Other occupation | -4.07 (-4.58, -3.55) | Ref | 0.87 (0.85, 0.89) | Ref | 192529
Healthcare | -5.02 (-6.03, -4.01) |  | 0.82 (0.79, 0.85) | ** | 56546
Not working / Unknown | -4.57 (-5.01, -4.13) |  | 0.85 (0.84, 0.87) |  | 242533
Not female
Other occupation | -2.95 (-3.53, -2.38) | Ref | 0.87 (0.85, 0.90) | Ref | 120789
Healthcare | -4.64 (-6.57, -2.70) |  | 0.78 (0.71, 0.86) | * | 12294
Not working / Unknown | -3.87 (-4.46, -3.28) | * | 0.85 (0.82, 0.87) |  | 116646

  * •

T-tests reflect test of difference in means between the category specified in
row and the reference category (Ref) within each Subset and Variable

  * •

*** indicates p ¡ 0.001; ** indicates p ¡ 0.01; * indicates p ¡ 0.05

  * •

Subgroups chosen using data from March 1-14th using specified outcome

Table 16: Isolation: data-driven subgroup heterogeneity (XGBoost estimates)

| Risk-difference | Risk-ratio |
---|---|---|---
Strata | Estimate (95% CI) | T-test | Estimate (95% CI) | T-test | N
18-24 years: Not White
Not female | -5.63 (-10.41, -0.85) | Ref | 0.83 ( 0.68, 0.97) | Ref | 1941
Female | -9.81 (-13.67, -5.95) |  | 0.74 ( 0.65, 0.84) |  | 3906
Unknown | 16.17 (-8.96, 41.31) |  | 1.39 ( 0.74, 2.05) |  | 172
18-24 years: White
Not female | -13.27 (-15.98, -10.56) | Ref | 0.65 ( 0.59, 0.72) | Ref | 5842
Female | -10.51 (-12.54, -8.49) |  | 0.74 ( 0.69, 0.78) | * | 15322
Unknown | -28.19 (-39.20, -17.19) | ** | 0.47 ( 0.29, 0.65) |  | 351
25+ years: Not White
Not female | -1.52 (-2.37, -0.66) | Ref | 0.90 ( 0.85, 0.96) | Ref | 43686
Female | -3.22 (-3.96, -2.48) | ** | 0.83 ( 0.79, 0.87) | * | 70434
Unknown | 1.90 (-2.90, 6.71) |  | 1.08 ( 0.88, 1.28) |  | 2537
25+ years: White
Not female | -2.86 (-3.27, -2.46) | Ref | 0.83 ( 0.81, 0.85) | Ref | 193701
Female | -3.02 (-3.33, -2.70) |  | 0.86 ( 0.85, 0.87) | * | 394616
Unknown | -6.03 (-9.36, -2.70) |  | 0.77 ( 0.65, 0.89) |  | 3839

  * •

T-tests reflect test of difference in means between the category specified in
row and the reference category (Ref) within each Subset and Variable

  * •

*** indicates p ¡ 0.001; ** indicates p ¡ 0.01; * indicates p ¡ 0.05

  * •

Subgroups chosen using data from March 1-14th using specified outcome

###  12.3 Interventional effects

Figure 13 displays the heterogeneity results from our XGBoost estimates,
analogous to Figure 8 in Section 5. The subsequent tables present results
pertaining to our mediation analysis. Table 17 contains all point estimates on
average across our analytic sample using our GLM estimates, while Table 18
presents our XGBoost estimates.

Figure 13: Mediation heterogeneity, complete-case estimates (XGBoost
estimates) Table 17: Mediation analysis: GLM estimates (95% CI)

Effect | Ref = 0 | Proportion (Ref = 0) | Ref = 1 | Proportion (Ref = 1)
---|---|---|---|---
IDE | -1.93 (-2.16, -1.70) | 51.76 (48.33, 55.18) | -2.06 (-2.31, -1.82) | 55.37 (51.54, 59.20)
IIE | -1.80 (-1.91, -1.68) | 48.24 (44.82, 51.67) | -1.66 (-1.72, -1.61) | 44.63 (40.80, 48.46)
IIE - Isolated | -1.45 (-1.56, -1.35) | 39.07 (36.07, 42.08) | -1.39 (-1.50, -1.28) | 37.42 (34.18, 40.66)
IIE - Health | -0.31 (-0.34, -0.28) | 8.28 (7.29, 9.28) | -0.24 (-0.29, -0.20) | 6.57 (5.22, 7.92)
IIE - Covariant | -0.03 (-0.06, -0.01) | 0.89 (0.25, 1.53) | -0.02 (-0.15, 0.10) | 0.65 (-0.79, 2.08)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 18: Mediation analysis: XGBoost estimates (95% CI)

Effect | Ref = 0 | Proportion (Ref = 0) | Ref = 1 | Proportion (Ref = 1)
---|---|---|---|---
IDE | -1.85 (-2.04, -1.65) | 49.43 (46.37, 52.50) | -2.10 (-2.32, -1.88) | 56.16 (52.63, 59.69)
IIE | -1.89 (-1.99, -1.78) | 50.57 (47.50, 53.63) | -1.64 (-1.69, -1.59) | 43.84 (40.31, 47.37)
IIE - Isolated | -1.63 (-1.73, -1.54) | 43.71 (41.00, 46.42) | -1.64 (-1.74, -1.54) | 43.97 (40.80, 47.13)
IIE - Health | -0.33 (-0.37, -0.30) | 8.93 (7.92, 9.94) | -0.28 (-0.32, -0.24) | 7.47 (6.24, 8.70)
IIE - Covariant | 0.08 (0.05, 0.10) | -2.07 (-2.78, -1.37) | 0.28 (0.17, 0.40) | -7.60 (-9.06, -6.13)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

The next sets of tables below display results contain results our subgroup
effect estimates with respect to our pre-specified subgroups. The first two
tables are on the risk-differences scale and set the indirect effect reference
category at 0 and 1, respectively. The second two tables express the
quantities as a proportion of the total effect. The final four tables repeat
these analyses using our XGBoost estimates.

Table 19: Heterogeneous mediated effects (Ref = 0): GLM estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | -2.39 (-3.19, -1.60) | -3.50 (-3.91, -3.09) | -3.01 (-3.39, -2.62) | -0.47 (-0.57, -0.37) | -0.02 (-0.10, 0.05)
35-64 years | -1.87 (-2.20, -1.53) | -1.88 (-2.05, -1.71) | -1.51 (-1.67, -1.36) | -0.35 (-0.40, -0.30) | -0.02 (-0.05, 0.01)
65 or more years | -1.71 (-2.00, -1.43) | -0.82 (-0.95, -0.68) | -0.60 (-0.72, -0.48) | -0.16 (-0.21, -0.11) | -0.06 (-0.10, -0.02)
No response | -3.61 (-4.88, -2.35) | -2.13 (-2.85, -1.42) | -1.67 (-2.33, -1.00) | -0.34 (-0.60, -0.08) | -0.13 (-0.30, 0.05)
Ethnicity
Hispanic | -1.01 (-1.85, -0.17) | -1.80 (-2.21, -1.39) | -1.43 (-1.82, -1.04) | -0.33 (-0.43, -0.22) | -0.04 (-0.13, 0.04)
No response | -3.90 (-5.04, -2.77) | -2.03 (-2.76, -1.31) | -1.60 (-2.28, -0.92) | -0.24 (-0.45, -0.02) | -0.20 (-0.38, -0.01)
Not Hispanic | -1.99 (-2.23, -1.75) | -1.79 (-1.91, -1.67) | -1.45 (-1.57, -1.34) | -0.31 (-0.34, -0.27) | -0.03 (-0.05, 0.00)
Gender
Female | -2.13 (-2.42, -1.83) | -1.87 (-2.01, -1.72) | -1.48 (-1.62, -1.35) | -0.35 (-0.39, -0.30) | -0.04 (-0.07, -0.01)
No response | -2.94 (-4.72, -1.15) | -1.57 (-2.53, -0.61) | -1.06 (-1.97, -0.15) | -0.59 (-0.91, -0.28) | 0.09 (-0.15, 0.33)
Not female | -1.47 (-1.83, -1.11) | -1.68 (-1.87, -1.48) | -1.43 (-1.61, -1.25) | -0.22 (-0.26, -0.17) | -0.03 (-0.07, 0.01)
High-risk conditions
Missing | -0.14 (-3.42, 3.13) | -1.99 (-3.37, -0.60) | -1.64 (-2.95, -0.34) | -0.05 (-0.42, 0.32) | -0.29 (-0.66, 0.07)
None | -1.67 (-2.05, -1.28) | -1.97 (-2.17, -1.77) | -1.70 (-1.89, -1.52) | -0.27 (-0.32, -0.22) | 0.00 (-0.04, 0.04)
One | -1.82 (-2.23, -1.41) | -1.71 (-1.92, -1.50) | -1.38 (-1.57, -1.19) | -0.29 (-0.35, -0.23) | -0.04 (-0.08, 0.01)
Two or more | -2.31 (-2.71, -1.92) | -1.69 (-1.89, -1.50) | -1.27 (-1.45, -1.09) | -0.37 (-0.43, -0.31) | -0.06 (-0.10, -0.02)
Race
Asian or Pacific Islander | -0.67 (-1.66, 0.31) | -1.58 (-2.07, -1.10) | -1.18 (-1.63, -0.73) | -0.40 (-0.54, -0.27) | 0.00 (-0.11, 0.12)
Black | -0.27 (-1.75, 1.21) | -1.34 (-2.16, -0.52) | -1.13 (-1.93, -0.33) | -0.11 (-0.27, 0.05) | -0.09 (-0.24, 0.05)
No response | -2.03 (-3.35, -0.71) | -2.21 (-2.94, -1.48) | -1.80 (-2.47, -1.14) | -0.36 (-0.56, -0.16) | -0.05 (-0.21, 0.12)
Other | -1.73 (-2.86, -0.61) | -1.69 (-2.23, -1.16) | -1.40 (-1.89, -0.90) | -0.26 (-0.42, -0.10) | -0.03 (-0.16, 0.09)
White | -2.09 (-2.33, -1.84) | -1.82 (-1.95, -1.70) | -1.48 (-1.59, -1.36) | -0.31 (-0.35, -0.28) | -0.03 (-0.06, -0.01)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 20: Heterogeneous mediated effects (Ref = 1): GLM estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | -2.76 (-3.64, -1.88) | -3.14 (-3.42, -2.85) | -2.90 (-3.34, -2.47) | -0.33 (-0.52, -0.13) | 0.09 (-0.42, 0.61)
35-64 years | -1.98 (-2.33, -1.63) | -1.76 (-1.82, -1.71) | -1.46 (-1.62, -1.30) | -0.28 (-0.35, -0.21) | -0.03 (-0.20, 0.15)
65 or more years | -1.77 (-2.07, -1.46) | -0.76 (-0.80, -0.73) | -0.55 (-0.66, -0.44) | -0.14 (-0.18, -0.11) | -0.07 (-0.20, 0.06)
No response | -3.75 (-5.19, -2.31) | -2.00 (-2.26, -1.74) | -1.46 (-2.09, -0.84) | -0.40 (-0.72, -0.08) | -0.14 (-0.89, 0.62)
Ethnicity
Hispanic | -1.17 (-2.06, -0.28) | -1.64 (-1.80, -1.48) | -1.50 (-1.91, -1.09) | -0.15 (-0.35, 0.05) | 0.01 (-0.45, 0.47)
No response | -3.91 (-5.19, -2.63) | -2.03 (-2.28, -1.78) | -1.48 (-2.13, -0.83) | -0.28 (-0.54, -0.02) | -0.27 (-1.05, 0.51)
Not Hispanic | -2.13 (-2.39, -1.87) | -1.66 (-1.71, -1.60) | -1.38 (-1.49, -1.26) | -0.26 (-0.30, -0.21) | -0.02 (-0.16, 0.11)
Gender
Female | -2.18 (-2.49, -1.87) | -1.81 (-1.86, -1.77) | -1.45 (-1.59, -1.31) | -0.33 (-0.38, -0.27) | -0.03 (-0.19, 0.12)
No response | -3.22 (-4.98, -1.46) | -1.28 (-1.76, -0.79) | -1.17 (-2.14, -0.20) | 0.22 (-0.48, 0.93) | -0.34 (-1.42, 0.75)
Not female | -1.75 (-2.16, -1.34) | -1.39 (-1.52, -1.26) | -1.29 (-1.49, -1.10) | -0.12 (-0.20, -0.04) | 0.02 (-0.22, 0.25)
High-risk conditions
Missing | -0.54 (-4.14, 3.07) | -1.59 (-2.24, -0.94) | -1.71 (-3.04, -0.38) | -0.18 (-0.85, 0.49) | 0.30 (-1.10, 1.69)
None | -1.70 (-2.13, -1.26) | -1.94 (-2.07, -1.81) | -1.69 (-1.89, -1.50) | -0.22 (-0.31, -0.12) | -0.03 (-0.27, 0.21)
One | -1.97 (-2.41, -1.53) | -1.56 (-1.62, -1.49) | -1.26 (-1.46, -1.07) | -0.27 (-0.34, -0.20) | -0.03 (-0.24, 0.19)
Two or more | -2.53 (-2.94, -2.12) | -1.48 (-1.54, -1.42) | -1.20 (-1.38, -1.01) | -0.25 (-0.33, -0.18) | -0.03 (-0.23, 0.18)
Race
Asian or Pacific Islander | -1.13 (-2.42, 0.17) | -1.13 (-1.77, -0.49) | -0.98 (-1.55, -0.42) | -0.43 (-0.75, -0.10) | 0.28 (-0.56, 1.13)
Black | -0.58 (-2.00, 0.83) | -1.03 (-1.31, -0.74) | -1.06 (-1.78, -0.34) | 0.19 (-0.29, 0.68) | -0.16 (-0.97, 0.65)
No response | -2.02 (-3.49, -0.55) | -2.22 (-2.54, -1.90) | -1.72 (-2.40, -1.05) | -0.34 (-0.68, -0.01) | -0.16 (-0.95, 0.64)
Other | -1.74 (-2.89, -0.60) | -1.68 (-1.90, -1.47) | -1.54 (-2.08, -1.00) | -0.07 (-0.29, 0.15) | -0.07 (-0.66, 0.51)
White | -2.21 (-2.47, -1.95) | -1.70 (-1.74, -1.66) | -1.41 (-1.52, -1.29) | -0.26 (-0.30, -0.21) | -0.03 (-0.16, 0.09)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 21: Heterogeneous proportion mediated (Ref = 0): GLM estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | 40.61 (32.05, 49.18) | 59.39 (50.82, 67.95) | 51.04 (43.43, 58.66) | 7.96 (5.98, 9.94) | 0.38 (-0.85, 1.62)
35-64 years | 49.78 (44.71, 54.85) | 50.22 (45.15, 55.29) | 40.40 (35.96, 44.85) | 9.37 (7.92, 10.82) | 0.45 (-0.38, 1.27)
65 or more years | 67.74 (62.59, 72.89) | 32.26 (27.11, 37.41) | 23.62 (19.16, 28.09) | 6.28 (4.20, 8.36) | 2.36 (0.68, 4.04)
No response | 62.86 (51.18, 74.54) | 37.14 (25.46, 48.82) | 28.98 (18.37, 39.58) | 5.95 (1.22, 10.68) | 2.22 (-0.89, 5.33)
Ethnicity
Hispanic | 35.89 (15.95, 55.84) | 64.11 (44.16, 84.05) | 50.96 (33.90, 68.02) | 11.64 (6.85, 16.43) | 1.51 (-1.60, 4.61)
No response | 65.74 (55.51, 75.97) | 34.26 (24.03, 44.49) | 26.96 (17.38, 36.54) | 4.00 (0.29, 7.71) | 3.30 (0.24, 6.36)
Not Hispanic | 52.70 (49.21, 56.19) | 47.30 (43.81, 50.79) | 38.44 (35.37, 41.50) | 8.14 (7.10, 9.18) | 0.72 (0.07, 1.37)
Gender
Female | 53.26 (49.24, 57.28) | 46.74 (42.72, 50.76) | 37.10 (33.61, 40.58) | 8.65 (7.40, 9.90) | 0.99 (0.28, 1.70)
No response | 65.18 (43.70, 86.66) | 34.82 (13.34, 56.30) | 23.58 (3.56, 43.60) | 13.19 (5.23, 21.14) | -1.94 (-7.40, 3.51)
Not female | 46.67 (39.86, 53.49) | 53.33 (46.51, 60.14) | 45.55 (39.41, 51.69) | 6.88 (5.30, 8.45) | 0.90 (-0.46, 2.27)
High-risk conditions
Missing | 6.65 (-136.05, 149.35) | 93.35 (-49.35, 236.05) | 77.21 (-40.18, 194.60) | 2.32 (-14.68, 19.31) | 13.82 (-17.02, 44.66)
None | 45.85 (39.57, 52.12) | 54.15 (47.88, 60.43) | 46.85 (41.18, 52.51) | 7.36 (5.79, 8.92) | -0.05 (-1.09, 0.99)
One | 51.57 (45.03, 58.11) | 48.43 (41.89, 54.97) | 39.08 (33.38, 44.77) | 8.28 (6.44, 10.13) | 1.07 (-0.25, 2.39)
Two or more | 57.73 (52.55, 62.90) | 42.27 (37.10, 47.45) | 31.67 (27.16, 36.19) | 9.18 (7.44, 10.93) | 1.41 (0.41, 2.42)
Race
Asian or Pacific Islander | 29.80 (-1.52, 61.12) | 70.20 (38.88, 101.52) | 52.47 (27.85, 77.10) | 17.89 (8.14, 27.65) | -0.17 (-5.10, 4.76)
Black | 16.96 (-61.45, 95.37) | 83.04 (4.63, 161.45) | 70.13 (-0.32, 140.58) | 7.06 (-4.04, 18.15) | 5.85 (-4.39, 16.10)
No response | 47.85 (29.14, 66.57) | 52.15 (33.43, 70.86) | 42.57 (26.50, 58.64) | 8.46 (3.06, 13.85) | 1.12 (-2.72, 4.97)
Other | 50.59 (32.15, 69.02) | 49.41 (30.98, 67.85) | 40.83 (24.87, 56.79) | 7.58 (1.96, 13.21) | 1.00 (-2.56, 4.55)
White | 53.40 (50.00, 56.79) | 46.60 (43.21, 50.00) | 37.81 (34.81, 40.82) | 7.94 (6.95, 8.93) | 0.85 (0.22, 1.48)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 22: Heterogeneous proportion mediated (Ref = 1): GLM estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | 46.79 (36.85, 56.73) | 53.21 (43.27, 63.15) | 49.26 (40.85, 57.68) | 5.54 (2.16, 8.92) | -1.59 (-6.48, 3.30)
35-64 years | 52.90 (47.44, 58.36) | 47.10 (41.64, 52.56) | 38.95 (34.25, 43.65) | 7.41 (5.45, 9.37) | 0.74 (-0.71, 2.19)
65 or more years | 69.82 (64.41, 75.23) | 30.18 (24.77, 35.59) | 21.83 (17.32, 26.33) | 5.62 (4.07, 7.18) | 2.73 (1.21, 4.25)
No response | 65.20 (51.27, 79.14) | 34.80 (20.86, 48.73) | 25.49 (14.56, 36.41) | 6.96 (1.00, 12.92) | 2.35 (-2.23, 6.93)
Ethnicity
Hispanic | 41.69 (20.98, 62.40) | 58.31 (37.60, 79.02) | 53.39 (34.84, 71.94) | 5.36 (-2.07, 12.80) | -0.44 (-6.17, 5.28)
No response | 65.80 (53.38, 78.23) | 34.20 (21.77, 46.62) | 24.96 (14.95, 34.98) | 4.68 (0.03, 9.32) | 4.56 (0.47, 8.65)
Not Hispanic | 56.25 (52.32, 60.18) | 43.75 (39.82, 47.68) | 36.39 (33.09, 39.70) | 6.77 (5.42, 8.11) | 0.59 (-0.94, 2.12)
Gender
Female | 54.60 (50.23, 58.98) | 45.40 (41.02, 49.77) | 36.37 (32.66, 40.08) | 8.15 (6.61, 9.69) | 0.88 (-0.27, 2.02)
No response | 71.59 (49.07, 94.10) | 28.41 (5.90, 50.93) | 25.93 (4.18, 47.68) | -4.96 (-21.10, 11.18) | 7.44 (-3.42, 18.31)
Not female | 55.67 (47.52, 63.83) | 44.33 (36.17, 52.48) | 41.17 (34.42, 47.92) | 3.75 (1.10, 6.39) | -0.59 (-4.74, 3.56)
High-risk conditions
Missing | 25.21 (-103.37, 153.79) | 74.79 (-53.79, 203.37) | 80.25 (-47.06, 207.56) | 8.41 (-32.29, 49.12) | -13.88 (-57.29, 29.53)
None | 46.66 (38.93, 54.39) | 53.34 (45.61, 61.07) | 46.60 (40.30, 52.91) | 5.92 (3.29, 8.54) | 0.82 (-2.74, 4.38)
One | 55.85 (48.83, 62.87) | 44.15 (37.13, 51.17) | 35.77 (29.77, 41.77) | 7.64 (5.32, 9.97) | 0.74 (-1.12, 2.59)
Two or more | 63.14 (57.77, 68.50) | 36.86 (31.50, 42.23) | 29.89 (25.12, 34.65) | 6.35 (4.33, 8.36) | 0.63 (-0.86, 2.12)
Race
Asian or Pacific Islander | 49.94 (7.89, 91.98) | 50.06 (8.02, 92.11) | 43.60 (15.04, 72.16) | 18.91 (2.35, 35.48) | -12.45 (-40.86, 15.96)
Black | 36.25 (-24.88, 97.37) | 63.75 (2.63, 124.88) | 65.89 (-1.45, 133.24) | -11.98 (-46.10, 22.14) | 9.85 (-8.29, 27.98)
No response | 47.57 (25.24, 69.91) | 52.43 (30.09, 74.76) | 40.68 (23.10, 58.26) | 8.09 (-0.64, 16.82) | 3.66 (-3.85, 11.17)
Other | 50.86 (31.28, 70.44) | 49.14 (29.56, 68.72) | 44.94 (26.65, 63.23) | 2.04 (-4.34, 8.41) | 2.17 (-4.16, 8.49)
White | 56.52 (52.85, 60.20) | 43.48 (39.80, 47.15) | 36.03 (32.85, 39.21) | 6.60 (5.35, 7.86) | 0.84 (-0.15, 1.84)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 23: Heterogeneous proportion mediated (Ref = 1): XGBoost estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | -2.18 (-2.84, -1.53) | -3.93 (-4.26, -3.59) | -3.86 (-4.17, -3.56) | -0.42 (-0.54, -0.30) | 0.36 (0.26, 0.45)
35-64 years | -1.75 (-2.03, -1.47) | -1.93 (-2.08, -1.77) | -1.58 (-1.72, -1.44) | -0.40 (-0.45, -0.36) | 0.06 (0.03, 0.09)
65 or more years | -1.79 (-2.03, -1.56) | -0.85 (-0.99, -0.72) | -0.65 (-0.76, -0.53) | -0.18 (-0.22, -0.13) | -0.03 (-0.07, 0.02)
No response | -2.73 (-4.19, -1.27) | -1.75 (-2.59, -0.91) | -1.48 (-2.27, -0.69) | -0.30 (-0.56, -0.04) | 0.03 (-0.19, 0.25)
Ethnicity
Hispanic | -0.71 (-1.35, -0.07) | -1.81 (-2.17, -1.45) | -1.60 (-1.91, -1.29) | -0.28 (-0.38, -0.18) | 0.07 (-0.04, 0.18)
No response | -3.23 (-4.44, -2.02) | -1.64 (-2.35, -0.93) | -1.53 (-2.19, -0.87) | -0.16 (-0.38, 0.06) | 0.05 (-0.14, 0.23)
Not Hispanic | -1.96 (-2.16, -1.75) | -1.91 (-2.02, -1.80) | -1.64 (-1.74, -1.54) | -0.35 (-0.38, -0.31) | 0.08 (0.05, 0.11)
Gender
Female | -1.96 (-2.21, -1.71) | -2.01 (-2.14, -1.88) | -1.70 (-1.82, -1.58) | -0.39 (-0.43, -0.34) | 0.07 (0.04, 0.10)
No response | -3.04 (-4.67, -1.41) | -1.12 (-2.27, 0.04) | -1.38 (-2.24, -0.51) | -0.39 (-0.70, -0.09) | 0.65 (0.20, 1.11)
Not female | -1.54 (-1.83, -1.24) | -1.71 (-1.87, -1.54) | -1.52 (-1.68, -1.37) | -0.23 (-0.27, -0.18) | 0.05 (0.01, 0.08)
High-risk conditions
Missing | -1.84 (-4.02, 0.34) | -2.70 (-3.84, -1.56) | -2.68 (-3.79, -1.56) | -0.11 (-0.59, 0.37) | 0.09 (-0.23, 0.40)
None | -1.44 (-1.77, -1.12) | -2.03 (-2.20, -1.86) | -1.85 (-2.01, -1.70) | -0.30 (-0.36, -0.25) | 0.13 (0.09, 0.17)
One | -1.68 (-2.04, -1.33) | -1.85 (-2.04, -1.66) | -1.57 (-1.75, -1.40) | -0.32 (-0.38, -0.26) | 0.04 (0.00, 0.09)
Two or more | -2.38 (-2.71, -2.04) | -1.76 (-1.94, -1.57) | -1.44 (-1.60, -1.27) | -0.38 (-0.44, -0.32) | 0.06 (0.01, 0.11)
Race
Asian or Pacific Islander | -0.81 (-1.57, -0.05) | -1.69 (-2.12, -1.25) | -1.32 (-1.71, -0.93) | -0.34 (-0.48, -0.21) | -0.02 (-0.14, 0.09)
Black | -0.53 (-1.65, 0.60) | -1.20 (-1.87, -0.52) | -1.23 (-1.86, -0.60) | -0.07 (-0.25, 0.11) | 0.11 (-0.05, 0.26)
No response | -1.19 (-2.32, -0.07) | -1.98 (-2.60, -1.35) | -1.70 (-2.29, -1.11) | -0.37 (-0.58, -0.16) | 0.10 (-0.06, 0.25)
Other | -1.11 (-1.93, -0.30) | -1.95 (-2.43, -1.48) | -1.91 (-2.32, -1.50) | -0.23 (-0.36, -0.10) | 0.19 (0.03, 0.34)
White | -2.06 (-2.27, -1.85) | -1.92 (-2.03, -1.80) | -1.64 (-1.74, -1.54) | -0.35 (-0.39, -0.31) | 0.07 (0.05, 0.10)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 24: Heterogeneous mediated effects (Ref = 1): XGBoost estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | -2.97 (-3.70, -2.23) | -3.14 (-3.37, -2.92) | -4.20 (-4.54, -3.87) | -0.40 (-0.55, -0.25) | 1.46 (1.06, 1.86)
35-64 years | -1.91 (-2.23, -1.59) | -1.77 (-1.84, -1.70) | -1.55 (-1.70, -1.40) | -0.36 (-0.42, -0.29) | 0.14 (-0.03, 0.32)
65 or more years | -1.94 (-2.19, -1.69) | -0.71 (-0.75, -0.67) | -0.58 (-0.68, -0.48) | -0.10 (-0.14, -0.07) | -0.02 (-0.14, 0.09)
No response | -2.99 (-4.75, -1.23) | -1.49 (-1.96, -1.02) | -1.21 (-2.06, -0.37) | -0.10 (-0.52, 0.32) | -0.17 (-1.19, 0.84)
Ethnicity
Hispanic | -0.67 (-1.35, 0.02) | -1.85 (-2.04, -1.67) | -1.68 (-2.00, -1.36) | -0.22 (-0.37, -0.08) | 0.05 (-0.32, 0.43)
No response | -3.14 (-4.60, -1.69) | -1.73 (-2.12, -1.34) | -1.48 (-2.17, -0.79) | 0.03 (-0.29, 0.36) | -0.28 (-1.11, 0.55)
Not Hispanic | -2.26 (-2.49, -2.02) | -1.61 (-1.66, -1.55) | -1.64 (-1.75, -1.54) | -0.29 (-0.34, -0.25) | 0.33 (0.21, 0.45)
Gender
Female | -2.26 (-2.54, -1.98) | -1.71 (-1.77, -1.65) | -1.73 (-1.85, -1.60) | -0.36 (-0.41, -0.30) | 0.37 (0.23, 0.51)
No response | -2.56 (-4.23, -0.90) | -1.59 (-2.21, -0.98) | -1.59 (-2.45, -0.74) | 0.49 (-0.04, 1.02) | -0.49 (-1.50, 0.52)
Not female | -1.75 (-2.09, -1.40) | -1.49 (-1.59, -1.40) | -1.48 (-1.65, -1.31) | -0.18 (-0.25, -0.11) | 0.17 (-0.03, 0.36)
High-risk conditions
Missing | -2.46 (-4.94, 0.01) | -2.08 (-2.77, -1.38) | -3.08 (-4.09, -2.07) | -0.03 (-0.51, 0.44) | 1.04 (-0.24, 2.31)
None | -1.55 (-1.91, -1.18) | -1.93 (-2.02, -1.84) | -1.83 (-2.00, -1.66) | -0.25 (-0.33, -0.18) | 0.15 (-0.05, 0.35)
One | -2.06 (-2.46, -1.65) | -1.47 (-1.56, -1.38) | -1.54 (-1.73, -1.35) | -0.29 (-0.37, -0.22) | 0.36 (0.15, 0.57)
Two or more | -2.66 (-3.03, -2.29) | -1.48 (-1.56, -1.39) | -1.51 (-1.67, -1.34) | -0.30 (-0.37, -0.23) | 0.33 (0.14, 0.52)
Race
Asian or Pacific Islander | -0.91 (-1.78, -0.03) | -1.59 (-1.77, -1.40) | -1.40 (-1.83, -0.96) | -0.38 (-0.57, -0.18) | 0.18 (-0.32, 0.69)
Black | -0.55 (-1.80, 0.71) | -1.18 (-1.46, -0.90) | -0.96 (-1.59, -0.33) | 0.00 (-0.24, 0.24) | -0.22 (-0.93, 0.48)
No response | -1.27 (-2.58, 0.04) | -1.90 (-2.26, -1.54) | -1.46 (-2.08, -0.84) | -0.22 (-0.53, 0.09) | -0.22 (-0.95, 0.51)
Other | -1.02 (-1.92, -0.12) | -2.04 (-2.32, -1.77) | -2.23 (-2.65, -1.80) | 0.11 (-0.09, 0.30) | 0.08 (-0.42, 0.57)
White | -2.37 (-2.61, -2.13) | -1.61 (-1.66, -1.55) | -1.63 (-1.74, -1.53) | -0.32 (-0.37, -0.27) | 0.34 (0.22, 0.47)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 25: Heterogeneous proportion mediated (Ref = 0): XGBoost estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | 35.76 (28.39, 43.12) | 64.24 (56.88, 71.61) | 63.22 (56.19, 70.24) | 6.88 (4.77, 8.99) | -5.85 (-7.55, -4.15)
35-64 years | 47.61 (42.98, 52.24) | 52.39 (47.76, 57.02) | 43.06 (39.00, 47.12) | 11.00 (9.47, 12.54) | -1.67 (-2.52, -0.83)
65 or more years | 67.79 (63.05, 72.53) | 32.21 (27.47, 36.95) | 24.46 (20.50, 28.42) | 6.67 (4.92, 8.41) | 1.09 (-0.61, 2.80)
No response | 60.97 (43.09, 78.85) | 39.03 (21.15, 56.91) | 33.06 (16.73, 49.39) | 6.73 (0.55, 12.92) | -0.76 (-5.69, 4.17)
Ethnicity
Hispanic | 28.17 (8.83, 47.51) | 71.83 (52.49, 91.17) | 63.51 (47.05, 79.97) | 11.10 (6.30, 15.91) | -2.78 (-7.17, 1.60)
No response | 66.30 (52.96, 79.64) | 33.70 (20.36, 47.04) | 31.36 (19.12, 43.60) | 3.32 (-1.31, 7.96) | -0.99 (-4.77, 2.80)
Not Hispanic | 50.67 (47.60, 53.74) | 49.33 (46.26, 52.40) | 42.44 (39.70, 45.18) | 8.94 (7.89, 9.99) | -2.05 (-2.74, -1.37)
Gender
Female | 49.41 (45.71, 53.11) | 50.59 (46.89, 54.29) | 42.72 (39.47, 45.97) | 9.72 (8.44, 11.00) | -1.85 (-2.65, -1.05)
No response | 73.15 (46.59, 99.70) | 26.85 (0.30, 53.41) | 33.10 (13.71, 52.49) | 9.47 (1.38, 17.57) | -15.72 (-28.00, -3.45)
Not female | 47.38 (41.89, 52.87) | 52.62 (47.13, 58.11) | 47.03 (42.00, 52.07) | 6.98 (5.39, 8.57) | -1.40 (-2.59, -0.21)
High-risk conditions
Missing | 40.47 (9.72, 71.22) | 59.53 (28.78, 90.28) | 58.99 (28.69, 89.28) | 2.43 (-8.21, 13.07) | -1.88 (-8.95, 5.19)
None | 41.50 (35.57, 47.44) | 58.50 (52.56, 64.43) | 53.38 (47.95, 58.81) | 8.77 (6.95, 10.59) | -3.65 (-4.90, -2.40)
One | 47.62 (41.61, 53.63) | 52.38 (46.37, 58.39) | 44.59 (39.28, 49.90) | 9.01 (7.08, 10.95) | -1.22 (-2.50, 0.05)
Two or more | 57.46 (52.96, 61.96) | 42.54 (38.04, 47.04) | 34.73 (30.86, 38.60) | 9.19 (7.61, 10.76) | -1.37 (-2.55, -0.20)
Race
Asian or Pacific Islander | 32.32 (10.18, 54.47) | 67.68 (45.53, 89.82) | 52.99 (35.26, 70.72) | 13.80 (7.10, 20.51) | 0.88 (-3.69, 5.45)
Black | 30.65 (-17.42, 78.72) | 69.35 (21.28, 117.42) | 71.51 (23.35, 119.67) | 4.11 (-6.31, 14.53) | -6.27 (-16.27, 3.73)
No response | 37.61 (13.62, 61.60) | 62.39 (38.40, 86.38) | 53.77 (32.56, 74.98) | 11.64 (3.61, 19.67) | -3.02 (-8.06, 2.02)
Other | 36.27 (17.42, 55.12) | 63.73 (44.88, 82.58) | 62.30 (45.29, 79.31) | 7.51 (2.82, 12.19) | -6.08 (-11.40, -0.76)
White | 51.78 (48.73, 54.82) | 48.22 (45.18, 51.27) | 41.26 (38.54, 43.97) | 8.80 (7.75, 9.85) | -1.83 (-2.51, -1.16)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 26: Heterogeneous proportion mediated (Ref = 1): XGBoost estimates

Label | IDE | IIE | IIE - Isolated | IIE - Health | IIE - Covariant
---|---|---|---|---|---
Age
18-34 years | 48.57 (40.75, 56.39) | 51.43 (43.61, 59.25) | 68.78 (60.31, 77.25) | 6.51 (3.99, 9.03) | -23.86 (-28.51, -19.22)
35-64 years | 51.94 (46.37, 57.51) | 48.06 (42.49, 53.63) | 42.19 (37.41, 46.98) | 9.72 (7.73, 11.72) | -3.86 (-5.81, -1.92)
65 or more years | 73.29 (68.88, 77.71) | 26.71 (22.29, 31.12) | 21.94 (18.26, 25.62) | 3.86 (2.44, 5.27) | 0.91 (-0.65, 2.46)
No response | 66.81 (43.00, 90.61) | 33.19 (9.39, 57.00) | 27.12 (7.96, 46.27) | 2.18 (-7.26, 11.62) | 3.90 (-6.80, 14.60)
Ethnicity
Hispanic | 26.43 (4.73, 48.12) | 73.57 (51.88, 95.27) | 66.73 (48.03, 85.43) | 8.90 (2.53, 15.26) | -2.05 (-9.44, 5.33)
No response | 64.50 (46.33, 82.67) | 35.50 (17.33, 53.67) | 30.40 (15.80, 45.00) | -0.69 (-7.40, 6.01) | 5.79 (-2.49, 14.07)
Not Hispanic | 58.42 (54.86, 61.97) | 41.58 (38.03, 45.14) | 42.49 (39.26, 45.71) | 7.63 (6.37, 8.88) | -8.53 (-10.02, -7.04)
Gender
Female | 56.89 (52.73, 61.05) | 43.11 (38.95, 47.27) | 43.47 (39.72, 47.23) | 8.95 (7.45, 10.44) | -9.31 (-11.01, -7.61)
No response | 61.68 (36.12, 87.24) | 38.32 (12.76, 63.88) | 38.35 (16.75, 59.96) | -11.81 (-25.61, 1.98) | 11.78 (-4.07, 27.63)
Not female | 53.90 (47.09, 60.72) | 46.10 (39.28, 52.91) | 45.65 (39.54, 51.76) | 5.62 (3.42, 7.82) | -5.17 (-8.04, -2.30)
High-risk conditions
Missing | 54.28 (21.32, 87.23) | 45.72 (12.77, 78.68) | 67.77 (31.10, 104.45) | 0.77 (-9.75, 11.28) | -22.82 (-42.27, -3.37)
None | 44.51 (37.38, 51.63) | 55.49 (48.37, 62.62) | 52.60 (46.31, 58.90) | 7.28 (4.95, 9.60) | -4.39 (-7.07, -1.70)
One | 58.29 (51.49, 65.10) | 41.71 (34.90, 48.51) | 43.61 (37.30, 49.91) | 8.33 (5.98, 10.68) | -10.23 (-12.97, -7.49)
Two or more | 64.30 (59.31, 69.30) | 35.70 (30.70, 40.69) | 36.46 (32.05, 40.87) | 7.21 (5.36, 9.07) | -7.98 (-10.26, -5.69)
Race
Asian or Pacific Islander | 36.42 (10.28, 62.56) | 63.58 (37.44, 89.72) | 55.93 (33.78, 78.07) | 15.04 (5.78, 24.31) | -7.39 (-15.23, 0.45)
Black | 31.65 (-23.31, 86.60) | 68.35 (13.40, 123.31) | 55.59 (9.93, 101.25) | -0.21 (-14.11, 13.69) | 12.98 (-6.03, 31.98)
No response | 40.03 (10.50, 69.56) | 59.97 (30.44, 89.50) | 46.12 (23.33, 68.90) | 6.92 (-3.24, 17.08) | 6.93 (-4.89, 18.76)
Other | 33.32 (11.37, 55.27) | 66.68 (44.73, 88.63) | 72.67 (51.08, 94.27) | -3.49 (-9.93, 2.94) | -2.50 (-11.53, 6.53)
White | 59.53 (56.02, 63.04) | 40.47 (36.96, 43.98) | 41.10 (37.94, 44.26) | 8.04 (6.78, 9.29) | -8.67 (-10.16, -7.19)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

###  12.4 Other estimands

We consider the effects of the observed distribution of vaccinations and
incremental effects on the propensity scores. Table 27 shows the results from
the XGBoost models, displaying the estimated rate of each outcome and uniform
confidence bands setting $\delta=0$ to $\delta=5$. Again $\delta$ is a
parameter that multiplies each individual’s odds of being vaccinated, and
reflects the expected prevalence of each outcome under the corresponding
intervention $\mathbb{P}_{n}[Y^{Q(\delta)}]$. We also consider the effect of
the observed distribution of vaccinations, which is simply the contrast
$\mathbb{P}_{n}[Y^{Q(1)}-Y^{Q(0)}]$.

Table 27: Incremental effects, XGBoost estimates (95% CI) Increment | Depression | Isolation | Health
---|---|---|---
0 | 19.2 (19.1, 19.3) | 20.3 (20.2, 20.4) | 28.4 (28.3, 28.6)
0.01 | 19.1 (19.0, 19.3) | 20.3 (20.1, 20.4) | 28.4 (28.2, 28.5)
0.25 | 18.6 (18.5, 18.7) | 19.8 (19.7, 19.9) | 27.7 (27.6, 27.9)
0.5 | 18.3 (18.2, 18.4) | 19.5 (19.4, 19.6) | 27.4 (27.3, 27.5)
0.75 | 18.1 (18.0, 18.2) | 19.4 (19.3, 19.5) | 27.2 (27.1, 27.3)
1 | 18.0 (17.9, 18.1) | 19.2 (19.1, 19.3) | 27.0 (26.9, 27.1)
1.5 | 17.8 (17.7, 17.8) | 19.0 (18.9, 19.1) | 26.8 (26.6, 26.9)
2 | 17.6 (17.5, 17.7) | 18.9 (18.8, 19.0) | 26.6 (26.5, 26.7)
2.5 | 17.4 (17.4, 17.5) | 18.8 (18.7, 18.9) | 26.4 (26.3, 26.5)
3 | 17.3 (17.2, 17.4) | 18.7 (18.6, 18.8) | 26.3 (26.2, 26.4)
3.5 | 17.2 (17.1, 17.3) | 18.6 (18.5, 18.7) | 26.2 (26.0, 26.3)
4 | 17.1 (17.0, 17.2) | 18.5 (18.4, 18.6) | 26.1 (25.9, 26.2)
4.5 | 17.1 (17.0, 17.2) | 18.4 (18.3, 18.6) | 26.0 (25.9, 26.1)
5 | 17.0 (16.9, 17.1) | 18.4 (18.3, 18.5) | 25.9 (25.8, 26.0)
Observed | -1.2 (-1.3, -1.1) | -1.1 (-1.2, -1.0) | -1.4 (-1.5, -1.3)
Proportion Observed | 32.7 (31.2, 34.2) | 33.5 (31.6, 35.3) | 34.5 (32.9, 36.1)
Total | -3.7 (-3.9, -3.5) | -3.2 (-3.4, -3.0) | -4.1 (-4.4, -3.9)

We estimate that the observed distribution of vaccinations in February 2021
caused a -1.2 (-1.3, -1.2), -1.1 (-1.2, -1.0), and -1.4 (-1.5, -1.3)
percentage point change in depression, isolation, and worries about health,
respectively. Using our GLM models we estimate -1.2 (-1.3, -1.1), -1.1 (-1.2,
-1.0), and -1.4 (-1.6, -1.3) percentage point decreases in each outcome (see
Table 28 below). This implies that the observed distribution of vaccinations
captured around one-third of the total estimated effects for each outcome. By
comparison, 36.7 percent of this sample was vaccinated.

The incremental effect estimates exhibit diminishing marginal returns with
respect to increasing the odds of vaccination. For example, increasing the
odds of vaccination two-fold would have yielded only approximately 0.3 to 0.4
percentage point reductions in the prevalence of each outcome, while
increasing the odds five-fold would only yield total reductions of
approximately 1 percentage point for each outcome. Taken together with our
average effect estimates, these estimates suggest that further investments in
vaccine production or distribution during this time-frame may not have been
“worth it” in terms of mental health past some point. Of course, a formal
cost-benefit analysis would both need to quantify the both the costs of such
an intervention, and the total benefits – not only in terms of mental health –
but economic and health benefits.

We also consider these estimands by age group and ethnicity. Figure 14
illustrates the incremental effect curves across a range of $\delta$. The
curves look somewhat different for each group: this reflects both the
heterogeneity in the treatment effects and the different distribution of
propensity scores across both groups. The observed distribution of
vaccinations changed depression by -1.3 (-1.9, -0.7) percentage points among
the youngest age group, accounting for approximately 11 percent of the total
effect among this group. The observed distribution of vaccinations reduced
depression by -1.3 (-1.4, -1.2) percentage points among non-Hispanic adults
aged 25 or older. On the other hand, a five-fold increase in the odds of
treatment by five among the youngest group would have further decreased
depression by an additional 3 percentage points, while a five-fold increase in
the treatment odds would have only decreased depression by an additional 0.9
percentage points. The effect curves also illustrate that the returns to
increasing the odds of vaccination decrease most slowly among the youngest
respondents relative to the other two groups.

These results are consistent with our previous findings that the youngest
respondents were most likely to benefit from COVID-19 vaccinations, while they
were also least likely to be vaccinated: 18.0 percent of the youngest group
were vaccinated, while 25.9 percent and 38.9 percent of the older Hispanic and
non-Hispanic groups were vaccinated. Our incremental effects analysis is
consistent with this finding, and further illustrates that the youngest
respondents would obtain the largest relative returns from an intervention
increasing everyone’s odds of vaccination.

Figure 14: Heterogeneous incremental effects, February 2021

The table below displays the incremental effects estimates using the GLM
estimates.

Table 28: Incremental effects, GLM estimates (95% CI) Increment | Depression | Isolation | Health
---|---|---|---
0 | 19.2 (19.0, 19.3) | 20.3 (20.2, 20.4) | 28.4 (28.3, 28.6)
0.01 | 19.1 (19.0, 19.3) | 20.3 (20.1, 20.4) | 28.4 (28.2, 28.6)
0.25 | 18.6 (18.5, 18.7) | 19.8 (19.7, 19.9) | 27.8 (27.7, 27.9)
0.5 | 18.3 (18.2, 18.4) | 19.5 (19.4, 19.7) | 27.4 (27.3, 27.6)
0.75 | 18.1 (18.0, 18.2) | 19.4 (19.3, 19.5) | 27.2 (27.1, 27.3)
1 | 18.0 (17.9, 18.1) | 19.2 (19.1, 19.3) | 27.0 (26.9, 27.1)
1.5 | 17.7 (17.7, 17.8) | 19.0 (18.9, 19.1) | 26.7 (26.6, 26.9)
2 | 17.6 (17.5, 17.7) | 18.9 (18.8, 19.0) | 26.5 (26.4, 26.6)
2.5 | 17.4 (17.3, 17.5) | 18.7 (18.6, 18.8) | 26.4 (26.2, 26.5)
3 | 17.3 (17.2, 17.4) | 18.6 (18.5, 18.7) | 26.2 (26.1, 26.3)
3.5 | 17.2 (17.1, 17.3) | 18.5 (18.4, 18.6) | 26.1 (26.0, 26.2)
4 | 17.1 (17.0, 17.2) | 18.5 (18.3, 18.6) | 26.0 (25.9, 26.1)
4.5 | 17.0 (16.9, 17.1) | 18.4 (18.3, 18.5) | 25.9 (25.8, 26.1)
5 | 17.0 (16.9, 17.1) | 18.3 (18.2, 18.4) | 25.8 (25.7, 26.0)
Observed | -1.2 (-1.3, -1.1) | -1.1 (-1.2, -1.0) | -1.4 (-1.6, -1.3)
Proportion Observed | 31.8 (29.9, 33.8) | 33.0 (30.5, 35.4) | 33.5 (31.3, 35.7)
Total | -3.7 (-4.0, -3.5) | -3.3 (-3.5, -3.0) | -4.3 (-4.5, -4.0)

The following tables display the incremental effect estimates using XGBoost
models, stratified by subgroup. The GLM estimates are available on request.

Table 29: Incremental effects by age: depression (95% CI) Increment | Outcome | 18-24 years | 25+ years: Hispanic | 25+ years: not Hispanic
---|---|---|---|---
0 | Depression | 50.1 ( 49.2, 50.9) | 18.9 ( 18.5, 19.2) | 17.9 ( 17.8, 18.0)
0.01 | Depression | 50.1 ( 49.1, 51.1) | 18.9 ( 18.5, 19.3) | 17.8 ( 17.7, 18.0)
0.25 | Depression | 49.8 ( 49.0, 50.6) | 18.7 ( 18.3, 19.0) | 17.2 ( 17.1, 17.3)
0.5 | Depression | 49.4 ( 48.7, 50.1) | 18.5 ( 18.2, 18.8) | 16.9 ( 16.8, 17.1)
0.75 | Depression | 49.1 ( 48.3, 49.8) | 18.4 ( 18.1, 18.7) | 16.8 ( 16.6, 16.9)
1 | Depression | 48.8 ( 48.1, 49.5) | 18.3 ( 18.0, 18.6) | 16.6 ( 16.5, 16.7)
1.5 | Depression | 48.3 ( 47.6, 49.0) | 18.2 ( 17.9, 18.5) | 16.4 ( 16.3, 16.5)
2 | Depression | 47.8 ( 47.1, 48.5) | 18.1 ( 17.7, 18.4) | 16.2 ( 16.1, 16.3)
2.5 | Depression | 47.4 ( 46.7, 48.2) | 18.0 ( 17.6, 18.3) | 16.1 ( 16.0, 16.2)
3 | Depression | 47.1 ( 46.4, 47.8) | 17.9 ( 17.6, 18.2) | 16.0 ( 15.9, 16.1)
3.5 | Depression | 46.8 ( 46.0, 47.5) | 17.8 ( 17.5, 18.2) | 15.9 ( 15.8, 16.0)
4 | Depression | 46.5 ( 45.7, 47.2) | 17.8 ( 17.4, 18.1) | 15.8 ( 15.7, 15.9)
4.5 | Depression | 46.2 ( 45.4, 47.0) | 17.7 ( 17.4, 18.1) | 15.8 ( 15.6, 15.9)
5 | Depression | 45.9 ( 45.1, 46.7) | 17.7 ( 17.3, 18.0) | 15.7 ( 15.6, 15.8)
Observed | Depression | -1.3 ( -1.9, -0.7) | -0.6 ( -0.8, -0.4) | -1.3 ( -1.4, -1.2)
Proportion Observed | Depression | 10.6 (6.6, 14.6) | 30.4 ( 21.5, 39.3) | 36.0 ( 34.1, 37.9)
Total | Depression | -12.2 (-13.7, -10.7) | -1.9 ( -2.6, -1.2) | -3.6 ( -3.8, -3.3)
Table 30: Incremental effects by age: isolation (95% CI) Increment | Outcome | 18-24 years | 25+ years: Hispanic | 25+ years: not Hispanic
---|---|---|---|---
0 | Isolation | 39.0 ( 38.2, 39.8) | 20.2 ( 19.9, 20.6) | 19.5 ( 19.4, 19.7)
0.01 | Isolation | 39.0 ( 38.0, 39.9) | 20.2 ( 19.8, 20.6) | 19.5 ( 19.3, 19.6)
0.25 | Isolation | 38.5 ( 37.8, 39.2) | 20.0 ( 19.7, 20.4) | 19.0 ( 18.8, 19.1)
0.5 | Isolation | 38.1 ( 37.4, 38.8) | 19.9 ( 19.5, 20.2) | 18.7 ( 18.6, 18.8)
0.75 | Isolation | 37.8 ( 37.1, 38.5) | 19.8 ( 19.4, 20.1) | 18.5 ( 18.4, 18.7)
1 | Isolation | 37.5 ( 36.8, 38.2) | 19.7 ( 19.3, 20.0) | 18.4 ( 18.3, 18.5)
1.5 | Isolation | 37.0 ( 36.3, 37.7) | 19.5 ( 19.2, 19.8) | 18.2 ( 18.1, 18.3)
2 | Isolation | 36.6 ( 35.9, 37.3) | 19.4 ( 19.1, 19.7) | 18.1 ( 18.0, 18.2)
2.5 | Isolation | 36.2 ( 35.6, 36.9) | 19.3 ( 19.0, 19.7) | 18.0 ( 17.9, 18.1)
3 | Isolation | 35.9 ( 35.2, 36.6) | 19.2 ( 18.9, 19.6) | 17.9 ( 17.8, 18.0)
3.5 | Isolation | 35.6 ( 34.9, 36.3) | 19.2 ( 18.8, 19.5) | 17.8 ( 17.7, 17.9)
4 | Isolation | 35.3 ( 34.6, 36.1) | 19.1 ( 18.8, 19.5) | 17.7 ( 17.6, 17.9)
4.5 | Isolation | 35.1 ( 34.4, 35.8) | 19.1 ( 18.7, 19.5) | 17.7 ( 17.6, 17.8)
5 | Isolation | 34.9 ( 34.1, 35.6) | 19.0 ( 18.6, 19.4) | 17.6 ( 17.5, 17.8)
Observed | Isolation | -1.5 ( -2.0, -0.9) | -0.6 ( -0.8, -0.4) | -1.1 ( -1.2, -1.0)
Proportion Observed | Isolation | 13.8 (9.9, 17.7) | 31.0 ( 21.7, 40.2) | 36.6 ( 34.3, 38.9)
Total | Isolation | -10.7 (-12.1, -9.3) | -1.9 ( -2.6, -1.2) | -3.0 ( -3.3, -2.8)
Table 31: Incremental effects by age: health (95% CI) Increment | Outcome | 18-24 years | 25+ years: Hispanic | 25+ years: not Hispanic
---|---|---|---|---
0 | Health | 35.6 (34.8, 36.4) | 48.0 (47.6, 48.5) | 25.6 (25.4, 25.8)
0.01 | Health | 35.6 (34.6, 36.5) | 48.0 (47.4, 48.5) | 25.5 (25.4, 25.7)
0.25 | Health | 35.1 (34.4, 35.8) | 47.5 (47.0, 47.9) | 24.9 (24.7, 25.0)
0.5 | Health | 34.8 (34.1, 35.5) | 47.2 (46.8, 47.6) | 24.5 (24.4, 24.7)
0.75 | Health | 34.6 (33.9, 35.3) | 46.9 (46.5, 47.4) | 24.3 (24.2, 24.4)
1 | Health | 34.4 (33.7, 35.1) | 46.8 (46.3, 47.2) | 24.2 (24.0, 24.3)
1.5 | Health | 34.1 (33.4, 34.8) | 46.4 (46.0, 46.9) | 23.9 (23.8, 24.0)
2 | Health | 33.8 (33.2, 34.5) | 46.2 (45.8, 46.6) | 23.7 (23.6, 23.9)
2.5 | Health | 33.6 (32.9, 34.3) | 46.0 (45.6, 46.4) | 23.6 (23.5, 23.7)
3 | Health | 33.4 (32.7, 34.1) | 45.8 (45.4, 46.3) | 23.5 (23.3, 23.6)
3.5 | Health | 33.2 (32.5, 33.9) | 45.7 (45.2, 46.2) | 23.4 (23.2, 23.5)
4 | Health | 33.0 (32.3, 33.7) | 45.6 (45.1, 46.0) | 23.3 (23.1, 23.4)
4.5 | Health | 32.9 (32.1, 33.6) | 45.5 (45.0, 45.9) | 23.2 (23.1, 23.3)
5 | Health | 32.7 (32.0, 33.5) | 45.4 (44.9, 45.9) | 23.1 (23.0, 23.3)
Observed | Health | -1.2 (-1.7, -0.7) | -1.3 (-1.6, -1.0) | -1.4 (-1.6, -1.3)
Proportion Observed | Health | 17.4 (11.7, 23.1) | 26.9 (22.4, 31.4) | 36.9 (34.9, 38.9)
Total | Health | -6.9 (-8.3, -5.6) | -4.7 (-5.6, -3.8) | -3.9 (-4.2, -3.7)

##  13 Sensitivity analysis

This section contains two propositions: first, one containing the derivation
of our sensitivity analysis used in Section 6. This result follows almost
immediately from results previously shown in [20]. Our second proposition
provides a simple extension to generate bounds on an estimand that does not
assume random sample selection.

Throughout we let $\bar{\mu}_{a}(x,a^{\prime})=\mathbb{E}[Y^{a}\mid
X=x,A=a^{\prime},Z=1]$ and again let $\mu_{a}(x)=\mathbb{E}[Y^{a}\mid
X=x,Z=1]$. We define the true (conditional) target of inference as
$\psi(x)=\mu_{1}(x)-\mu_{0}(x)$ and the biased target of the observed data
functionals as $\bar{\psi}(x)=\bar{\mu}_{1}(x,1)-\bar{\mu}_{0}(x,0)$. Our goal
is to bound $\mathbb{P}_{n}[\psi(X)]$ using only functions of the observed
data.

####  13.0.1 Sensitivity analysis 1

In this subsection we propose a sensitivity analysis for the primary estimand
$\mathbb{P}_{n}[\mu_{1}(X)-\mu_{0}(X)]$. Recall the assumption in (7) that
there is some known $\tau$ satisfying:

$\displaystyle\left(\frac{1}{1-\tau}\right)\geq\frac{\bar{\mu}_{a}(x,a^{\prime})}{\bar{\mu}_{a}(x,a)}\geq
1-\tau\qquad\forall(x,a,a^{\prime})$

######  Proposition 6.

For a fixed $\tau$ satisfying (7), we obtain the bounds:

$\displaystyle\psi(x)$
$\displaystyle\leq\bar{\psi}(x)+\left(\frac{\tau}{1-\tau}\right)\bar{\mu}_{1}(x,1)P(A=0\mid
X=x,Z=1)$ $\displaystyle+\tau\bar{\mu}_{0}(x,0)P(A=1\mid X=x,Z=1)$
$\displaystyle\psi(x)$
$\displaystyle\geq\bar{\psi}(x)-\tau\bar{\mu}_{1}(x,1)P(A=0\mid X=x,Z=1)$
$\displaystyle-\left(\frac{\tau}{1-\tau}\right)\bar{\mu}_{0}(x,0)P(A=1\mid
X=x,Z=1)$

###### Proof of Proposition 6.

$\displaystyle\mathbb{E}[Y^{a}\mid X=x,Z=1]$
$\displaystyle=\sum_{a^{\star}\in\\{a,a^{\prime}\\}}\bar{\mu}_{a}(x,a^{\star})P(A=a^{\star}\mid
X=x,Z=1)$ $\displaystyle=\bar{\mu}_{a}(x,a)+P(A=a^{\prime}\mid
X=x,Z=1)[\bar{\mu}_{a}(x,a^{\prime})-\bar{\mu}_{a}(x,a)]$ (31)

where the first equality holds by the law of iterated expectations, and the
second by rearranging terms. For a fixed $\tau$, (7) implies that:

$\displaystyle\left(\frac{\tau}{1-\tau}\right)\bar{\mu}_{a}(x,a)\geq\bar{\mu}_{a}(x,a^{\prime})-\bar{\mu}_{a}(x,a)\geq-\bar{\mu}_{a}(x,a)\tau$

Plugging this into (31), we obtain the following inequalities:

$\displaystyle\left(\frac{\tau}{1-\tau}\right)\bar{\mu}_{a}(x,a)P(A=a^{\prime}\mid
X=x,Z=1)$ $\displaystyle\geq\mu_{a}(x)-\bar{\mu}_{a}(x,a)$
$\displaystyle\geq-\tau\bar{\mu}_{a}(x,a)P(A=a^{\prime}\mid X=x,Z=1)$

The result follows by taking the upper bound of $\mu_{1}(x)$ minus the lower
bound for $\mu_{0}(x)$ to an upper bound on $\psi(x)$, and vice versa for the
lower bound. ∎

######  Remark 11.

To obtain bounds on the average effects, we can simply choose a $\tau$ valid
for all values of $(x,a)$ and average the expression over the relevant
covariate distribution.

######  Remark 12.

These bounds are expressed in terms of the observed data distribution. In
order to estimate them we need to account for the uncertainty in our estimates
of the nuisance functions. We use influence-function based estimators of these
quantities (averaged over the empirical covariate distribution). We refer to
[20] for more details.

###  13.1 Sensitivity analysis 2

Our target estimand is defined with respect to the observed sample and the
above sensitivity analysis does not account for the fact that the prevalence
of potential outcomes in our sample may not be representative. For instance,
consider the following two estimands:

$\displaystyle\mathbb{P}_{n}(\mathbb{E}[Y^{1}-Y^{0}\mid X,V=1])$ (32)
$\displaystyle\mathbb{P}_{n}(\mathbb{E}[Y^{1}-Y^{0}\mid X,Z=1])$ (33)

Random sample selection implies that equations are equal (see Appendix 10).
This equality implies that while the CTIS may have a non-representative
covariate distribution, our statistical target of inference generalizes across
covariate distributions of CTIS non-respondents, and that we could reweight
our estimates to generalize to populations with different covariate
distributions.

We now instead consider the case where we these quantities are not equal due
to non-random sample selection. For example, if the selection process were a
function of observed or potential outcomes our sample estimand be large in
magnitude while the effects among non-respondents were zero. To be clear, this
would imply that our effect estimates cannot generalize to a comparable
covariate distribution of CTIS non-respondents.

We therefore consider targeting (32) instead of (33). To obtain a bound on
this estimand, we only assume the following:

$\displaystyle\frac{1}{1-\tau}\geq\frac{\mathbb{E}[Y^{a}\mid
X=x,V=1,Q_{a}=a^{\prime}]}{\mathbb{E}[Y\mid X=x,V=1,Q_{a}=a]}\geq
1-\tau\qquad\forall(x,a,a^{\prime})$ (34)

where $Q_{a}=\mathds{1}(A=a)RS$. We next derive bounds for equation (32) while
relaxing the assumption of Random Sample Selection (equation (6)).

######  Proposition 7.

Define $\tilde{\mu}_{a}(x,a^{\prime})=\mathbb{E}[Y^{a}\mid
X=x,V=1,Q_{a}=a^{\prime}]$,
$\tilde{\psi}=\tilde{\mu}_{1}(x,1)-\tilde{\mu}_{0}(x,0)$, and let
$\dot{\mu}_{a}(x)=\mathbb{E}[Y^{a}\mid X,V=1]$. Assume that (34) holds for a
known $\tau$ for all $(x,a,a^{\prime})$. Then for any $X=x$:

$\displaystyle\dot{\mu}_{1}(x)-\dot{\mu}_{0}(x)\leq\tilde{\psi}(x)+\tilde{\mu}_{1}(x,1)\left(\frac{1}{1-\tau}\right)+\tau\tilde{\mu}_{0}(x,0)$
$\displaystyle\dot{\mu}_{1}(x)-\dot{\mu}_{0}(x)\geq\tilde{\psi}(x)-\tau\tilde{\mu}_{1}(x,1)-\tilde{\mu}_{0}(x,0)\left(\frac{\tau}{1-\tau}\right)$

###### Proof of Proposition 7.

The result follows by following the same steps in the proof of Proposition 6,
but iterating expectation on the variable $Q_{a}$. The challenge is that we
neither know nor can estimate $P(Q_{a}=1\mid X=x,V=1)$, since we do not
observe any characteristics about survey non-respondents. On the other hand,
this value must always be less than 1. This then yields the following
inequality:

$\displaystyle\left(\frac{\tau}{1-\tau}\right)\tilde{\mu}_{a}(x,a)\geq\left(\frac{\tau}{1-\tau}\right)\tilde{\mu}_{a}(x,a)P(Q_{a}=a^{\prime}\mid
X=x,V=1)$ $\displaystyle\geq\dot{\mu}_{a}(x)-\tilde{\mu}_{a}(x,a)$
$\displaystyle\geq-\tau\tilde{\mu}_{a}(x,a)P(Q_{a}=a^{\prime}\mid
X=x,V=1)\geq-\tau\bar{\mu}_{a}(x,a)$

The result follows by taking the upper bound for $\dot{\mu}_{1}(x)$ and
subtracting the lower bound for $\dot{\mu}_{0}(x)$ for the upper bound of
$\dot{\psi}(x)$, and vice versa for the lower bound. ∎

######  Remark 13.

We can again average this expression over the empirical covariate distribution
to obtain bounds on $\dot{\psi}$, and can estimate these bounds using
influence-function based estimators to account for the uncertainty in the
estimates of the nuisance functions.

######  Remark 14.

For our application we are only interested in an upper bound, and, in
particular, calculating a value of $\tau^{\star}$ that would explain away the
estimated treatment effect. Letting
$\tilde{\psi}_{a}=\mathbb{E}[\tilde{\mu}_{a}(X,a)]$, this would occur where:

$\displaystyle\tau^{\star}=1-\sqrt{\frac{\tilde{\psi}_{1}}{\tilde{\psi}_{0}}}$

While a simple formula, this ignores the uncertainty in the estimates.

##  14 Robustness checks

This section presents several robustness checks. These primarily involve
running our analyses on different subsets of the data, and / or including /
excluding different covariates. We describe each check in detail below. We
rerun our mediation analyses across all of the specified checks. The results,
when not provided, were similar to the primary analyses and are available on
request.

###  14.1 Vaccine-accepting sample

Consider the target estimand:

$\displaystyle\psi^{va}=\frac{1}{\sum_{i=1}^{n}V}\sum_{i:V=1}^{n}\mathbb{E}[Y^{1}-Y^{0}\mid
X,VS=1]$

In contrast to our primary estimand, this estimand includes the incomplete-
cases. As a first approach we directly derive point estimates for this
quantity. These estimates require no additional assumptions beyond those
previously invoked, but do require using inverse-weighting with respect to the
probability of being a complete-case (see Appendix 11). As a second approach
we instead derive bounds on this quantity.

####  14.1.1 Point estimates

Our estimates are qualitatively similar to our primary analysis; however, the
variance estimates increase substantially. Table 34 displays the outcome
analysis using logistic regression while Table 35 displays the results using
XGBoost. For our mediation analysis, Table 34 displays the results using
logistic regression, and Table 35 displays the results using XGBoost. The
XGBoost estimates are all statistically insignificant. This appears primarily
driven by the more extreme complete-case weights that we estimate using these
models, suggesting positivity violations. We present plots displaying the full
data heterogeneity analysis below in Figures 15, 16, 17, 18.

Table 32: Effect estimates, GLM estimates, full data (95% CI)  Outcome | Adjusted RD | Adjusted RR | Unadjusted RD | Unadjusted RR
---|---|---|---|---
Depressed | -4.17 (-4.55, -3.78) | 0.78 (0.76, 0.80) | -9.82 (-9.98, -9.66) | 0.55 (0.54, 0.55)
Isolated | -3.09 (-3.43, -2.76) | 0.84 (0.83, 0.86) | -8.39 (-8.57, -8.22) | 0.62 (0.62, 0.63)
Worried about health | -4.59 (-5.12, -4.06) | 0.84 (0.82, 0.86) | -11.35 (-11.55, -11.16) | 0.64 (0.63, 0.64)
RD indicates risk-differences; RR indicates risk-ratio
Table 33: Effect estimates, XGBoost models, full data (95% CI)  Outcome | Adjusted RD | Adjusted RR | Unadjusted RD | Unadjusted RR
---|---|---|---|---
Depressed | -2.06 (-4.20, 0.07) | 0.88 (0.77, 1.00) | -9.82 (-9.98, -9.66) | 0.55 (0.54, 0.55)
Isolated | -1.65 (-3.37, 0.08) | 0.91 (0.82, 1.00) | -8.39 (-8.57, -8.22) | 0.62 (0.62, 0.63)
Worried about health | -3.76 (-5.90, -1.61) | 0.86 (0.79, 0.93) | -11.35 (-11.55, -11.16) | 0.64 (0.63, 0.64)
RD indicates risk-differences; RR indicates risk-ratio
Table 34: Mediation analysis: GLM estimates, full data (95% CI) (95% CI)

Effect | Ref = 0 | Proportion (Ref = 0) | Ref = 1 | Proportion (Ref = 1)
---|---|---|---|---
IDE | -2.91 (-3.25, -2.57) | 69.77 (65.31, 74.24) | -1.90 (-2.29, -1.50) | 45.50 (39.38, 51.62)
IIE | -1.26 (-1.47, -1.05) | 30.23 (25.76, 34.69) | -2.27 (-2.37, -2.17) | 54.50 (48.38, 60.62)
IIE - Isolated | -1.53 (-1.70, -1.37) | 36.77 (32.89, 40.64) | -1.53 (-1.68, -1.38) | 36.64 (32.51, 40.78)
IIE - Health | -0.41 (-0.48, -0.34) | 9.90 (7.92, 11.88) | -0.25 (-0.31, -0.19) | 5.92 (4.25, 7.59)
IIE - Covariant | 0.69 (0.58, 0.79) | -16.44 (-19.75, -13.13) | -0.50 (-0.69, -0.30) | 11.94 (9.45, 14.43)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Table 35: Mediation analysis: XGBoost estimates, full data (95% CI)

Effect | Ref = 0 | Proportion (Ref = 0) | Ref = 1 | Proportion (Ref = 1)
---|---|---|---|---
IDE | -1.58 (-3.10, -0.06) | 76.50 (34.24, 118.76) | -1.17 (-2.73, 0.39) | 56.73 (23.78, 89.69)
IIE | -0.48 (-1.65, 0.68) | 23.50 (-18.76, 65.76) | -0.89 (-1.19, -0.59) | 43.27 (10.31, 76.22)
IIE - Isolated | -0.58 (-1.67, 0.51) | 28.23 (-9.91, 66.37) | -0.88 (-1.73, -0.03) | 42.51 (4.10, 80.92)
IIE - Health | -0.47 (-0.79, -0.15) | 22.60 (-7.40, 52.60) | -0.27 (-0.48, -0.06) | 13.18 (0.98, 25.37)
IIE - Covariant | 0.56 (0.12, 1.01) | -27.33 (-67.20, 12.53) | 0.26 (-0.71, 1.22) | -12.42 (-35.01, 10.16)

  * •

IDE represents the interventional direct effect; IIE represents the total
interventional indirect effect; IIE - X represents interventional indirect
effect via the indicated channel X; Ref represents the reference category for
the indirect effects

Figure 15: Outcome heterogeneity, full data estimates (GLM models) Figure 16:
Outcome heterogeneity, full data estimates (XGBoost models) Figure 17:
Mediation heterogeneity: full data estimates (GLM models) Figure 18: Mediation
heterogeneity: full data estimates (XGBoost models)

####  14.1.2 Bounds

We can obtain upper bounds on $\psi^{va}$ by assuming that effects on the
$R=0$ stratum are not greater than zero on average. This removes the
positivity requirement required to estimate $\psi^{va}$ – (26) in Appendix 10.

Letting $p_{r}$ indicate the proportion of complete-cases over the total
number of vaccine-accepting respondents, we can scale our estimates of $\psi$
by $p_{r}$ (approximately 86 percent) to obtain a valid upper bound on
$\psi^{va}$.252525This percent excludes non-respondents to the vaccine-
hesitancy question. Technically, $p_{r}$ is not point identified. We can
generalize this approach to cover any other portion of the data that we do not
include in our primary sample (e.g. those with missing ZIP code information,
who live in Alaska, or who are vaccine-hesitant). Notably, we can never fully
explain away our effect estimates under this assumption: we would scale them
by at most 64%, the complete-case percent of the initial sample.

We may also wish to make inferences while allowing our estimates to be biased,
either due to violations of no unmeasured confounding or random sample-
selection. Fortunately, the sensitivity parameters we estimated previously in
Section 6 remain valid for $\psi^{va}$. This follows since, by assumption, the
effect on the unobserved portion of the data is not greater than zero. This
logic generalizes to any portion of the data excluded from our primary
analysis.

###  14.2 Hesitant included

Table 36 presents our primary estimates when including vaccine-hesitant
respondents. Consistent with our expectations detailed in Section 6, the
effect estimates for the outcomes anlaysis move closer to zero.

Table 36: Estimate sensitivity: hesitant included Outcome | Analytic data | Hesitant included
---|---|---
Depressed | -3.72 (-3.98, -3.47) | -3.01 (-3.29, -2.74)
Isolated | -3.26 (-3.53, -2.99) | -2.55 (-2.83, -2.26)
Worried about health | -4.26 (-4.55, -3.96) | -0.53 (-0.84, -0.22)

###  14.3 Bad controls

Table 37 presents our results when we do not control for occupation,
employment status, or worries about finances. Consistent with our expectations
detailed in Section 6, these results move further away from zero.

Table 37: Estimate sensitivity: employment status, financial worry, occupation not controlled Outcome | Effects
---|---
Depression | -5.53 (-5.72, -5.33)
Isolation | -6.05 (-6.26, -5.85)
Health | -6.90 (-7.14, -6.67)

###  14.4 Including hesitancy non-response

Our primary analysis excludes all individuals who report vaccine hesitancy, or
who do not respond to the question. Implicitly, this analysis assumes that all
non-responses were vaccine-hesitant. We run our analysis when including the
75,568 respondents who did not respond to the vaccine hesitancy question (and
who either did not respond to the vaccination question or indicated that they
had not previously received the COVID-19 vaccine). However, this only adds
1,053 respondents to our analytic sample. Table 38 compares the primary
outcome analysis to this analysis, and shows that the estimates are
consistent.

Table 38: Estimate sensitivity: missing hesitancy included Outcome | Analytic data | Missing hesitancy included
---|---|---
Depressed | -3.72 (-3.98, -3.47) | -3.72 (-3.97, -3.47)
Isolated | -3.26 (-3.53, -2.99) | -3.26 (-3.53, -2.99)
Worried about health | -4.26 (-4.55, -3.96) | -4.24 (-4.54, -3.94)

###  14.5 Omitting suspicious responses

We also run our analysis excluding individuals who give suspicious responses.
To identify these observations, we roughly follow a script used in [6], and
exclude people who report any values that fall outside the range of the
responses:

  * •

Household size between 0 and 30

  * •

Number of sick in household between 0 and 30

  * •

Number of work contacts between 0 and 100

  * •

Number of shopping contacts between 0 and 100

  * •

Number of work contacts between 0 and 100

  * •

Number of social contacts between 0 and 100

  * •

Number of other contacts between 0 and 100

  * •

Number of high-risk health conditions less than all options minus 1

  * •

Number of symptoms less than all options minus 1

These omissions account for approximately 2.5 percent of responses on our
primary dataset, and approximately 2.1 percent of the complete-case subset.
Table 39 displays the results when excluding these responses. The results are
quite close to our primary estimates. Of course, our classifications of
unreasonable answers might be incorrect, and any other forms of measurement
error are also possible. However, our results demonstrate some robustness to
the possibility of measurement error.

Table 39: Estimate sensitivity: suspicious responses excluded Outcome | Analytic data | Suspicious responses excluded
---|---|---
Depressed | -3.72 (-3.98, -3.47) | -3.81 (-4.06, -3.55)
Isolated | -3.26 (-3.53, -2.99) | -3.34 (-3.61, -3.07)
Worried about health | -4.26 (-4.55, -3.96) | -4.16 (-4.46, -3.86)