 91 | 2,060 | 6 | 09.12% | 00.17% | 02.65% | 00.01%
3 | 3,327 | 64 | 1,255 | 6 | 04.28% | 00.12% | 01.62% | 00.01%
4 | 1,589 | 64 | 73 | 6 | 02.05% | 00.12% | 00.09% | 00.01%
5 | 775 | 61 | 73 | 6 | 01.00% | 00.11% | 00.09% | 00.01%
6 | 744 | 20 | 73 | 6 | 00.96% | 00.04% | 00.09% | 00.01%
7 | 615 | 20 | 45 | 6 | 00.79% | 00.04% | 00.06% | 00.01%
8 | 547 | 20 | 45 | 6 | 00.70% | 00.04% | 00.06% | 00.01%
9 | 536 | 20 | 33 | 6 | 00.69% | 00.04% | 00.04% | 00.01%
10 | 441 | 20 | 33 | 6 | 00.57% | 00.04% | 00.04% | 00.01%
Supplementary Table 21:  Number and proportions of affected patients at
increasing level of relative gender risk of DDI pair co-administration,
$RRI^{g}_{i,j}>x$ (1st column). Number of patients by gender, is shown in
columns 2 and 3. Number of patients by gender and major DDI, is shown in
columns 4 and 5. The relative proportion of affected patients in relation to
the Pronto population is shown in columns 6 through 9. See also Supplementary
Table 20.

###  5.2 Relative Risk per severity

severity $s$ | $|U^{\Phi,M}_{s}|$ | $|U^{\Psi,F}_{s}|$ | $RRI^{F}_{s}$
---|---|---|---
Major | 1,433 | 3791 | 1.8739
Moderate | 3,951 | 8760 | 1.5705
Minor | 247 | 281 | 0.8059
None | 409 | 905 | 1.5674
* | 39 | 140 | 2.5428
Supplementary Table 22:  Absolute number of patients and relative risk
measures per gender ($g$) and severity score ($s$, 1st column). Columns 2 and
3 lists absolute number of males ($g=M$) and females ($g=F$) affected by at
least one DDI for each severity score, respectively. Column 4 lists the
relative risk of interaction given a specific severity score and gender. DDIs
or drugs not found in Drugs.com are labeled as None or *, respectively Notice
that the same patient may have been administered DDI of more than one severity
type.

###  5.3 Risk Measures per age

$[y_{1},y_{2}]$ | $|U^{[y_{1},y_{2}]}|$ | $|U^{\nu\geq 2,[y_{1},y_{2}]}|$ | $|U^{\Psi,[y_{1},y_{2}]}|$ | $|U^{\Phi,[y_{1},y_{2}]}|$ | $RC^{[y_{1},y_{2}]}$ | $RI^{[y_{1},y_{2}]}$
---|---|---|---|---|---|---
00-04 | 8,946 | 7,195 | 6,810 | 20 | 0.9465 | 0.0029
05-09 | 6,390 | 4,688 | 4,362 | 7 | 0.9305 | 0.0016
10-14 | 5,631 | 3,794 | 3,507 | 25 | 0.9244 | 0.0071
15-19 | 8,305 | 6,094 | 5,705 | 139 | 0.9362 | 0.0244
20-24 | 10,382 | 7,819 | 7,334 | 237 | 0.9380 | 0.0323
25-29 | 9,725 | 7,305 | 6,835 | 301 | 0.9357 | 0.0440
30-34 | 9,100 | 6,787 | 6,386 | 525 | 0.9409 | 0.0822
35-39 | 8,844 | 6,696 | 6,259 | 687 | 0.9347 | 0.1098
40-44 | 9,184 | 7,043 | 6,615 | 1,023 | 0.9392 | 0.1546
45-49 | 10,085 | 8,039 | 7,610 | 1,426 | 0.9466 | 0.1874
50-54 | 10,650 | 8,617 | 8,200 | 1,868 | 0.9516 | 0.2278
55-59 | 9,236 | 7,686 | 7,386 | 1,956 | 0.9610 | 0.2648
60-64 | 8,179 | 7,049 | 6,801 | 2,006 | 0.9648 | 0.2950
65-69 | 6,315 | 5,572 | 5,444 | 1,794 | 0.9770 | 0.3295
70-74 | 4,412 | 3,916 | 3,843 | 1,311 | 0.9814 | 0.3411
75-79 | 3,398 | 3,042 | 2,968 | 1,057 | 0.9757 | 0.3561
80-84 | 2,129 | 1,909 | 1,874 | 638 | 0.9817 | 0.3404
85-89 | 1,174 | 1,029 | 1,007 | 349 | 0.9786 | 0.3466
90+ | 637 | 531 | 515 | 158 | 0.9699 | 0.3068
Supplementary Table 23:  Absolute number of patients and risk measures per age range ($[y_{1},y_{2}]$, 1st column). Columns 2 through 5 lists, per age range, absolute numbers of: patients ($|U^{[y_{1},y_{2}]}|$), patients with at least $2$ drug administrations ($|U^{\nu\geq 2,[y_{1},y_{2}]}|$), patients with at least one co-administration ($|U^{\Psi,[y_{1},y_{2}]}|$), and patients with at least one known DDI co-administration ($|U^{\Phi,[y_{1},y_{2}]}|$). Per age range risk for both co-administration ($RC^{[y_{1},y_{2}]}$) and known DDI co-administration ($RI^{[y_{1},y_{2}]}$) are listed in columns 6 and 7, respectively.  $[y_{1},y_{2}]$ | $|U^{M,[y_{1},y_{2}]}|$ | $|U^{\nu\geq 2,M,[y_{1},y_{2}]}|$ | $|U^{\Psi,M,[y_{1},y_{2}]}|$ | $|U^{\Phi,M,[y_{1},y_{2}]}|$ | $RC^{M,[y_{1},y_{2}]}$ | $RI^{M,[y_{1},y_{2}]}$
---|---|---|---|---|---|---
00-04 | 4,537 | 3,664 | 3,473 | 8 | 0.9479 | 0.0023
05-09 | 3,319 | 2,416 | 2,239 | 3 | 0.9267 | 0.0013
10-14 | 2,932 | 1,926 | 1,776 | 14 | 0.9221 | 0.0079
15-19 | 3,518 | 2,390 | 2,247 | 33 | 0.9402 | 0.0147
20-24 | 4,204 | 3,020 | 2,838 | 76 | 0.9397 | 0.0268
25-29 | 4,066 | 2,890 | 2,708 | 99 | 0.9370 | 0.0366
30-34 | 3,692 | 2,641 | 2,500 | 1,68 | 0.9466 | 0.0672
35-39 | 3,428 | 2,488 | 2,317 | 1,90 | 0.9313 | 0.0820
40-44 | 3,504 | 2,559 | 2,394 | 2,79 | 0.9355 | 0.1165
45-49 | 3,945 | 3,043 | 2,892 | 4,17 | 0.9504 | 0.1442
50-54 | 4,142 | 3,219 | 3,048 | 5,25 | 0.9469 | 0.1722
55-59 | 3,638 | 2,953 | 2,829 | 6,06 | 0.9580 | 0.2142
60-64 | 3,257 | 2,731 | 2,622 | 6,26 | 0.9601 | 0.2387
65-69 | 2,525 | 2,197 | 2,148 | 6,45 | 0.9777 | 0.3003
70-74 | 1,729 | 1,494 | 1,461 | 4,27 | 0.9779 | 0.2923
75-79 | 1,303 | 1,162 | 1,127 | 3,44 | 0.9699 | 0.3052
80-84 | 718 | 649 | 637 | 1,86 | 0.9815 | 0.2920
85-89 | 361 | 312 | 304 | 98 | 0.9744 | 0.3224
90+ | 214 | 168 | 163 | 49 | 0.9702 | 0.3006
Supplementary Table 24:  Absolute number of _male_ patients and risk measures per age range ($[y_{1},y_{2}]$, 1st column). Columns 2 through 5 lists, per age range, absolute numbers of: male patients ($|U^{y}|$), male patients with at least $2$ drug administrations ($|U^{\nu\geq 2,M,[y_{1},y_{2}]}|$), male patients with at least one co-administration ($|U^{\Psi,M,[y_{1},y_{2}]}|$), and male patients with at least one known DDI co-administration ($|U^{\Phi,M,[y_{1},y_{2}]}|$). Per age range women risk for both co-administration ($RC^{M,[y_{1},y_{2}]}$) and known DDI co-administration ($RI^{M,[y_{1},y_{2}]}$) are listed in columns 6 and 7, respectively.  $[y_{1},y_{2}]$ | $|U^{F,[y_{1},y_{2}]}|$ | $|U^{\nu\geq 2,F,[y_{1},y_{2}]}|$ | $|U^{\Psi,F,[y_{1},y_{2}]}|$ | $|U^{\Phi,F,[y_{1},y_{2}]}|$ | $RC^{F,[y_{1},y_{2}]}$ | $RI^{F,[y_{1},y_{2}]}$
---|---|---|---|---|---|---
00-04 | 4,409 | 3,531 | 3,337 | 12 | 0.9451 | 0.0036
05-09 | 3,071 | 2,272 | 2,123 | 4 | 0.9344 | 0.0019
10-14 | 2,699 | 1,868 | 1,731 | 11 | 0.9267 | 0.0064
15-19 | 4,787 | 3,704 | 3,458 | 106 | 0.9336 | 0.0307
20-24 | 6,178 | 4,799 | 4,496 | 161 | 0.9369 | 0.0358
25-29 | 5,659 | 4,415 | 4,127 | 202 | 0.9348 | 0.0489
30-34 | 5,408 | 4,146 | 3,886 | 357 | 0.9373 | 0.0919
35-39 | 5,416 | 4,208 | 3,942 | 497 | 0.9368 | 0.1261
40-44 | 5,680 | 4,484 | 4,221 | 744 | 0.9413 | 0.1763
45-49 | 6,140 | 4,996 | 4,718 | 1,009 | 0.9444 | 0.2139
50-54 | 6,508 | 5,398 | 5,152 | 1,343 | 0.9544 | 0.2607
55-59 | 5,598 | 4,733 | 4,557 | 1,350 | 0.9628 | 0.2962
60-64 | 4,922 | 4,318 | 4,179 | 1,380 | 0.9678 | 0.3302
65-69 | 3,790 | 3,375 | 3,296 | 1,149 | 0.9766 | 0.3486
70-74 | 2,683 | 2,422 | 2,382 | 884 | 0.9835 | 0.3711
75-79 | 2,095 | 1,880 | 1,841 | 713 | 0.9793 | 0.3873
80-84 | 1,411 | 1,260 | 1,237 | 452 | 0.9817 | 0.3654
85-89 | 813 | 717 | 703 | 251 | 0.9805 | 0.3570
90+ | 423 | 363 | 352 | 109 | 0.9697 | 0.3097
Supplementary Table 25:  Absolute number of _female_ patients and risk
measures per age range ($[y_{1},y_{2}]$, 1st column). Columns 2 through 5
lists, per age range, absolute numbers of: female patients ($|U^{y}|$), female
patients with at least $2$ drug administrations ($|U^{\nu\geq
2,F,[y_{1},y_{2}]}|$), female patients with at least one co-administration
($|U^{\Psi,F,[y_{1},y_{2}]}|$), and female patients with at least one known
DDI co-administration ($|U^{\Phi,F,[y_{1},y_{2}]}|$). Per age range women risk
for both co-administration ($RC^{F,[y_{1},y_{2}]}$) and known DDI co-
administration ($RI^{F,[y_{1},y_{2}]}$) are listed in columns 6 and 7,
respectively.

###  5.4 Risk Ratios per number of drug

# of drugs $\nu$ | $|U^{\nu}|$ | $|U^{\Psi,\nu}|$ | $|U^{\Phi,\nu}|$ | $RRC^{\nu}$ | $RRI^{\nu}$
---|---|---|---|---|---
1 | 27,911 | - | - | - | -
2 | 25,032 | 20,517 | 283 | 1.0 | 1.0
3 | 19,163 | 18,468 | 677 | 1.1758 | 3.1249
4 | 14,305 | 14,185 | 929 | 1.2098 | 5.7443
5 | 11,026 | 11,010 | 1,208 | 1.2183 | 9.6908
6 | 8,587 | 8,583 | 1,425 | 1.2195 | 14.6785
7 | 6,438 | 6,438 | 1,512 | 1.2201 | 20.7735
8 | 4,970 | 4,970 | 1,477 | 1.2201 | 26.2865
9 | 3,877 | 3,877 | 1,417 | 1.2201 | 32.3283
10 | 2,932 | 2,932 | 1,335 | 1.2201 | 40.2742
11 | 2,264 | 2,264 | 1,089 | 1.2201 | 42.5462
12 | 1,691 | 1,691 | 936 | 1.2201 | 48.9600
13 | 1,214 | 1,214 | 754 | 1.2201 | 54.9366
14 | 937 | 937 | 641 | 1.2201 | 60.5101
15 | 618 | 618 | 413 | 1.2201 | 59.1113
16 | 482 | 482 | 368 | 1.2201 | 67.5320
17 | 366 | 366 | 285 | 1.2201 | 68.8768
18 | 268 | 268 | 218 | 1.2201 | 71.9500
19 | 177 | 177 | 142 | 1.2201 | 70.9617
20 | 131 | 131 | 105 | 1.2201 | 70.8969
>20 | 333 | 333 | 313 | 1.2201 | 83.1398
Supplementary Table 26:  Absolute number of patients, join probabilities and
relative risk per number of distinct drugs dispensed, $\nu^{u}$ (1st column).
By definition, patients who had only one distinct drug dispensed could not
have had any co-administration or interaction. Columns 2 through 4 lists, per
distinct drugs dispensed, absolute numbers of: patients ($|U^{\nu}|$),
patients with at least one co-administration ($|U^{\Psi,\nu}|$), and patients
with at least one known DDI co-administration ($|U^{\Phi,\nu}|$). Per number
of distinct drugs dispensed relative risks for both co-administration
($RRC^{\nu}$) and known DDI co-administration ($RRI^{\nu}$) are listed in
columns 5 and 6, respectively.

## Supplementary Note 6 DDI Networks

For all pair of drugs known to interact we built two different networks, which
are weighted versions of $\Delta$. In these networks weights are defined by
either $\tau^{\Phi}_{i,j}$ or $|U^{\Phi}_{i,j}|$. In this section we show
alternatives plotting schemes, additional subgraphs, and tables containing
values used for plotting or inference. We also show a Principal Component
Analysis and two clustering methods performed on the networks.

Supplementary Figure 7:  Left. Node degree, $deg(i)$, and node degree
strength, $degstr(i)=\sum_{j}\tau^{\Phi}_{i,j}$, of weighted version of
network $\Delta$ where weights are defined by $\tau^{\Phi}_{i,j}$. Right. Edge
distribution of weighted version of network $\Delta$, where weights are
defined by either $\tau^{\Phi}_{i,j}$ or $|U^{\Phi}_{i,j}|$.

Supplementary Figure 8:  A weighted version of network $\Delta$ where weights
are defined by $|U^{\Phi}_{i,j}|$. Top left. Female DDI network. Top right.
Male DDI network. Bottom left. Major DDI network. Bottom center. Moderate DDI
network. Bottom right. Minor DDI network. Nodes denote drugs $i$ involved in
at least one co-administration known to be a DDI. Node color represents the
highest level of primary action class, as retrieved from Drugs.com (see
legend) Node size represents the probability of interaction, $PI(i)$, as
defined in main text. Edges weights are the value of $|U^{\Phi}_{i,j}|$, the
number of patients affected by the DDI. Edge colors denote $RRI^{g}_{i,j}$,
where $g\in\\{\text{M},\text{F}\\}$, to identify DDI edges that are higher
risk for females (blue) or males (red). Color intensity for $RRI^{g}_{i,j}$
varies in $[1,5]$; that is, values are clipped at 5.

Supplementary Figure 9:  A weighted version of network $\Delta$ where weights
are defined by $\tau^{\Phi}_{i,j}$. Top left. Female DDI network. Top right.
Male DDI network. Bottom left. Major DDI network. Bottom center. Moderate DDI
network. Bottom right. Minor DDI network. Nodes denote drugs $i$ involved in
at least one co-administration known to be a DDI. Node color represents the
highest level of primary action class, as retrieved from Drugs.com (see
legend) Node size represents the probability of interaction, $PI(i)$, as
defined in main text. Edges weights are the value of $\tau^{\Phi}_{i,j}$,
obtained from Equation 4, a normalized measure of the degree to which a
specific DDI is co-prescribed. Edge colors denote $RRI^{g}_{i,j}$, where
$g\in\\{\text{M},\text{F}\\}$, to identify DDI edges that are higher risk for
females (blue) or males (red). Color intensity for $RRI^{g}_{i,j}$ varies in
$[1,5]$; that is, values are clipped at 5.

Supplementary Figure 10:  Principal Component Analysis (PCA) of network where weights are defined by $\tau^{\Phi}_{i,j}$. Top Left. Explained variance ratio for the first 9 principal components. Additional plots. Projection of network nodes (drugs) given the respective principal component. Nodes with loading $\geq 2$ s.d. in either component are annotated.  Supplementary Figure 11:  Principal Component Analysis (PCA) of network where weights are defined by $|U^{\Phi}_{i,j}|$. Top Left. Explained variance ratio for the first 9 principal components. Additional plots. Projection of network nodes (drugs) given the respective principal component. Nodes with loading $\geq 2$ s.d. in either component are annotated.  $i$ | $deg(i)$ | $degstr(i)$ | $betweenness(i)$ | $PI(i)$ | class
---|---|---|---|---|---
Phenytoin | 24 | 6.51 | 0.30 | 0.20 | CNS agents
Phenobarbital | 15 | 2.17 | 0.28 | 0.05 | CNS agents
Ethinyl Estradiol | 9 | 1.78 | 0.03 | 0.04 | Hormones
Doxycycline | 8 | 1.39 | 0.02 | 0.04 | Anti-infectives
Prednisone | 7 | 0.96 | 0.02 | 0.03 | Hormones
Prednisolone | 6 | 0.54 | 0.03 | 0.00 | Hormones
Diazepam | 5 | 1.12 | 0.05 | 0.09 | CNS agents
Erythromycin | 5 | 0.20 | 0.18 | 0.01 | Anti-infectives
Estradiol | 4 | 0.57 | 0.00 | 0.01 | Hormones
Estrogens Conj. | 4 | 0.58 | 0.00 | 0.01 | Hormones
Norethisterone | 3 | 0.73 | 0.00 | 0.00 | Hormones
Levonorgestrel | 3 | 0.79 | 0.00 | 0.00 | Hormones
Medroxyproges. Ac. | 3 | 1.06 | 0.00 | 0.00 | Hormones
Omeprazole | 3 | 0.85 | 0.00 | 0.05 | Gastrointestinal agents
Folic acid | 2 | 0.50 | 0.00 | 0.00 | Nutritional Products
Clonazepam | 2 | 0.42 | 0.00 | 0.09 | CNS agents
Amoxicillin | 2 | 0.30 | 0.00 | 0.00 | Anti-infectives
Clavulanate | 2 | 0.23 | 0.00 | 0.00 | Anti-infectives
Sulfadiazine | 1 | 0.51 | 0.00 | 0.01 | Anti-infectives
Trimethoprim | 1 | 0.16 | 0.00 | 0.00 | Anti-infectives
Carbamazepine | 18 | 4.84 | 0.20 | 0.18 | CNS agents
Fluoxetine | 10 | 3.41 | 0.02 | 0.06 | Psychotherapeutic agents
Haloperidol | 6 | 2.32 | 0.03 | 0.20 | Psychotherapeutic agents
Lithium | 9 | 2.05 | 0.13 | 0.17 | Psychotherapeutic agents
Fluconazole | 10 | 1.74 | 0.09 | 0.11 | Anti-infectives
Salbutamol | 7 | 1.53 | 0.00 | 0.03 | Respiratory agents
Amitriptyline | 5 | 1.47 | 0.00 | 0.08 | Psychotherapeutic agents
Imipramine | 5 | 1.31 | 0.01 | 0.07 | Psychotherapeutic agents
Nortriptyline | 5 | 1.30 | 0.00 | 0.09 | Psychotherapeutic agents
Fenoterol | 8 | 0.81 | 0.13 | 0.01 | Respiratory agents
Biperiden | 1 | 0.70 | 0.00 | 0.13 | CNS agents
Methylphenidate | 1 | 0.24 | 0.00 | 0.02 | CNS agents
Losartan | 1 | 0.21 | 0.00 | 0.00 | Cardiovascular agents
Captopril | 1 | 0.18 | 0.00 | 0.00 | Cardiovascular agents
Metronidazole | 3 | 0.17 | 0.16 | 0.00 | Anti-infectives
Enalapril | 1 | 0.16 | 0.00 | 0.00 | Cardiovascular agents
Methyldopa | 7 | 2.30 | 0.01 | 0.06 | Cardiovascular agents
Iron (II) Sulfate | 5 | 1.12 | 0.02 | 0.04 | Nutritional Products
Levodopa | 3 | 0.97 | 0.03 | 0.01 | CNS agents
Ciprofloxacin | 4 | 0.35 | 0.21 | 0.01 | Anti-infectives
Norfloxacin | 2 | 0.29 | 0.00 | 0.01 | Anti-infectives
Metoclopramide | 1 | 0.11 | 0.00 | 0.00 | Gastrointestinal agents
Supplementary Table 27:  Louvain modules of weighted version of network $\Delta$ where weights are defined by $\tau^{\Phi}_{i,j}$. Each Louvain module is shown separated by a horizontal line. Drugs nodes ($i$; 1nd column) and their respective degree, degree strength, and betweenness centrality measure, shown in columns 2, 3, and 4, respectively Column 5 shows the drug probability of interaction, $PI(i)$. Drug class is shown in column 6. Continues on Supplementary Table 28.  $i$ | $deg(i)$ | $degstr(i)$ | $betweenness(i)$ | $PI(i)$ | class
---|---|---|---|---|---
Digoxin | 9 | 3.70 | 0.03 | 0.24 | Cardiovascular agents
Warfarin | 14 | 3.31 | 0.17 | 0.13 | Coagulation modifiers
Diltiazem | 6 | 2.66 | 0.03 | 0.13 | Cardiovascular agents
Amiodarone | 3 | 1.40 | 0.00 | 0.02 | Cardiovascular agents
Furosemide | 5 | 1.31 | 0.05 | 0.04 | Cardiovascular agents
Levothyroxine | 3 | 1.15 | 0.00 | 0.01 | Hormones
Simvastatin | 4 | 1.07 | 0.00 | 0.02 | Metabolic agents
Propylthiouracil | 2 | 0.87 | 0.00 | 0.01 | Hormones
Hydrochlorothiazide | 2 | 0.69 | 0.00 | 0.00 | Cardiovascular agents
Spironolactone | 1 | 0.55 | 0.00 | 0.02 | Cardiovascular agents
Allopurinol | 1 | 0.46 | 0.00 | 0.01 | Metabolic agents
Amlodipine | 1 | 0.34 | 0.00 | 0.00 | Cardiovascular agents
Acetaminophen | 1 | 0.22 | 0.00 | 0.00 | CNS agents
Gentamicin | 1 | 0.12 | 0.00 | 0.02 | Anti-infectives
Diclofenac | 2 | 0.09 | 0.03 | 0.01 | CNS agents
Tobramycin | 1 | 0.08 | 0.00 | 0.00 | Topical Agents
Azithromycin | 1 | 0.07 | 0.00 | 0.00 | Anti-infectives
Alendronate | 1 | 0.04 | 0.00 | 0.01 | Metabolic agents
Aminophylline | 10 | 1.93 | 0.23 | 0.01 | Respiratory agents
Hydrocortisone | 3 | 0.06 | 0.20 | 0.01 | Hormones
Timolol | 7 | 1.11 | 0.16 | 0.06 | Cardiovascular agents
Ibuprofen | 7 | 1.28 | 0.06 | 0.05 | CNS agents
Atenolol | 8 | 2.22 | 0.05 | 0.06 | Cardiovascular agents
Propranolol | 14 | 4.81 | 0.06 | 0.10 | Cardiovascular agents
ASA | 7 | 1.57 | 0.01 | 0.07 | CNS agents
Verapamil | 4 | 1.11 | 0.01 | 0.04 | Cardiovascular agents
Glyburide | 5 | 2.29 | 0.00 | 0.12 | Metabolic agents
Carvedilol | 6 | 1.70 | 0.00 | 0.07 | Cardiovascular agents
Gliclazide | 5 | 1.64 | 0.00 | 0.12 | Metabolic agents
Chlorpromazine | 1 | 0.33 | 0.00 | 0.00 | CNS agents
Dexamethasone | 3 | 0.24 | 0.00 | 0.03 | Hormones
Maprotiline | 1 | 0.23 | 0.00 | 0.01 | Psychotherapeutic agents
Epinephrine | 1 | 0.0 | 0.0 | 0.02 | Respiratory agents
Supplementary Table 28:  Continuation. See Supplementary Table 27 for column description.  $i$ | $deg(i)$ | $degstr(i)$ | $betweenness(i)$ | $PI(i)$ | class
---|---|---|---|---|---
Phenytoin | 24 | 6.51 | 0.30 | 0.20 | CNS agents
Phenobarbital | 15 | 2.17 | 0.28 | 0.05 | CNS agents
Ethinyl Estradiol | 9 | 1.78 | 0.03 | 0.04 | Hormones
Doxycycline | 8 | 1.39 | 0.02 | 0.04 | Anti-infectives
Prednisone | 7 | 0.96 | 0.02 | 0.03 | Hormones
Prednisolone | 6 | 0.54 | 0.03 | 0.00 | Hormones
Estradiol | 4 | 0.57 | 0.00 | 0.01 | Hormones
Estrogens Conj. | 4 | 0.58 | 0.00 | 0.01 | Hormones
Dexamethasone | 3 | 0.24 | 0.00 | 0.03 | Hormones
Norethisterone | 3 | 0.73 | 0.00 | 0.00 | Hormones
Hydrocortisone | 3 | 0.06 | 0.20 | 0.01 | Hormones
Levonorgestrel | 3 | 0.79 | 0.00 | 0.00 | Hormones
Medroxyproges. Ac. | 3 | 1.06 | 0.00 | 0.00 | Hormones
Folic acid | 2 | 0.50 | 0.00 | 0.00 | Nutritional Products
Amoxicillin | 2 | 0.30 | 0.00 | 0.00 | Anti-infectives
Clavulanate | 2 | 0.23 | 0.00 | 0.00 | Anti-infectives
Sulfadiazine | 1 | 0.51 | 0.00 | 0.01 | Anti-infectives
Trimethoprim | 1 | 0.16 | 0.00 | 0.00 | Anti-infectives
Propranolol | 14 | 4.81 | 0.06 | 0.10 | Cardiovascular agents
Methyldopa | 7 | 2.30 | 0.01 | 0.06 | Cardiovascular agents
Glyburide | 5 | 2.29 | 0.00 | 0.12 | Metabolic agents
Atenolol | 8 | 2.22 | 0.05 | 0.06 | Cardiovascular agents
Aminophylline | 10 | 1.93 | 0.23 | 0.01 | Respiratory agents
Carvedilol | 6 | 1.70 | 0.00 | 0.07 | Cardiovascular agents
Gliclazide | 5 | 1.64 | 0.00 | 0.12 | Metabolic agents
ASA | 7 | 1.57 | 0.01 | 0.07 | CNS agents
Salbutamol | 7 | 1.53 | 0.00 | 0.03 | Respiratory agents
Ibuprofen | 7 | 1.28 | 0.06 | 0.05 | CNS agents
Iron (II) Sulfate | 5 | 1.12 | 0.02 | 0.04 | Nutritional Products
Timolol | 7 | 1.11 | 0.16 | 0.06 | Cardiovascular agents
Verapamil | 4 | 1.11 | 0.01 | 0.04 | Cardiovascular agents
Levodopa | 3 | 0.97 | 0.03 | 0.01 | CNS agents
Ciprofloxacin | 4 | 0.35 | 0.21 | 0.01 | Anti-infectives
Chlorpromazine | 1 | 0.33 | 0.00 | 0.00 | CNS agents
Norfloxacin | 2 | 0.29 | 0.00 | 0.01 | Anti-infectives
Maprotiline | 1 | 0.23 | 0.00 | 0.01 | Psychotherapeutic agents
Metoclopramide | 1 | 0.11 | 0.00 | 0.00 | Gastrointestinal agents
Supplementary Table 29:  InfoMap modules of weighted version of network $\Delta$ where weights are defined by $\tau^{\Phi}_{i,j}$. Each InfoMap module is shown separated by a horizontal line. Drugs nodes ($i$; 1nd column) and their respective degree, total degree strength (, and betweenness centrality measure, shown in columns 2, 3, and 4, respectively Column 5 shows the drug probability of interaction, $PI(i)$. Drug class is shown in column 6. Continues on Supplementary Table 30.  $i$ | $deg(i)$ | $degstr(i)$ | $betweenness(i)$ | $PI(i)$ | class
---|---|---|---|---|---
Carbamazepine | 18 | 4.84 | 0.20 | 0.18 | CNS agents
Fluoxetine | 10 | 3.41 | 0.02 | 0.06 | Psychotherapeutic agents
Fluconazole | 10 | 1.74 | 0.09 | 0.11 | Anti-infectives
Amitriptyline | 5 | 1.47 | 0.00 | 0.08 | Psychotherapeutic agents
Imipramine | 5 | 1.31 | 0.01 | 0.07 | Psychotherapeutic agents
Nortriptyline | 5 | 1.30 | 0.00 | 0.09 | Psychotherapeutic agents
Fenoterol | 8 | 0.81 | 0.13 | 0.01 | Respiratory agents
Methylphenidate | 1 | 0.24 | 0.00 | 0.02 | CNS agents
Digoxin | 9 | 3.70 | 0.03 | 0.24 | Cardiovascular agents
Warfarin | 14 | 3.31 | 0.17 | 0.13 | Coagulation modifiers
Furosemide | 5 | 1.31 | 0.05 | 0.04 | Cardiovascular agents
Levothyroxine | 3 | 1.15 | 0.00 | 0.01 | Hormones
Propylthiouracil | 2 | 0.87 | 0.00 | 0.01 | Hormones
Hydrochlorothiazide | 2 | 0.69 | 0.00 | 0.00 | Cardiovascular agents
Spironolactone | 1 | 0.55 | 0.00 | 0.02 | Cardiovascular agents
Allopurinol | 1 | 0.46 | 0.00 | 0.01 | Metabolic agents
Acetaminophen | 1 | 0.22 | 0.00 | 0.00 | CNS agents
Gentamicin | 1 | 0.12 | 0.00 | 0.02 | Anti-infectives
Tobramycin | 1 | 0.08 | 0.00 | 0.00 | Topical Agents
Azithromycin | 1 | 0.07 | 0.00 | 0.00 | Anti-infectives
Haloperidol | 6 | 2.32 | 0.03 | 0.20 | Psychotherapeutic agents
Lithium | 9 | 2.05 | 0.13 | 0.17 | Psychotherapeutic agents
Biperiden | 1 | 0.70 | 0.00 | 0.13 | CNS agents
Losartan | 1 | 0.21 | 0.00 | 0.00 | Cardiovascular agents
Captopril | 1 | 0.18 | 0.00 | 0.00 | Cardiovascular agents
Metronidazole | 3 | 0.17 | 0.16 | 0.00 | Anti-infectives
Enalapril | 1 | 0.16 | 0.00 | 0.00 | Cardiovascular agents
Diltiazem | 6 | 2.66 | 0.03 | 0.13 | Cardiovascular agents
Amiodarone | 3 | 1.40 | 0.00 | 0.02 | Cardiovascular agents
Simvastatin | 4 | 1.07 | 0.00 | 0.02 | Metabolic agents
Amlodipine | 1 | 0.34 | 0.00 | 0.00 | Cardiovascular agents
Diazepam | 5 | 1.12 | 0.05 | 0.09 | CNS agents
Omeprazole | 3 | 0.85 | 0.00 | 0.05 | Gastrointestinal agents
Clonazepam | 2 | 0.42 | 0.00 | 0.09 | CNS agents
Erythromycin | 5 | 0.20 | 0.18 | 0.01 | Anti-infectives
Diclofenac | 2 | 0.09 | 0.03 | 0.01 | CNS agents
Alendronate | 1 | 0.04 | 0.00 | 0.01 | Metabolic agents
Epinephrine | 1 | 0.0 | 0.0 | 0.02 | Respiratory agents
Supplementary Table 30:  Continuation. See Supplementary Table 29 for column
description.

## Supplementary Note 7 Null Model for $RI^{y}$

To test if sheer combinatorics explains the increased risk of DDI in older
age, we compared the observed risk of interactions $RI^{y}$ with a random null
model, $H^{rnd}_{0}$. We separated all patients $u$ in our dataset per age
range $y$. From these subset of patients $U^{[y1,y2]}$ we also separated which
drugs $d$ were prescribed in their age range as $D^{[y1-y2]}$. For clarity, we
will refer to all measures previously reported with an added star ($\star$) in
the notation to indicate that these values are calculated for the null model
(e.g., $RI^{y\star}$ is the null model value of the risk of interaction per
age range, $RI^{y}$).

The null model is then computed by proportionally sampling patients for each
age range, $u\in U^{[y1-y2]}$. For each drawn patient $u$ we sampled $|D^{u}|$
drugs available to patients in the patient’s age range $D^{[y1,y2]}$, and then
randomly drew $\Psi^{u}$ co-administrations from the patient’s possible
pairwise combinations $\binom{|D^{u}|}{2}$ of drugs, thus yielding random drug
pairs $\psi^{u\star}_{i,j}$ that matched the observed number of co-
administrations, $\Psi^{u}\equiv\Psi^{u\star}$. To decide if a co-
administration is an interaction in the null model, we compare the randomly
drawn pair of drugs against DrugBank to decide if $\varphi^{u\star}_{i,j}$ is
an interaction or not.

This null model allow us to measure what is the expected number of
interactions given the increase of co-administrations observed with age,
assuming drugs are prescribed completely at random. In other words, it
measures the risk of DDI if only age, and the drugs available to patients in
these ages, were given to them at random with the same number of co-
administrations.

To compute confidence intervals for the number of patients in the null model,
we proportionally sampled the same number of patients observed in each age
range, 100 times. Confidence intervals can be seen as background fills in
Figures 2 and 4. To measure the significance of our null models, Supplementary
Table 31 shows the chi-square tests against the expected number of patients in
each age bin, $|U^{[y1,y2]}|$, from our data. The null model rejects the
hypothesis it was sampled from the same distribution as our data. This means
the observed increase in DDI with age, seen in our data, cannot be explained
alone by the increased combinatorics of drug co-administrations alone.

| model | chi-square |  $p$-value
---|---|---|---
1 | $H^{rnd}_{0}$ | 22378.5912 | 0.0
Supplementary Table 31:  Chi-square statistic when the number of patients in
the null model, $|U^{y\star}|$, is compared to the observed values, $|U^{y}|$.

## Supplementary Note 8 Interactions per Neighborhood

Supplementary Figure 12 shows the number of drugs dispensed for each
neighborhood $N$, colored by the average income of its residents, R$ (Reais).
Naturally, the larger the neighborhood population ($\Omega^{N}$), the more
drugs are dispensed ($\alpha^{N}$), leading to a fairly clear linear
relationship ($R^{2}=623$, $p=0.0$). Some observed exceptions above and below
the regression line are noteworthy, though. Three neighborhoods—Itoupavazinha,
Velha Central and Água Verde—display dispensation levels below what is
expected for their population (circled in Cyan in Supplementary Figure
12-left). On the other hand, two neighborhoods that are also not among the
wealthiest—Fortaleza and Tribess—are well above the expected drug dispensation
(circled in magenta). Looking at these specific neighborhoods will require
further work to be better understood. In any case, their identification
highlights the benefits of analyzing EHR and a data science approach to
support responsive public health policy.

For a visual inspection of how both official survey numbers and those analyzed
in the main manuscript related geographically in the city of Blumenau, we have
mapped neighborhoods to results in Supplementary Figures 13 and 14. The first
figure denotes neighborhoods mapped to official numbers from IBGE[63], such as
population, gender rate and income distribution. The second figure denotes
dispensed drug intervals, distinct drugs, co-administrations and interactions
mapped to each neighborhood.

Supplementary Figure 12:  Left. Number of drugs intervals dispensed
$\alpha^{N}$ against population $\Omega^{N}$ in each neighborhood $N$. Right.
Number of drug intervals dispensed ($\alpha^{N}$) versus number of
interactions ($\Phi^{N}$), per neighborhood ($N$), normalized by population
($\Omega^{N}$). Color denotes the average per capita income of neighborhood,
in Brazilian Reais (R$). Regression line shown in green. Patients who reported
living in neighborhood Other were discarded from computation. Cartographic
shapes from IBGE [63].

Supplementary Figure 13:  Data from IBGE [63] mapped to geographical
neighbourhoods in the city of Blumenau. Left. Population probability,
$P(\Omega^{N})$. Center. Gender rate, $\Omega^{N,g=F}/\Omega^{N,g=M}$. Right.
Average income in Brazilian Reais (R$/month). See Supplementary Note 9 for
details on income. Cartographic shapes from IBGE [63].

Supplementary Figure 14:  Results from Pronto data mapped to geographical
neighbourhoods in the city of Blumenau. Top left. Number of drug interval
dispensed per capita, $\alpha^{N}/\Omega^{N}$. Top right. Distinct drugs
dispensed per capita, $\nu^{N}/\Omega^{N}$. Bottom left. Number of co-
adminstrations per capita, $\Psi^{N}/\Omega^{N}$. Bottom right. Number of
interactions per capita, $\Phi^{N}/\Omega^{N}$. Cartographic shapes from IBGE
[63].

## Supplementary Note 9 Projected Cost of DDI in hospitalizations

Estimating the financial burden of DDI prescribed in primary and secondary
care is difficult, since outcomes vary by a large margin and only few result
in short-term symptoms requiring hospitalization. Measuring hospitalizations
due to DDI are also strenuous, since underestimation of true risk can be
masked in practitioners and pharmacists failing to recognize adverse patient
outcomes caused by DDI as such. However, drug- and cohort-focused studies have
shown that the number of DDI is associated with a significantly increased risk
of hospitalization [77, 78]. A review paper in 2007 [79] estimated that DDI
were held responsible for 0.054% of emergency room (ER) visits, 0.57% of
hospital admissions (4.8% in the elderly population) and 0.12% of re-
hospitalizations. The most common outcomes were gastrointestinal bleeding
(32.8%), hypertension/hypotension (18%) and cardiac rhythm disturbances (18%).

In this section a study of the financial burden of possible DDI-related
hospitalizations is presented. It considers various rates of hospitalization
expected for major DDI co-administrations, and is based on a cost estimate of
ADR hospitalizations in Canada [80], and average hospitalization costs for
Brazil at city, state and national levels. As average hospitalization costs
were not found for the United States, results in Canadian dollars were also
converted to US dollars. Our estimation then relies on guessing what
proportion of patients with major DDI co-administrations are likely to have an
ADR requiring hospitalization.

|  | Blumenau | Santa Catarina | Brazil | Ontario
---|---|---|---|---|---
|  | city | state | national | province
Population |  | 338,876 | 6,819,190 | 204,450,649 | 13,680,425
Hospitalization | Elective | 9,761 | 146,395 | 3,391,088 | -
Urgent | 24,592 (5,808) | 507,189 (110,748) | 13,440,043 (2,711,527) | -
Work Accident | 87 | 2,106 | 64,485 | -
External Causes | 786 | 902 | 110,922 | -
Total | 35,226 | 656,592 | 17,006,538 | -
Avg. Cost | Elective | R$ 3,764.62 | R$ 1,533.10 | R$ 1,583.45 | -
Urgent | R$ 2,606.03 | R$ 1,379.13 | R$ 1,083.23 | C$ 8,443.14
Work Accident | R$ 1,663.27 | R$ 2,595.45 | R$ 1,541.38 | -
External Causes | R$ 2,321.31 | R$ 2,203.50 | R$ 1,256.36 | -
Supplementary Table 32:  Population, number of hospitalizations, and average
cost per hospitalization in the analyzed period shown for city, state and
national levels. Population follows the official projections for 2015.
Hospitalization numbers and cost shown by type. Urgent hospitalization values
in parenthesis shown for patients over 64 years old. Note Blumenau has a much
higher average cost per hospitalization than state and national levels. Brazil
data from Hospitalization Information System (Sistema de Informações
Hospitalares do SUS; SIH/SUS) [81]. Ontario data from [80], adjusted for
inflation.

To compute costs we gathered number of public health care hospitalizations and
average costs for each level (see Supplementary Table 32) from the national
Hospitalization Information System (Sistema de Informações Hospitalares do
SUS; SIH/SUS), a data source managed by the Informatics Department under the
Executive Secretary of Brazil’s Ministry of Health [81].

As reported, the number of patients prescribed a major DDI in Blumenau (city
level) was $|U^{\Phi,s=major}|=5,224$. For state and national levels, we
estimated this number from the percentage of hospitalizations it represents at
city level, a reasonable assumption due the lack of data that generalizes
medical practice in Blumenau for the state and country. For example, say 261
(or 5%) Pronto patients prescribed a major DDI had to be hospitalized. In
hospitalization terms, that accounts for 1.06% of all hospitalizations in the
same period. At the state and national level, the same 1.06% accounts for
5,376 and 142,564 patients, respectively. Costs are then estimated by
multiplying the number of patients assumed hospitalized by the average
hospitalization cost in each level.

[80] argued in 2007 that the average cost of ADR-related hospitalization for
all adults over 65 in the province of Ontario (pop. 12M in 2006; 13.6M in
2014) was C$ 7,528 (C$ 8,443.14 or $7,380.78 in 2014 when adjusted for
inflation and exchange rate) for a total annual cost of C$ 13.6 million (C$
15.2M or $13.3M after adjusting), or estimated C$ 35.7 million (C$ 40M or $35M
after adjusting) in Canada. In an attempt to compare results, we also
multiplied the number of patients assumed to have been hospitalized to their
average cost of ADR-relation hospitalization (see columns 6 and 7 of
Supplementary Table 33). Moreover, Supplementary Tables 33, 34 and 35 show the
estimated costs at different percentages of hospitalizations at city, state
and national levels, respectively. Costs in Brazilian Reais (columns 4 and 5)
are computed based on the average cost of hospitalization in Brazil. Costs in
C$ use [80] as reference (columns 6 and 7), and then converted to US$ with the
average exchange rate between the two currencies for the whole period of our
data (columns 8 and 9). The average exchange rate in the period was C$1.00
Canadian dollar equals to $0.8742 US dollar, and maximum and minimum rates
were $.9418$ in January 4th 2014 and $.7821$ in March 14th 2015, respectively.

Our cost analysis first considers two previous studies of the proportion of
emergency room visits that are due to DDI and ADR. [79] reported that 0.57% of
all hospital admissions they observed were due to DDI, which in our data would
correspond to 140 patients, or $p_{h}=2.68\%$ of all patients dispensed a
major DDI (see Supplementary Table 33). [80], on the other hand, argued that
0.75% of all hospitalizations of patients over 65 years of age were due to ADR
(not only from DDI), which corresponds in our data to 436 patients, or
$p_{h}=8.35\%$ of all patients who were co-administered a major DDI. Both of
these conjectures are likely to err on the side of under-reporting emergency
room admissions due to DDI or ADR, since this a well-known problem in studies
of this phenomenon [82, 83, 84, 85, 86]. Indeed, the proportion of hospital
admissions due to ADR has been reported in the literature to vary anywhere
between 0.5% to 12% [84], with DDI reportedly being responsible for 15% [85]
to 30% [87] of all ADR. These ranges, if correct, put the proportion of
hospital admissions due to DDI anywhere between $0.5\%\times 15\%=0.075\%$ and
$12\%\times 30\%=3.6\%$, which in our Blumenau data would mean between 18 and
885 emergency room patients, or $p_{h}\in[0.35,16.95]\%$ of all patients
dispensed a major DDI. These ranges could be higher, since even in the more
controlled hospital environment, the proportion of patients with ADR can be as
high as 41% [88]. Therefore, in addition to the costs derived from the numbers
provided by [79] and [80], tables in this section also report cost estimates
for various values of $p_{h}$, so that readers can judge what is an
appropriate value to consider. Given the ranges just outlined, it is
reasonable to assume, for instance, that $p_{h}=10\%$ of all patients
dispensed a major DDI will have to be hospitalized (522 patients).

The lowest estimate ($p_{h}=2.68\%$, via [79]) leads to a cost of DDI-related
hospitalization in Blumenau of over $1M in the 18-month period, after
adjusting for Canadian cost, inflation and exchange rate to US dollar. The
extrapolated costs to the state and the country are $21M and $565M,
respectively (see Supplementary Tables 34 and 35). The estimated costs
obtained via [80] ($p_{h}=8.35\%$) reach $3.2M, $61M, and $1.5B, for the city,
state and country levels respectively. Finally, if we assume $p_{h}=10\%$, the
estimated costs reach $3.9M, $79M, and $2.1B, for the city, state and country
levels respectively.

All estimations lead to very substantial costs for the various levels of
government. To compare them to the costs found for Canada [80], we computed
per capita measures of the burden of DDI-related hospitalizations. For
instance, the lowest estimate $p_{h}=2.68\%$ leads to a per capita cost for
Blumenau of $2.03, while the inflation-adjusted cost for Ontario (Canada) is
$0.97, suggesting that the financial burden of DDI is more severe than
previously thought—even when considering only the lowest estimate of the
proportion of hospitalizations that derive from co-administration of known
major DDIs. For the state of Santa Catarina and Brazil as a whole, these
numbers are $2.09 and $1.84, respectively. If we consider the higher estimates
of $p_{h}=8.35\%$ or $p_{h}=10\%$, the per capita cost for Blumenau is $6.33
and $7.58, respectively.

To put these numbers in context, Brazil’s minimum monthly wage was R$724
(R$9,412/year333Brazilians receive a 13th salary in December. Thus, yearly
gross income is calculated by a 13, and not by a 12, multiplier.) in 2014, and
workers in Blumenau received on average 2.9 wages a month [63]. This
constitutes an average gross income of R$2,099.60 a month (R$27,294.80/year).
If we assume the same 140 patients were hospitalized due to ADR caused by DDI,
the direct cost of such hospitalizations is equal to 3,707 lost productive
worker/days (considering an 8 hour working day), with possible much higher
indirect costs.

Some limitations should be noted. When comparing to [79], data from [63]
includes patients over 64, while in their work the authors included patients
over 65 years old. Our analysis then possibly contains additional patients
exactly age 65, although we do not believe this affects the results presented
given their large difference. In general, other studies [79] divide hospital
admissions only between two categories, emergency room (ER) visits and
hospitalizations. It is not possible to conclude whether electives or external
causes are included in their hospitalization numbers. SIH/SUS data are only
available for patients that were hospitalized in the public system, meaning
the cost of hospitalization was billed to the public system. Therefore, if a
patient was hospitalized and his/her private insurance covered the costs, the
SIH/SUS would have no record of it. Furthermore, SIH/SUS provides the number
of hospitalizations broken down by type. These consist of “electives” (e.g.,
schedules cesareans), “urgencies”, “work accidents”, and “other external
causes” (codes V01 to Y98 of
ICD-10444http://www.datasus.gov.br/cid10/V2008/WebHelp/v01_y98.htm; e.g., car
accident, poisoning, and drowning). To better approximate reality, we have
calculated the cost of DDI-related hospitalizations only using the number of
urgent hospitalizations.

|  |  | Cost R$ | Cost CA$ | Cost US$
---|---|---|---|---|---
$p_{h}$ | $|U^{\Phi}_{major}|$ | % of hosp. | 18 months | 12 months | 18 months | 12 months | 18 months | 12 months
100% | 5,224 | 21.24% | 13,613,909 | 9,075,940 | 44,106,963 | 29,404,642 | 38,557,213 | 25,704,809
50% | 2,612 | 10.62% | 6,806,955 | 4,537,970 | 22,053,482 | 14,702,321 | 19,278,606 | 12,852,404
30% | 1,567 | 6.37% | 4,083,652 | 2,722,434 | 13,230,400 | 8,820,267 | 11,565,688 | 7,710,458
25% | 1,306 | 5.31% | 3,403,477 | 2,268,985 | 11,026,741 | 7,351,161 | 9,639,303 | 6,426,202
20% | 1,044 | 4.25% | 2,720,697 | 1,813,798 | 8,814,638 | 5,876,425 | 7,705,538 | 5,137,025
10% | 522 | 2.12% | 1,360,349 | 906,899 | 4,407,319 | 2,938,213 | 3,852,769 | 2,568,513
5% | 261 | 1.06% | 680,174 | 453,450 | 2,203,660 | 1,469,106 | 1,926,384 | 1,284,256
2.68% | 140 | 0.57% | 364,844 | 243,230 | 1,182,040 | 788,026 | 1,033,310 | 688,873
8.35% | 436 | 0.75% | 1,136,230 | 757,487 | 3,681,209 | 2,454,139 | 3,218,022 | 2,145,348
Supplementary Table 33:  Projected cost of DDI for the city of Blumenau in Reais (R$), Canadian Dollars (C$) and US dollars (US$) for the analysis period (18 months) and yearly (12 months). Each row calculates the associated cost based on different proportion of patients who had at least one major DDI and required hospitalization. Last row shows the projected cost when only $0.75\%$ of all hospitalizations of patients over 64 years old are considered, based on results of [80]. Similarly, second-to-last row shows projected cost when only $0.57\%$ of all hospitalization are considered, based on results of [79]. In the 18 month period, Blumenau had a total of 24,592 public health care emergency hospitalizations, from which 5,808 were of patients age over 64 years old. Average cost per hospitalization in the city is R$ 2,606.03. US$ costs were calculated based on C$ exchange rate of $.8742$, the average rate in the study period.  |  |  | Cost in R$ | Cost in CA$ | Cost in US$
---|---|---|---|---|---
$p_{h}$ | $|U^{\Phi}_{major}|$ | % of hosp. | 18 months | 12 months | 18 months | 12 months | 18 months | 12 months
100% | 107,726 | 21.24% | 148,567,620 | 99,045,080 | 909,545,700 | 606,363,800 | 795,102,280 | 530,068,187
50% | 53,863 | 10.62% | 74,283,810 | 49,522,540 | 454,772,850 | 303,181,900 | 397,551,140 | 265,034,093
30% | 32,307 | 6.37% | 44,555,391 | 29,703,594 | 272,772,524 | 181,848,349 | 238,450,972 | 158,967,314
25% | 26,931 | 5.31% | 37,141,215 | 24,760,810 | 227,382,203 | 151,588,136 | 198,771,880 | 132,514,586
20% | 21,555 | 4.25% | 29,727,039 | 19,818,026 | 181,991,883 | 121,327,922 | 159,092,788 | 106,061,859
10% | 10,752 | 2.12% | 14,828,352 | 9,885,568 | 90,780,641 | 60,520,428 | 79,358,184 | 52,905,456
5% | 5,376 | 1.06% | 7,414,176 | 4,942,784 | 45,390,321 | 30,260,214 | 39,679,092 | 26,452,728
2.68% | 2,890 | 0.57% | 3,985,671 | 2,657,114 | 24,400,675 | 16,267,116 | 21,330,464 | 14,220,309
7.71% | 8,306 | 0.75% | 21,645,699 | 14,430,466 | 70,128,721 | 46,752,481 | 61,304,788 | 40,869,858
Supplementary Table 34:  Projected cost of DDI for the state of Santa Catarina in Reais (R$), Canadian Dollars (C$) and US dollars (US$) for the analysis period (18 months) and yearly (12 months). Each row calculates the associated cost based on different proportion of patients who had at least one major DDI and required hospitalization. Last row shows the projected cost when only $0.75\%$ of all hospitalizations of patients over 64 years old are considered, based on results of [80]. Similarly, second-to-last row shows projected cost when only $0.57\%$ of all hospitalization are considered, based on results of [79]. In the 18 month period, Santa Catarina had a total of 507,189 public health care emergency hospitalizations. Average cost per hospitalization in the state is R$ 1,379.13. US$ costs were calculated based on C$ exchange rate of $.8742$, the average rate in the study period.  |  |  | Cost in R$ | Cost in CA$ | Cost in US$
---|---|---|---|---|---
$p_{h}$ | $|U^{\Phi}_{major}|$ | % of hosp. | 18 months | 12 months | 18 months | 12 months | 18 months | 12 months
100% | 2,854,665 | 21.24% | 3,092M | 2,061M | 24,102M | 16,068M | 21,070M | 14,046M
50% | 1,427,332 | 10.62% | 1,546M | 1,031M | 12,051M | 8,034M | 10,535M | 7,023M
30% | 856,130 | 6.37% | 927M | 618M | 7,228M | 4,819M | 6,319M | 4,213M
25% | 713,666 | 5.31% | 773M | 515M | 6,026M | 4,017M | 5,267M | 3,512M
20% | 571,201 | 4.25% | 619M | 412M | 4,823M | 3,215M | 4,216M | 2,811M
10% | 284,928 | 2.12% | 309M | 206M | 2,406M | 1,604M | 2,103M | 1,402M
5% | 142,464 | 1.06% | 154M | 103M | 1,203M | 802M | 1,051M | 701M
2.68% | 76,608 | 0.57% | 83M | 55M | 647M | 431M | 565M | 377M
7.12% | 203,365 | 0.75% | 530M | 353M | 1,717M | 1,145M | 1,501M | 1,001M
Supplementary Table 35:  Projected cost of DDI for Brazil in Reais (R$),
Canadian Dollars (C$) and US dollars (US$) for the analysis period (18 months)
and yearly (12 months). Each row calculates the associated cost based on
different proportion of patients who had at least one major DDI and required
hospitalization. Last row shows the projected cost when only $0.75\%$ of all
hospitalizations of patients over 64 years old are considered, based on
results of [80]. Similarly, second-to-last row shows projected cost when only
$0.57\%$ of all hospitalization are considered, based on results of [79]. In
the 18 month period, Brazil had a total of 13,440,043 public health care
emergency hospitalizations. Average cost per hospitalization in the country is
R$ 1,083.23. US$ costs were calculated based on C$ exchange rate of $.8742$,
the average rate in the study period.

## Supplementary Note 10 Statistical modeling

Here we show the complete results from runs of simple regression (SR),
polynomial regression (PR), ordinary multiple regression (OMR) and linear
mixed model (LMM) that were mentioned in the original text. For further
details on LMM see [89].

A SR is is a linear regression model with a single explanatory variable. It
works by fitting a line through the data that minimizes the sum of the squared
of the residual, where the residuals are differences between the observed
values to the predicted values of the model. For example, when predicting the
number of interactions from the number co-administrations, the SR equation
would look like

$\Phi^{u}(x)=\beta^{0}+\beta^{1}x+\epsilon^{u}$ (16)

where $\beta^{0}$ is the intercept (or bias), $\beta^{1}$ is the coefficient
(or slope) and $\epsilon^{u}$ are the residuals.

Similarly, PR is a regression where the dependent variable being modeled is
fitted with a $n$th degree polynomial, but still a single explanatory
variable. In the main manuscript we modeled $RRI^{y}$ with a cubic (3rd
degree) polynomial. In our case, the PR equation would look like

$RRI^{y}(x)=\beta^{0}+\beta^{1}(x^{3})+\beta^{2}(x^{2})+\beta^{3}x+\epsilon^{y}$
(17)

where $\beta^{0}$ is the intercept (or bias), $\beta^{1}$, $\beta^{2}$ and
$\beta^{3}$ are coefficients (giving the characteristic shape of the cubic
curve) and $\epsilon^{y}$ are the residuals.

An OMR is a widely used type of regression for predicting the value of one
dependent variable from the value of a set of independent variables. Similar
to SR, it works by fitting a hyperplane through the data that minimizes the
sum of the squared of the residuals.

In our case, the OMR equation would look like

$\Phi^{u}=\beta^{0}+\beta^{1}x^{u,1}+\beta^{2}x^{u,2}+\;...\;\beta^{j}x^{u,i}+\epsilon^{u}$
(18)

Where $\beta^{0}$ is the intercept (or bias), $\beta^{j}$ are the coefficients
(or slopes) and each $x^{u,i}$ is a predictor (covariate, regressor) such as
age or number of drugs. $\epsilon^{u}$ is the error associated with the fit.

A LMM (also known as multilevel, mixed effects, random effects or hierarchical
linear model) can be seen as extensions of the OMR where instances of the data
belong to certain groups—like children in classrooms or cities in states. In
our case, they are patients in specific neighborhoods.

The individual levels are usually defined as level-1 (within-group), and
level-2 (between-group) for a two level model. Separate level-1 models (e.g.,
patients) are developed for each level-2 (e.g., neighborhoods). Considering
only one predictor, level-1 models take the form of simple regressions:

$\Phi^{u,n}=\beta^{0,n}+\beta^{1,n}x^{u,n}+r^{u,n}$ (19)

where $\beta^{0,n}$ is the intercept for the $n$ neighborhood, $\beta^{1,n}$
is a coefficient (slope) associated with predictor $x^{u,n}$, and $r^{u,n}$ is
the error.

In the level-2 models, the level-1 regression coefficients ($\beta^{0,n}$ and
$\beta^{1,n}$) are used as outcome variables and are related to each of the
level-2 predictors.

$\beta^{0,n}=\gamma^{0,0}+\gamma^{0,1}g^{n}+u^{0,n}$ (20)
$\beta^{1,n}=\gamma^{1,0}+\gamma^{1,1}g^{n}+u^{1,n}$ (21)

where $g^{n}$ is the level-2 predictor, $\gamma^{0,0}$ and $\gamma^{1,0}$ are
the overall mean intercept adjusted for $g$. $\gamma^{0,1}$ ($\gamma^{1,1}$)
is the regression coefficient associated with $g$ relative to level-1
intercept (slope) and $u^{0,n}$ ($u^{1,n}$) are level-2 random effects
adjusted for $g$ on the intercept (slope).

A combined two-level model is created by substituting Supplementary Equations
20 and 21 into Supplementary Equation 19:

$\Phi^{u,n}=\gamma^{0,0}+\gamma^{1,0}x^{u,n}+\gamma^{0,1}g^{n}+\gamma^{1,1}g^{n}x^{u,n}+u^{1,n}x^{0,n}+u^{0,n}+\epsilon^{u,n}$
(22)

The combined model incorporates the level-1 and level-2 predictors ($x^{u,n}$
and $g^{n}$), a cross-level term ($g^{n}x^{u,n}$) as well as the composite
error ($u^{1,n}x^{u,n}+u^{0,n}+r^{u,n}$).

In practice, LMM coefficients are estimated using maximum likelihood methods.

###  10.1 Simple Regression (SR) models

In Figure 3 of the main manuscript we show single regression models predicting
the number of interactions. Specifically, $\nu^{u}$ predicts $\Psi^{u}$ best
with a quadratic regression ($R^{2}=.857$) as shown in Figure 3-left. When it
comes to predicting number of interactions (Figure 3, center and right), on
the other hand, there is much more dispersion of the data, which leads to a
relatively small linear correlation between $\Psi^{u}$ and $\Phi^{u}$
($R^{2}=.487$)—though better than the linear correlation between $\nu^{u}$ and
$\Phi^{u}$ ($R^{2}=.304$). However, higher order regressions do not improve
the prediction of the variance of $\Phi^{u}$, as demonstrated by the Pareto
front in Fig. 3-top-right (see also Supplementary Note 11)—thus discarding the
hypothesis of a clear nonlinear relationship between co-administrations and
interactions, which could explain the growth of RI with age.

Supplementary Tables below display additional regression models.

Listing 1: $\Psi^{u}$ from $\nu^{u}$ linear model

⬇

===================================================

$\Psi^{u}$

$\nu^{u}$ 3.891*** (0.007)

Constant -8.818*** (0.037)

\---------------------------------------------------

Observations 132,722

R2 0.712

Adjusted R2 0.712

Residual Std. Error 8.650 (df = 132720)

F Statistic 328,478.000*** (df = 1; 132720)

===================================================

Note: *p<0.1; **p<0.05; ***p<0.01

Listing 2: $\Psi^{u}$ from $\nu^{u}$ quadratic model

⬇

===================================================

$\Psi^{u}$

$\nu^{u}$ -0.121*** (0.012)

$(\nu^{u})^{2}$ 0.273*** (0.001)

Constant -0.023 (0.036)

\---------------------------------------------------

Observations 132,722

R2 0.857

Adjusted R2 0.857

Residual Std. Error 6.088 (df = 132719)

F Statistic 399,075.300*** (df = 2; 132719)

===================================================

Note: *p<0.1; **p<0.05; ***p<0.01

Listing 3: $\Phi^{u}$ from $\nu^{u}$ linear model

⬇

==================================================

$\Phi^{u}$

$\nu^{u}$ 0.110*** (0.0005)

Constant -0.267*** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.304

Adjusted R2 0.304

Residual Std. Error 0.580 (df = 132720)

F Statistic 58,011.640*** (df = 1; 132720)

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

Listing 4: $\Phi^{u}$ from $\nu^{u}$ quadratic model

⬇

==================================================

$\Phi^{u}$

$\nu^{u}$ -0.009*** (0.001)

$(\nu^{u})^{2}$ 0.008*** (0.0001)

Constant -0.007** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.372

Adjusted R2 0.372

Residual Std. Error 0.551 (df = 132719)

F Statistic 39,357.930*** (df = 2; 132719)

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

Listing 5: $\Phi^{u}$ from $\Psi^{u}$ linear model

⬇

===================================================

$\Phi^{u}$

$\Psi^{u}$ 0.030*** (0.0001)

Constant -0.033*** (0.002)

\---------------------------------------------------

Observations 132,722

R2 0.487

Adjusted R2 0.487

Residual Std. Error 0.498 (df = 132720)

F Statistic 126,232.900*** (df = 1; 132720)

===================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.1.1 $RC^{y}$ models

In Figure 2 of the main manuscript two regressions were calculated to predict
the growth of $RC^{y}$ and $RI^{y}$ based on age range ($y=[y1-y2]$). Both
$RC^{y}$ and $RI^{y}$ can be best approximated by a cubic polynomial
regression (see Fig. 2 for $R^{2}$) The regression lines show different growth
processes for co-administration and interaction risks. $RC^{y}$ first
decreases in children age range $[\text{5-14}]$, followed by an almost flat
level between ages $[\text{15,44}]$ before a steeper growth is observed for
older age groups (see shaded area in Fig 2-left). In contrast, $RI^{y}$ is
initially quite flat and only starts to increase after the age of 15, after
which it has a much steeper growth curve than $RC^{[}y]$ (note the difference
in scale).

In addition, Supplementary Tables below contain other regression models that
were computed along with their respective ANOVA comparison, when appropriate.

A linear model is the simplest model one could fit to the increased risk of
co-administration.

Listing 6: $RC^{y}$ linear model

⬇

===============================================

$RC^{y}$

\-----------------------------------------------

$y$ 0.003*** (0.0004)

Constant 0.926*** (0.004)

\-----------------------------------------------

Observations 19

R2 0.798

Adjusted R2 0.787

Residual Std. Error 0.009 (df = 17)

F Statistic 67.336*** (df = 1; 17)

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

A quadratic model fits slightly better but the increased model complexity is
not significant.

Listing 7: $RC^{y}$ quadratic model

⬇

===============================================

$RC^{y}$

\-----------------------------------------------

$(y)^{2}$ 0.0001 (0.0001)

$y$ 0.001 (0.001)

Constant 0.931*** (0.005)

\-----------------------------------------------

Observations 19

R2 0.820

Adjusted R2 0.798

Residual Std. Error 0.009 (df = 16)

F Statistic 36.493*** (df = 2; 16)

\-----------------------------------------------

Model 1: $RC^{y}$ ~ $y$

Model 2: $RC^{y}$ ~ $(y)^{2}$ + $y$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 17 0.0013609

2 16 0.0012139 1 0.00014698 1.9374 0.183

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

A cubic model gives almost perfect fit while being significant for the more
complex model.

Listing 8: $RC^{y}$ cubic model

⬇

===============================================

$RC^{y}$

\-----------------------------------------------

$(y)^{3}$ -0.0001*** (0.00001)

$(y)^{2}$ 0.001*** (0.0003)

$y$ -0.008*** (0.002)

Constant 0.943*** (0.004)

\-----------------------------------------------

Observations 19

R2 0.936

Adjusted R2 0.923

Residual Std. Error 0.005 (df = 15)

F Statistic 72.789*** (df = 3; 15)

\-----------------------------------------------

Model 1: $RC^{y}$ ~ $y$

Model 2: $RC^{y}$ ~ $(y)^{2}$ + $y$

Model 3: $RC^{y}$ ~ $(y)^{3}$ + $(y)^{2}$ + $y$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 17 0.00136086

2 16 0.00121387 1 0.00014698 5.0807 0.0395787 *

3 15 0.00043394 1 0.00077993 26.9599 0.0001094 ***

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.1.2 $RI^{y}$ models

Similarly to how we modeled $RI^{y}$, with the risk of known DDI co-
administration ($RI^{y}$) we start with the simplest linear model possible.

Listing 9: $RI^{y}$ linear model

⬇

===============================================

$RI^{y}$

\-----------------------------------------------

$y$ 0.024*** (0.002)

Constant -0.032* (0.016)

\-----------------------------------------------

Observations 19

R2 0.932

Adjusted R2 0.928

Residual Std. Error 0.037 (df = 17)

F Statistic 233.631*** (df = 1; 17)

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

A quadratic model fits slightly better but the increased model complexity is
not significant.

Listing 10: $RI^{y}$ quadratic model

⬇

===============================================

$RI^{y}$

\-----------------------------------------------

$(y)^{2}$ -0.0004 (0.0003)

$y$ 0.030*** (0.006)

Constant -0.050** (0.023)

\-----------------------------------------------

Observations 19

R2 0.937

Adjusted R2 0.930

Residual Std. Error 0.037 (df = 16)

F Statistic 119.823*** (df = 2; 16)

\-----------------------------------------------

Model 1: $RC^{y}$ ~ $y$

Model 2: $RC^{y}$ ~ $(y)^{2}$ + $y$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 17 0.023355

2 16 0.021550 1 0.001805 1.3401 0.264

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

Finally, a cubic model gives us almost perfect fit while being significant for
the more complex model.

Listing 11: $RI^{y}$ Cubic model

⬇

===============================================

$RI^{y}$

\-----------------------------------------------

$(y)^{3}$ -0.0003*** (0.00001)

$(y)^{2}$ 0.007*** (0.0004)

$y$ -0.019*** (0.003)

Constant 0.013** (0.006)

\-----------------------------------------------

Observations 19

R2 0.997

Adjusted R2 0.997

Residual Std. Error 0.008 (df = 15)

F Statistic 1,927.479*** (df = 3; 15)

\-----------------------------------------------

Model 1: $RI^{y}$ ~ $y$

Model 2: $RI^{y}$ ~ $(y)^{2}$ + $y$

Model 3: $RI^{y}$ ~ $(y)^{3}$ + $(y)^{2}$ + $y$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 17 0.0233550

2 16 0.0215500 1 0.001805 30.391 5.96e-05 ***

3 15 0.0008909 1 0.020659 347.842 8.66e-12 ***

===============================================

Note: *p<0.1; **p<0.05; ***p<0.01

###  10.2 Multiple Regression (MR) models

This section displays several MR models that were generated in order to
analyze the possible prediction of drug interaction based on patient
demographics. Tables below contain the model results and also their respective
ANOVA comparison when appropriate.

####  10.2.1 Baseline (no transformation)

This is the baseline MR model with no transformation.

Listing 12: Baseline linear regression model

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.026*** (0.001)

$\Psi^{u}$ 0.035*** (0.0002)

Constant 0.041*** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.492

Adjusted R2 0.492

Residual Std. Error 0.496 (df = 132719)

F Statistic 64,377.810*** (df = 2; 132719)

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.2 Baseline (transformed)

These are other baseline MR model with transformed variables

Listing 13: Transformed baseline MR model

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.004*** (0.001)

$\Psi^{u}$ 0.040*** (0.0002)

$(\nu^{u})^{2}$ -0.003*** (0.0001)

Constant -0.006** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.497

Adjusted R2 0.497

Residual Std. Error 0.493 (df = 132718)

F Statistic 43,696.240*** (df = 3; 132718)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + $(\nu^{u})^{2}$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132718 32304 1 288.37 1184.7 < 2.2e-16 ***

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.033*** (0.001)

$\Psi^{u}$ 0.038*** (0.0002)

$(\Psi^{u})^{2}$ -0.00002*** (0.00000)

Constant 0.053*** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.494

Adjusted R2 0.494

Residual Std. Error 0.495 (df = 132718)

F Statistic 43,145.430*** (df = 3; 132718)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + $(\Psi^{u})^{2}$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132718 32508 1 84.745 345.99 < 2.2e-16 ***

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.008*** (0.001)

$\Psi^{u}$ 0.041*** (0.0003)

$(\nu^{u})^{2}$ -0.003*** (0.0001)

$(\Psi^{u})^{2}$ -0.00000*** (0.00000)

Constant 0.001 (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.497

Adjusted R2 0.497

Residual Std. Error 0.493 (df = 132717)

F Statistic 32,786.680*** (df = 4; 132717)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + $(\nu^{u})^{2}$ +
$(\Psi^{u})^{2}$

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132717 32297 2 295.59 607.33 < 2.2e-16 ***

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.3 Baseline + age + gender

This section shows the MR results when age and gender are included as
dependent variables in the baseline model.

Listing 14: Baseline MR model added variables age and gender.

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.027*** (0.001)

$\Psi^{u}$ 0.034*** (0.0002)

age 0.002*** (0.0001)

C(gender)Male -0.010*** (0.003)

Constant -0.021*** (0.004)

\--------------------------------------------------

Observations 132,722

R2 0.496

Adjusted R2 0.496

Residual Std. Error 0.494 (df = 132717)

F Statistic 32,639.900*** (df = 4; 132717)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + age + C(gender)

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132717 32369 2 223.56 458.33 < 2.2e-16 ***

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.4 Baseline (replacing $\Psi^{u}$ with $y$)

Interestingly, number of co-administrations ($\Psi^{u}$) and age ($y$) are
virtually exchangeable.

Listing 15: Baseline MR model exchanging variables $\Psi^{u}$ and $y$.

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\Psi^{u}$ 0.029*** (0.0001)

age 0.002*** (0.0001)

Constant -0.100*** (0.003)

\--------------------------------------------------

Observations 132,722

R2 0.491

Adjusted R2 0.491

Residual Std. Error 0.496 (df = 132719)

F Statistic 63,937.920*** (df = 2; 132719)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\Psi^{u}$ + age

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132719 32702 0 -110.03

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.5 Baseline + education level

This section shows the OMR results when education level is included as one of
the dependent variables in the model.

Note that this model fits a smaller dataset because the number of patients
that have given their education level is smaller than the full dataset.

Listing 16: Baseline MR model added education level variable.

⬇

================================================================

$\Phi^{u}$

\----------------------------------------------------------------

$\nu^{u}$ -0.015*** (0.001)

$\Psi^{u}$ 0.033*** (0.0002)

C(education)Cant read/write -0.027** (0.014)

C(education)Complete college -0.007 (0.018)

C(education)Complete elementary 0.037*** (0.013)

C(education)Complete high school 0.003 (0.013)

C(education)Doctoral -0.106 (0.132)

C(education)Espec./Residency 0.009 (0.045)

C(education)Incomplete college 0.004 (0.018)

C(education)Incomplete elementary 0.024** (0.011)

C(education)Incomplete high school -0.006 (0.014)

C(education)Masters -0.050 (0.119)

Constant 0.018 (0.011)

\----------------------------------------------------------------

Observations 61,060

R2 0.511

Adjusted R2 0.511

Residual Std. Error 0.602 (df = 61047)

F Statistic 5,312.884*** (df = 12; 61047)

\----------------------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + C(education)

Res.Df RSS Df Sum of Sq F Pr(>F)

1 61057 22127

2 61047 22107 10 19.845 5.4801 3.472e-08 ***

================================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.6 Baseline + marital status

This section shows the OMR results when marital status is included as one of
the dependent variables in the model.

Listing 17: Baseline MR model added marital status variable.

⬇

=====================================================

$\Phi^{u}$

\-----------------------------------------------------

$\nu^{u}$ -0.027*** (0.001)

$\Psi^{u}$ 0.035*** (0.0002)

C(marital)Divorced 0.105*** (0.025)

C(marital)Ignored -0.029*** (0.008)

C(marital)Married -0.005 (0.008)

C(marital)Not informed -0.072*** (0.008)

C(marital)Separated 0.080*** (0.011)

C(marital)Single -0.014* (0.008)

C(marital)Widower 0.019* (0.011)

Constant 0.077*** (0.008)

\-----------------------------------------------------

Observations 132,722

R2 0.494

Adjusted R2 0.494

Residual Std. Error 0.495 (df = 132712)

F Statistic 14,420.090*** (df = 9; 132712)

\-----------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + C(marital)

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132712 32464 7 128.13 74.829 < 2.2e-16 ***

=====================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.7 Baseline + average neighborhood income assigned to patients

Listing 18: Baseline MR model added average neighborhood income variable.

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.026*** (0.001)

$\Psi^{u}$ 0.035*** (0.0002)

avg_income 0.00003*** (0.00000)

Constant 0.016*** (0.005)

\--------------------------------------------------

Observations 132,722

R2 0.493

Adjusted R2 0.493

Residual Std. Error 0.495 (df = 132718)

F Statistic 42,944.890*** (df = 3; 132718)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + avg_income

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132718 32582 1 9.9727 40.622 1.853e-10 ***

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.8 Baseline + neighborhood safety variables assigned to patients

Listing 19: Baseline MR model added neighborhood safety variables.

⬇

==================================================

$\Phi^{u}$

\--------------------------------------------------

$\nu^{u}$ -0.026*** (0.001)

$\Psi^{u}$ 0.035*** (0.0002)

theft_pc -0.737*** (0.283)

robbery_p1000 -0.004 (0.003)

suicide_p1000 0.006 (0.009)

transitcrime_p1000 0.022*** (0.002)

traffic_p1000 0.008*** (0.002)

rape_p1000 -0.002 (0.004)

Constant 0.024*** (0.004)

\--------------------------------------------------

Observations 132,722

R2 0.493

Adjusted R2 0.493

Residual Std. Error 0.495 (df = 132713)

F Statistic 16,148.060*** (df = 8; 132713)

\--------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + theft_pc +

robbery_p1000 + suicide_p1000 +

transitcrime_p1000 + traffic_p1000 +

rape_p1000

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132713 32538 6 54.096 36.773 < 2.2e-16 ***

==================================================

Note: *p<0.1; **p<0.05; ***p<0.01

####  10.2.9 Baseline + neighborhood

Listing 20: Baseline MR model added neighborhood as categorical variables.

⬇

======================================================

$\Phi^{u}$

\------------------------------------------------------

$\nu^{u}$ -0.026*** (0.001)

$\Psi^{u}$ 0.035*** (0.0002)

C(hood)BADENFURT -0.021 (0.014)

C(hood)BOA VISTA 0.009 (0.024)

C(hood)BOM RETIRO 0.150*** (0.036)

C(hood)CENTRO 0.012 (0.013)

C(hood)DA GLORIA -0.009 (0.013)

C(hood)DO SALTO -0.005 (0.016)

C(hood)ESCOLA AGRICOLA -0.041*** (0.012)

C(hood)FIDELIS 0.005 (0.013)

C(hood)FORTALEZA -0.030*** (0.011)

C(hood)FORTALEZA ALTA -0.029** (0.014)

C(hood)GARCIA -0.009 (0.011)

C(hood)ITOUPAVA CENTRAL 0.005 (0.011)

C(hood)ITOUPAVA NORTE -0.023** (0.011)

C(hood)ITOUPAVA SECA -0.037** (0.019)

C(hood)ITOUPAVAZINHA 0.012 (0.012)

C(hood)JARDIM BLUMENAU -0.053 (0.047)

C(hood)NOVA ESPERANCA -0.055*** (0.014)

C(hood)OTHER -0.067*** (0.010)

C(hood)PASSO MANSO 0.025* (0.015)

C(hood)PONTA AGUDA -0.009 (0.013)

C(hood)PROGRESSO -0.006 (0.011)

C(hood)RIBEIRAO FRESCO 0.010 (0.021)

C(hood)SALTO DO NORTE 0.019 (0.015)

C(hood)SALTO WEISSBACH 0.018 (0.018)

C(hood)TESTO SALTO -0.009 (0.015)

C(hood)TRIBESS -0.041*** (0.012)

C(hood)VALPARAISO -0.015 (0.014)

C(hood)VELHA -0.015 (0.011)

C(hood)VELHA CENTRAL -0.009 (0.013)

C(hood)VELHA GRANDE -0.031* (0.017)

C(hood)VICTOR KONDER 0.026 (0.024)

C(hood)VILA FORMOSA -0.225*** (0.053)

C(hood)VILA ITOUPAVA 0.015 (0.017)

C(hood)VILA NOVA -0.041*** (0.015)

C(hood)VORSTADT -0.028** (0.014)

Constant 0.067*** (0.010)

\------------------------------------------------------

Observations 132,722

R2 0.494

Adjusted R2 0.494

Residual Std. Error 0.495 (df = 132684)

F Statistic 3,502.150*** (df = 37; 132684)

\------------------------------------------------------

Model 1: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$

Model 2: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + C(hood)

Res.Df RSS Df Sum of Sq F Pr(>F)

1 132719 32592

2 132684 32486 35 106.61 12.441 < 2.2e-16 ***

======================================================

Note: *p<0.1; **p<0.05; ***p<0.01

###  10.3 Linear Mixed-Effect (LMM) models

To be sure there were not nested effects between variables gender and age, we
also ran a linear mixed-model (LMM) where variable gender is nested within
age. This model accounts for specific differences within patient age and
across different genders. Intuitively, if there are large variations in the
number of interaction that are explained by the nestedness of gender and age,
these groups would help explain a large portion of the variance in the data.
The results indicate that is not the case. In fact, the variance attributed to
gender (within age) group is $0.00016$ while the age group is a little higher,
$0.00217$.

Listing 21: Linear Mixed Model with age nested within gender.

⬇

Linear mixed model fit by maximum likelihood [’lmerMod’]

ForFormula: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + (1 | age/gender)

Data: data

AIC BIC logLik deviance df.resid

189314.1 189372.9 -94651.1 189302.1 132716

Scaled residuals:

Min 1Q Median 3Q Max

-13.1102 -0.2048 -0.0734 0.0394 19.2402

Random effects:

Groups Name Variance Std.Dev.

gender:age (Intercept) 0.0001645 0.01282

age (Intercept) 0.0021678 0.04656

Residual 0.2432636 0.49322

Number of obs: 132722, groups: gender:age, 213; age, 109

Fixed effects:

Estimate Std. Error t value

(Intercept) 0.0483215 0.0055929 8.64

$\nu^{u}$ -0.0262493 0.0007287 -36.02

$\Psi^{u}$ 0.0343219 0.0001590 215.87

Correlation of Fixed Effects:

(Intr) $\nu^{u}$

$\nu^{u}$ -0.367

$\Psi^{u}$ 0.224 -0.831

To be sure that neighborhood did not differ in their DDI observations, we also
ran a linear mixed-model (LMM) with neighborhood as a random effect.
Intuitively, if there are variations in the number of interactions between
neighborhoods that cannot be explained by the independent variables alone—due
to, say, differences in policies or practices—we should see the random effect
variable explaining a great deal of the variance in the model. Our results
indicate that is not the case. In fact, the variance attributed to the
neighborhood random effect is $0.00059$ and therefore too small. This shows
that at least in predicting the number of DDI, there is neighborhood
homogeneity in how they are being prescribed and thus dispensed.

Listing 22: Linear Mixed Model with neighborhood as random effect.

⬇

Linear mixed model fit by maximum likelihood [’lmerMod’]

Formula: $\Phi^{u}$ ~ $\nu^{u}$ + $\Psi^{u}$ + (1 | hood)

Data: data

AIC BIC logLik deviance df.resid

189980.7 190029.6 -94985.3 189970.7 132717

Scaled residuals:

Min 1Q Median 3Q Max

-13.1462 -0.1846 -0.0678 0.0180 19.1046

Random effects:

Groups Name Variance Std.Dev.

hood (Intercept) 0.0005935 0.02436

Residual 0.2448642 0.49484

Number of obs: 132722, groups: hood, 36

Fixed effects:

Estimate Std. Error t value

(Intercept) 0.0544948 0.0050850 10.72

$\nu^{u}$ -0.0264618 0.0007270 -36.40

$\Psi^{u}$ 0.0348255 0.0001572 221.58

Correlation of Fixed Effects:

(Intr) $\nu^{u}$

$\nu^{u}$ -0.411

$\Psi^{u}$ 0.268 -0.841

## Supplementary Note 11 Patient classification

We applied machine learning classifiers in order to predict if a specific
patient had at least one DDI in the whole 18 month period. A binary
classification task. Support Vector Machine (SVM)[90] and Logistic Regression
(LR)[91] are considered both standard and reliable machine learning algorithm
for binary classification problems. We built models for each classifier
considering different sets of features, including demographic (i.e., age &
gender) and drugs the patient was prescribed in the period. For baseline
comparison we also ran against three null model classifiers. One with a “coin-
toss” probability of classification (Uniform), another with a bias with
respect to class probability (Biased), and a custom made (AgeGender) which
finds the best age cutoff for each gender from which it consider all patients
older than the cutoff as having a DDI. Regression and classification models
were computed using R and Python [92].

We present results as measures derived from a confusion matrix, also called a
contingency table[93]. The confusion matrix contains four categories: true
positives ($TP$), patients correctly labeled as having a DDI; false positives
($FP$), patients incorrectly classified as having a DDI; true negative ($TN$),
patients correctly labeled as not having a DDI; and finally false negatives
($FN$), patients with DDI but mislabeled as not having them. A contingency
table example can be seen in Table 36.

| DDI | no DDI
---|---|---
predicted DDI | $TP$ | $FP$
predicted no DDI | $FN$ | $TN$
Supplementary Table 36:  Confusion Matrix.

From the confusion matrix we compute Precision and Recall as

$\text{Precision}=\frac{TP}{TP+FP}\quad,\quad\text{Recall}=\frac{TP}{TP+FN}\quad,$
(23)

where Precision is the fraction of patients with DDI correctly predicted,
among all predicted patients with DDI; while Recall is the fraction of
patients with DDI correctly predicted, among all patients with DDI. We also
compute True Positive Rate (TPR) and False Positive Rate (FPR) measures as

$TPR=\frac{TP}{TP+FN}\quad,\quad FPR=\frac{FP}{FP+TN}\quad,$ (24)

where TPR measures the fraction of patients with DDI that are correctly
classified and FPR measures the fraction of patients with no DDI incorrectly
classified as having DDI. These four measures enables the plotting of the
Receiver Operator Characteristic (ROC) and the Precision and Recall (P/R)
space. In ROC space we plot FPR against TPR while in P/R space we plot
Precision against Recall (Figure 15 displays the results). These plots are
typically generated to evaluate the performance of machine learning
algorithms, and to enable system users to inspect the trained algorithm’s
precision at a specific recall level, for example. From both ROC and P/R
curves we computes their respective interpolated area under the curve
(AUC)[93].

From Precision and Recall we also compute the $F_{1}\text{-score}$ (also
called $F\text{-score}$ or $F\text{-measure}$) as

$F_{1}=2\times\frac{\text{Precision}\times\text{Recall}}{\text{Precision}+\text{Recall}}\quad.$
(25)

We also compute Matthew’s Correlation Coefficient (MCC)[94], which is regarded
as an ideal measure of the quality of binary classification in unbalanced
scenarios[95], as

$MCC=\frac{TP\times TN-FP\times
FN}{\sqrt{(TP+FP)+(TP+FN)+(TN+FP)+(TN+FN)}}\quad.$ (26)

Below, we display results as measures of Precision, Recall,
$F_{1}\text{-score}$, MCC, AUC ROC curve and AUC P/R curve.

We also display the full table of feature weights for both classifiers. Since
these are both linear classifiers, one can interpret positive (negative)
values as contributing to the positive (negative) class—having a DDI. The
higher (smaller) the weight, the bigger (smaller) the contribution. All
results are based on 4-fold cross validation.

† Gender is used as a categorical variable and expanded into the binary
features ($g=M$ and $g=F$).

‡ Education level is used as a categorical variable expanded into individuals
binary features (“Cant read/write”, “Can read/write a note”, “Incomplete
elementary”, “Complete elementary”, “Incomplete high school”, “Complete high
school”, “Incomplete college”, “Complete college”, “Espec./Residency”,
“Masters”, and “Doctoral”).

###  11.1 Simple model

Patients:

132,722

DDI (positive):

15,527 (11.70%)

no DDI (negative):

117,195 (88.30%)

Features:

127

Demographic:

gender† ($g$), age ($y$), number of drugs ($\nu^{u}$), number of co-
administrations ($\Psi^{u}$).

Neighborhood:

average income, number of thefts per capita, number of robberies per capita,
number of suicides per capita, number of transit crimes per capita, number of
traffic accidents per capita, number of rapes per capita.

Drug:

all drugs $D$.

Fold | Precision | Recall | $F_{1}$ | MCC | AUC ROC | AUC P/R
---|---|---|---|---|---|---
1 | 0.8196 | 0.6309 | 0.7130 | 0.6877 | 0.9676 | 0.8269
2 | 0.8241 | 0.6494 | 0.7264 | 0.7011 | 0.9702 | 0.8365
3 | 0.8127 | 0.6504 | 0.7226 | 0.6957 | 0.9697 | 0.8315
4 | 0.8187 | 0.6436 | 0.7207 | 0.6949 | 0.9690 | 0.8311
Mean | 0.8188 | 0.6436 | 0.7207 | 0.6948 | 0.9691 | 0.8315
Supplementary Table 37:  Individual fold and mean performance of Support Vector Machine (SVM) classifier on stratified 4-fold cross-validation, using demographic and drug features. Measures of performance shown are: Precision, Recall, F1 (balanced Precision and Recall), Matthew’s Correlation Coefficient, the Area Under the Receiver Operating Characteristic Curve, and the Area Under the Precision and Recall Curve.  Fold | Precision | Recall | $F_{1}$ | MCC | AUC ROC | AUC P/R
---|---|---|---|---|---|---
1 | 0.8085 | 0.6535 | 0.7228 | 0.6953 | 0.9675 | 0.8249
2 | 0.8096 | 0.6669 | 0.7314 | 0.7037 | 0.9700 | 0.8337
3 | 0.7991 | 0.6662 | 0.7266 | 0.6977 | 0.9697 | 0.8299
4 | 0.8092 | 0.6612 | 0.7277 | 0.7002 | 0.9691 | 0.8304
Mean | 0.8066 | 0.6619 | 0.7271 | 0.6992 | 0.9691 | 0.8297
Supplementary Table 38:  Individual fold and mean performance of Logistic Regression (LR) classifier on stratified 4-fold cross-validation, using demographic and drug features. Measures of performance shown are: Precision, Recall, F1 (balanced Precision and Recall), Matthew’s Correlation Coefficient, the Area Under the Receiver Operating Characteristic Curve, and the Area Under the Precision and Recall Curve.  Classifier | Precision | Recall | $F_{1}$ | MCC | AUC ROC | AUC P/R
---|---|---|---|---|---|---
Uniform | 0.1181 | 0.5075 | 0.1916 | 0.0035 | 0.5 | 0.5585
Biased | 0.1147 | 0.1153 | 0.1150 | -0.0026 | 0.4987 | 0.1668
GenderAge | 0.2044 | 0.8834 | 0.3320 | 0.2751 | 0.7139 | 0.5507
Supplementary Table 39:  Mean performance of Uniform (coin-toss), Biased
(biased coin-toss on class distribution) and GenderAge (hard cutoff for gender
and gender) classifiers on stratified 4-fold cross-validation, using
demographic and drug features. Measures of performance shown are: Precision,
Recall, F1 (balanced Precision and Recall), Matthew’s Correlation Coefficient,
the Area Under the Receiver Operating Characteristic Curve, and the Area Under
the Precision and Recall Curve.

###  11.2 Complete model

Patients:

132,722

DDI (positive):

15,527 (11.70%)

no DDI (negative):

117,195 (88.30%)

Features:

154

Demographic:

gender† ($g$), age ($y$), number of drugs ($\nu^{u}$), number of co-
administrations ($\Psi^{u}$), education levels‡.

Neighborhood:

average income, number of thefts per capita, number of robberies per capita,
number of suicides per capita, number of transit crimes per capita, number of
traffic accidents per capita, number of rapes per capita.

Drug:

all drugs $D$.

Classifier | Precision | Recall | $F_{1}$ | MCC | AUC ROC | AUC P/R
---|---|---|---|---|---|---
SVM | 0.8186 | 0.6442 | 0.7210 | 0.6951 | 0.9690 | 0.8312
LR | 0.8070 | 0.6619 | 0.7273 | 0.6994 | 0.9690 | 0.8295