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Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

titleThe ATLAS experiment at the CERN large hadron collider

titleThe CMS experiment at the CERN LHC

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleGEM: A new concept for electron amplification in gas detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleThe COMPASS experiment at CERN

titleThe APV25 deep submicron readont chip for CMS detectors

titleCOMPASS++/AMBER, A new QCD facility at the M2 beam line of the CERN SPS

titleATLAS NSW Electronics Specifications Component: VMM3a

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleImplementation of the VMM ASIC in the Scalable Readout System

journaltitleThe European Physical Journal C-Particles and Fields
titlePassage of particles through matter

titleTechniques for Nuclear and Particle Physics Experiments (1994

titleAstroparticle physics

titleExperimental techniques

titleInstrumentation for high-energy physics

noteFrom StatisticsHowTo.com: Elementary Statistics for the rest of us!
titleLandau Distribution: Definition, Parameters

notePart of a series of lectures offered at the DESY website
titleGaseous detectors

INFN-BARI,	PoliBa

notePart of a series of lectures for a PHD course at INFN-BARI, PoliBa
titleMultiplication and charge avalanche

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titlePosition-sensitive detector with microstrip anode for electron multiplication with gases

Helmholtz-Institut für Strahlen- und Kernphysik

noteMaster Thesis
titleGEM Detectors for the Tracking System of the Missing Energy Experiment NA64 at CERN SPS

journaltitleIEEE Transactions on Nuclear Science
titleTriple GEM tracking detectors for COMPASS

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleConstruction, test and commissioning of the triple-GEM tracking detector for COMPASS

University of Bonn

noteMaster Thesis
titleInvestigations on ASIC readout of MPGDs

journaltitleProceedings of the 2003 ICFA School on Instrumentation, Itacuruca, Brazil
titleAnalog and digital electronics for detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleDesign and results from the APV25, a deep sub-micron CMOS front-end chip for the CMS tracker

journaltitlePhysik-Department E18 Technische Universitat Munchen
titleCommissioning of the GEM Detectors in the COMPASS Experiment

titleVMM3, an ASIC for Micropattern Detectors

IOP Publishing

journaltitleJournal of Instrumentation
titleDevelopment of the scalable readout system for micro-pattern gas detectors and other applications

titleSOFTWARE Manual for VMM3 Slow Control

booktitleIEEE NPSS Short Course, 1993 Nuclear Science Symposium, San Francisco, California
titlePulse processing and analysis
noteFrom electronics-notes.com
titleFlicker, 1/f Noise

Macmillan International Higher Education

titleElectronic noise and low noise design

noteprovided by M. Lupberger.
titleEquivalent noise charge of the VMM hybrid of the Scalable Readout System

Chestnut Ridge, NY

LeCroy Corporation

titleX-Stream Oscilloscopes Remote Control Manual

journaltitleDostupné z WWW: http://optics. eee. nottingham. ac. uk/vxi11
titleVXI11 Ethernet Protocol for Linux
scpi2017r   sonline

titleIntroducing SCPI Commands

titleVMEbus Extensions for Instrumentation: TCP/IP Instrument Protocol Specification VXI-11 Revision 1.0, July 17, 1995, VXIbus Consortium

Lentzeallee, Berlin

BESSY GmbH

titleVXI-11 and HP E2050A A Programmer’s Guide

Agilent Technologies

note(The article can be accessed via the 28 May calendar point in the url)
titleUsing Linux to control LAN-based instruments
family=Karl Jonathan Flöthner,

Rheinische Friedrich-Wilhelms-Universität Bonn

noteMaster Thesis
titleInvestigations of the Triple-GEM-Tracking Detector for COMPASS++/AMBER

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

titleThe ATLAS experiment at the CERN large hadron collider

titleThe CMS experiment at the CERN LHC

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleGEM: A new concept for electron amplification in gas detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleThe COMPASS experiment at CERN

titleThe APV25 deep submicron readont chip for CMS detectors

titleCOMPASS++/AMBER, A new QCD facility at the M2 beam line of the CERN SPS

titleATLAS NSW Electronics Specifications Component: VMM3a

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleImplementation of the VMM ASIC in the Scalable Readout System

journaltitleThe European Physical Journal C-Particles and Fields
titlePassage of particles through matter

titleTechniques for Nuclear and Particle Physics Experiments (1994

titleAstroparticle physics

titleExperimental techniques

titleInstrumentation for high-energy physics

noteFrom StatisticsHowTo.com: Elementary Statistics for the rest of us!
titleLandau Distribution: Definition, Parameters

notePart of a series of lectures offered at the DESY website
titleGaseous detectors

INFN-BARI,	PoliBa

notePart of a series of lectures for a PHD course at INFN-BARI, PoliBa
titleMultiplication and charge avalanche

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titlePosition-sensitive detector with microstrip anode for electron multiplication with gases

Helmholtz-Institut für Strahlen- und Kernphysik

noteMaster Thesis
titleGEM Detectors for the Tracking System of the Missing Energy Experiment NA64 at CERN SPS

journaltitleIEEE Transactions on Nuclear Science
titleTriple GEM tracking detectors for COMPASS

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleConstruction, test and commissioning of the triple-GEM tracking detector for COMPASS

University of Bonn

noteMaster Thesis
titleInvestigations on ASIC readout of MPGDs

journaltitleProceedings of the 2003 ICFA School on Instrumentation, Itacuruca, Brazil
titleAnalog and digital electronics for detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleDesign and results from the APV25, a deep sub-micron CMOS front-end chip for the CMS tracker

journaltitlePhysik-Department E18 Technische Universitat Munchen
titleCommissioning of the GEM Detectors in the COMPASS Experiment

titleVMM3, an ASIC for Micropattern Detectors

IOP Publishing

journaltitleJournal of Instrumentation
titleDevelopment of the scalable readout system for micro-pattern gas detectors and other applications

titleSOFTWARE Manual for VMM3 Slow Control

booktitleIEEE NPSS Short Course, 1993 Nuclear Science Symposium, San Francisco, California
titlePulse processing and analysis
noteFrom electronics-notes.com
titleFlicker, 1/f Noise

Macmillan International Higher Education

titleElectronic noise and low noise design

noteprovided by M. Lupberger.
titleEquivalent noise charge of the VMM hybrid of the Scalable Readout System

Chestnut Ridge, NY

LeCroy Corporation

titleX-Stream Oscilloscopes Remote Control Manual

journaltitleDostupné z WWW: http://optics. eee. nottingham. ac. uk/vxi11
titleVXI11 Ethernet Protocol for Linux
scpi2017r   sonline

titleIntroducing SCPI Commands

titleVMEbus Extensions for Instrumentation: TCP/IP Instrument Protocol Specification VXI-11 Revision 1.0, July 17, 1995, VXIbus Consortium

Lentzeallee, Berlin

BESSY GmbH

titleVXI-11 and HP E2050A A Programmer’s Guide

Agilent Technologies

note(The article can be accessed via the 28 May calendar point in the url)
titleUsing Linux to control LAN-based instruments
family=Karl Jonathan Flöthner,

Rheinische Friedrich-Wilhelms-Universität Bonn

noteMaster Thesis
titleInvestigations of the Triple-GEM-Tracking Detector for COMPASS++/AMBER

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

titleThe ATLAS experiment at the CERN large hadron collider

titleThe CMS experiment at the CERN LHC

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleGEM: A new concept for electron amplification in gas detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleThe COMPASS experiment at CERN

titleThe APV25 deep submicron readont chip for CMS detectors

titleCOMPASS++/AMBER, A new QCD facility at the M2 beam line of the CERN SPS

titleATLAS NSW Electronics Specifications Component: VMM3a

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleImplementation of the VMM ASIC in the Scalable Readout System

journaltitleThe European Physical Journal C-Particles and Fields
titlePassage of particles through matter

titleTechniques for Nuclear and Particle Physics Experiments (1994

titleAstroparticle physics

titleExperimental techniques

titleInstrumentation for high-energy physics

noteFrom StatisticsHowTo.com: Elementary Statistics for the rest of us!
titleLandau Distribution: Definition, Parameters

notePart of a series of lectures offered at the DESY website
titleGaseous detectors

INFN-BARI,	PoliBa

notePart of a series of lectures for a PHD course at INFN-BARI, PoliBa
titleMultiplication and charge avalanche

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titlePosition-sensitive detector with microstrip anode for electron multiplication with gases

Helmholtz-Institut für Strahlen- und Kernphysik

noteMaster Thesis
titleGEM Detectors for the Tracking System of the Missing Energy Experiment NA64 at CERN SPS

journaltitleIEEE Transactions on Nuclear Science
titleTriple GEM tracking detectors for COMPASS

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleConstruction, test and commissioning of the triple-GEM tracking detector for COMPASS

University of Bonn

noteMaster Thesis
titleInvestigations on ASIC readout of MPGDs

journaltitleProceedings of the 2003 ICFA School on Instrumentation, Itacuruca, Brazil
titleAnalog and digital electronics for detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleDesign and results from the APV25, a deep sub-micron CMOS front-end chip for the CMS tracker

journaltitlePhysik-Department E18 Technische Universitat Munchen
titleCommissioning of the GEM Detectors in the COMPASS Experiment

titleVMM3, an ASIC for Micropattern Detectors

IOP Publishing

journaltitleJournal of Instrumentation
titleDevelopment of the scalable readout system for micro-pattern gas detectors and other applications

titleSOFTWARE Manual for VMM3 Slow Control

booktitleIEEE NPSS Short Course, 1993 Nuclear Science Symposium, San Francisco, California
titlePulse processing and analysis
noteFrom electronics-notes.com
titleFlicker, 1/f Noise

Macmillan International Higher Education

titleElectronic noise and low noise design

noteprovided by M. Lupberger.
titleEquivalent noise charge of the VMM hybrid of the Scalable Readout System

Chestnut Ridge, NY

LeCroy Corporation

titleX-Stream Oscilloscopes Remote Control Manual

journaltitleDostupné z WWW: http://optics. eee. nottingham. ac. uk/vxi11
titleVXI11 Ethernet Protocol for Linux
scpi2017r   sonline

titleIntroducing SCPI Commands

titleVMEbus Extensions for Instrumentation: TCP/IP Instrument Protocol Specification VXI-11 Revision 1.0, July 17, 1995, VXIbus Consortium

Lentzeallee, Berlin

BESSY GmbH

titleVXI-11 and HP E2050A A Programmer’s Guide

Agilent Technologies

note(The article can be accessed via the 28 May calendar point in the url)
titleUsing Linux to control LAN-based instruments
family=Karl Jonathan Flöthner,

Rheinische Friedrich-Wilhelms-Universität Bonn

noteMaster Thesis
titleInvestigations of the Triple-GEM-Tracking Detector for COMPASS++/AMBER

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

titleThe ATLAS experiment at the CERN large hadron collider

titleThe CMS experiment at the CERN LHC

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleGEM: A new concept for electron amplification in gas detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleThe COMPASS experiment at CERN

titleThe APV25 deep submicron readont chip for CMS detectors

titleCOMPASS++/AMBER, A new QCD facility at the M2 beam line of the CERN SPS

titleATLAS NSW Electronics Specifications Component: VMM3a

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleImplementation of the VMM ASIC in the Scalable Readout System

journaltitleThe European Physical Journal C-Particles and Fields
titlePassage of particles through matter

titleTechniques for Nuclear and Particle Physics Experiments (1994

titleAstroparticle physics

titleExperimental techniques

titleInstrumentation for high-energy physics

noteFrom StatisticsHowTo.com: Elementary Statistics for the rest of us!
titleLandau Distribution: Definition, Parameters

notePart of a series of lectures offered at the DESY website
titleGaseous detectors

INFN-BARI,	PoliBa

notePart of a series of lectures for a PHD course at INFN-BARI, PoliBa
titleMultiplication and charge avalanche

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titlePosition-sensitive detector with microstrip anode for electron multiplication with gases

Helmholtz-Institut für Strahlen- und Kernphysik

noteMaster Thesis
titleGEM Detectors for the Tracking System of the Missing Energy Experiment NA64 at CERN SPS

journaltitleIEEE Transactions on Nuclear Science
titleTriple GEM tracking detectors for COMPASS

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleConstruction, test and commissioning of the triple-GEM tracking detector for COMPASS

University of Bonn

noteMaster Thesis
titleInvestigations on ASIC readout of MPGDs

journaltitleProceedings of the 2003 ICFA School on Instrumentation, Itacuruca, Brazil
titleAnalog and digital electronics for detectors

journaltitleNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
titleDesign and results from the APV25, a deep sub-micron CMOS front-end chip for the CMS tracker

journaltitlePhysik-Department E18 Technische Universitat Munchen
titleCommissioning of the GEM Detectors in the COMPASS Experiment

titleVMM3, an ASIC for Micropattern Detectors

IOP Publishing

journaltitleJournal of Instrumentation
titleDevelopment of the scalable readout system for micro-pattern gas detectors and other applications

titleSOFTWARE Manual for VMM3 Slow Control

booktitleIEEE NPSS Short Course, 1993 Nuclear Science Symposium, San Francisco, California
titlePulse processing and analysis
noteFrom electronics-notes.com
titleFlicker, 1/f Noise

Macmillan International Higher Education

titleElectronic noise and low noise design

noteprovided by M. Lupberger.
titleEquivalent noise charge of the VMM hybrid of the Scalable Readout System

Chestnut Ridge, NY

LeCroy Corporation

titleX-Stream Oscilloscopes Remote Control Manual

journaltitleDostupné z WWW: http://optics. eee. nottingham. ac. uk/vxi11
titleVXI11 Ethernet Protocol for Linux
scpi2017r   sonline

titleIntroducing SCPI Commands

titleVMEbus Extensions for Instrumentation: TCP/IP Instrument Protocol Specification VXI-11 Revision 1.0, July 17, 1995, VXIbus Consortium

Lentzeallee, Berlin

BESSY GmbH

titleVXI-11 and HP E2050A A Programmer’s Guide

Agilent Technologies

note(The article can be accessed via the 28 May calendar point in the url)
titleUsing Linux to control LAN-based instruments
family=Karl Jonathan Flöthner,

Rheinische Friedrich-Wilhelms-Universität Bonn

noteMaster Thesis
titleInvestigations of the Triple-GEM-Tracking Detector for COMPASS++/AMBER

§ CURRICULUM VITAE

§.§ Personal Details

Name     Johann Schmidt

Date of Birth

Email<EMAIL_ADDRESS>
Family status     Single

§.§ Education

1997–2003     Abitur, ABC Secondary School, Hamburg, Germany

2004–2007     BSc in Physics, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany.

2006     CERN Summer Student, Geneva, Switzerland.

2007–2009      MSc in Physics Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany.

2009–2012      PhD in Physics, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany.

2012     Advanced Data Analysis School, Frankfurt, Germany.

§.§ Professional Experience

2004     Summer Student at CERN, Geneva, Switzerland.

2007–2012     Doctoral work at the University of Bonn, Germany.

2008–2009     Fieldwork at CERN, Geneva, Switzerland.

2011     Talk at the Advanced Physics Conference, Timbucto

§.§ Languages

German     Mother tongue

English     Fluent

Russian     Basic


# Contrastive Learning of Temporal Distinctiveness for Survival Analysis in
Electronic Health Records

Mohsen Nayebi Kerdabadi<EMAIL_ADDRESS>University of
KansasLawrenceKSUSA ,  Arya Hadizadeh Moghaddam<EMAIL_ADDRESS>University of KansasLawrenceKSUSA ,  Bin Liu<EMAIL_ADDRESS>West
Virginia UniversityMorgantownWVUSA ,  Mei Liu<EMAIL_ADDRESS>University of
FloridaGainesvilleFLUSA and  Zijun Yao<EMAIL_ADDRESS>University of
KansasLawrenceKSUSA

(2023)

###### Abstract.

Survival analysis plays a crucial role in many healthcare decisions, where the
risk prediction for the events of interest can support an informative outlook
for a patient’s medical journey. Given the existence of data censoring, an
effective way of survival analysis is to enforce the pairwise temporal
concordance between censored and observed data, aiming to utilize the time
interval before censoring as partially observed time-to-event labels for
supervised learning. Although existing studies mostly employed ranking methods
to pursue an ordering objective, contrastive methods which learn a
discriminative embedding by having data contrast against each other, have not
been explored thoroughly for survival analysis. Therefore, in this paper, we
propose a novel Ontology-aware Temporality-based Contrastive Survival
(OTCSurv) analysis framework that utilizes survival durations from both
censored and observed data to define temporal distinctiveness and construct
negative sample pairs with varying hardness for contrastive learning.
Specifically, we first use an ontological encoder and a sequential self-
attention encoder to represent the longitudinal EHR data with rich contexts.
Second, we design a temporal contrastive loss to capture varying survival
durations in a supervised setting through a hardness-aware negative sampling
mechanism. Last, we incorporate the contrastive task into the time-to-event
predictive task with multiple loss components. We conduct extensive
experiments using a large EHR dataset to forecast the risk of hospitalized
patients who are in danger of developing acute kidney injury (AKI), a critical
and urgent medical condition. The effectiveness and explainability of the
proposed model are validated through comprehensive quantitative and
qualitative studies.

Survival Analysis, Contrastive Learning, Electronic Health Records

††journalyear: 2023††copyright: rightsretained††conference: Proceedings of the
32nd ACM International Conference on Information and Knowledge Management;
October 21–25, 2023; Birmingham, United Kingdom††booktitle: Proceedings of the
32nd ACM International Conference on Information and Knowledge Management
(CIKM ’23), October 21–25, 2023, Birmingham, United Kingdom††doi:
10.1145/3583780.3614824††isbn: 979-8-4007-0124-5/23/10††ccs: Information
systems Data mining††ccs: Applied computing Health informatics

##  1\. Introduction

The increasingly abundant electronic health records (EHRs) have provided an
unprecedented opportunity to apply predictive analytics to support healthcare
decisions (Yadav et al., 2018; Rajkomar et al., 2018). To achieve the optimal
outcomes for a patient’s medical journey, an important question faced by
healthcare providers is how to precisely anticipate the adversarial events
(e.g., kidney injury, heart failure, and stroke), so that these critical
incidents can be responded to timely with sufficient clinical attention.
Therefore, it is crucial to investigate the application of survival analysis
(SA) in longitudinal EHR data, which aims to identify the significant factors
that influence the degree of risks and to further forecast the time to events
of interest.

For survival analysis, a key challenge is how to deal with the existence of
censored data for time-to-event modeling. In the case of censoring, events of
interest may not be observed for some patients due to the limited duration of
observation or the withdrawal of patients during the study. In order to
address this challenge, various traditional survival analysis models have been
developed although they suffer from multiple limitations. Parametric survival
models (Mittal et al., 2013) assume a specific distribution for the baseline
hazard function, such as the exponential, Weibull, or log-normal distribution.
However, events in the real world are usually too complex to be captured by
such predefined distributions. On the other hand, although the semi-parametric
Cox model (Cox, 1972a) makes no assumptions about the baseline hazard
function, it requires the hazard function to be multiplicatively proportional
to the covariates. Moreover, most of these approaches (e.g., Cox-based models)
only focus on predicting the relative ordering of survival durations of
individuals, overlooking their actual event time. Therefore, the capability of
time estimation for future event occurrences is unfortunately compromised.

To overcome the limitations of early studies, deep learning techniques have
been increasingly applied to survival predictive tasks (Ren et al., 2019;
Giunchiglia et al., 2018; Lee et al., 2018) which offer the capacity to
capture complex survival patterns without making explicit distributional
assumptions. While some studies have explored the enforcement of patient
concordance by survival probabilities to accommodate both observed and
censored survival data, there exists very limited literature on contrastive
learning (CL) methods aimed at learning a discriminative representation of
patient records to achieve better predictive performance. In contrastive
learning, data are contrasted against each other in self-supervised (Chen et
al., 2020), semi-supervised (Zhang et al., 2022), or supervised (Khosla et
al., 2020) settings. Generally, it trains an objective to distinguish the
subtle characteristics in data, by maximizing the similarity between positive
pairs (instances that belong to the same labels) and minimizing the similarity
between negative pairs (instances that have different labels). Although the
positive vs. negative labeling strategy for contrasted pairs has been defined
by self-augmentation (i.e., whether the pair originates from a single data
point) or supervised classes (Hong et al., 2022) (i.e., whether the pair
belongs to the same class), the exploration of contrasting labeling based on
temporal distinctiveness (which is based on the time difference between the
two survival durations) for survival analysis is still lacking. Furthermore,
given that survival duration is a numerical entity, accounting for the
hardness defined by the time difference for contrastive labels can help the
model learn the survival data with more flexibility.

Another challenge associated with survival analysis in EHR is the possible
data insufficiency. Usually, a large variety of medical codes are recorded in
a dataset, but many codes may have a relatively small number of occurrences
(e.g., rare diseases). As a result, for patients with rare codes or sparse
visits, the embedding of their medical history is often sub-optimal. One way
to address this issue is to incorporate the domain-specific knowledge inherent
in medical ontology into the representation of EHR features (Yao et al.,
2023). Medical ontology is a hierarchical classification structure of medical
concepts (e.g., diagnosis, medications, etc.), which can serve as an auxiliary
categorization for knowledge representation (Choi et al., 2017; Ma et al.,
2018; Song et al., 2019). For example, GRAM (Choi et al., 2017) proposes a
graph-based attention model that employs the attention mechanism on
hierarchical levels of each medical code to learn medically meaningful EHR
feature embeddings. With ontological encoding, survival models can better
build the association between codes or patients, and transfer the medical
knowledge from one sample to another. Therefore, to further improve the
quality of patient profiling, the ontology learning of EHR features can be
integrated with the contrastive learning core of survival analysis.

In this paper, we introduce an Ontology-aware Temporality-based Contrastive
Survival analysis framework called OTCSurv, which combines the ontology-
enhanced EHR data encoder, the contrastive learning of temporal
distinctiveness, and the survival probability predictor with multiple loss
components, for interpretable, data-efficient, and discriminative survival
analysis. Specifically, the main contributions of this study can be summarized
in three-fold:

  * •

We design a Supervised Weighted Contrastive (SupWCon) Learning loss function
that uses survival duration as its pairing criteria which is able to utilize
both observed and censored observations. SupWCon considers the hardness of
negative pairs based on the survival duration differences to enrich the grain
of contrastive learning.

  * •

We used a sequential attention-based ontological encoder to learn medically
informed embeddings for sequential hospital visits of patients. Ontology
information brings data efficiency to our model by referring to higher-level
medical concepts when the observation is sparse.

  * •

We optimize survival prediction through multiple loss components, focusing on
two key goals: accurately predicting survival duration time and precisely
ranking the risks or survival probabilities of patients at each time point. We
train our model with a meticulous configuration of SupWCon, accompanied by
three more loss functions, guiding the training towards an optimum point
satisfying these two goals.

Finally, we evaluate our proposed method and demonstrate the strength of our
model on a real-world EHR dataset for Acute Kidney Injury (AKI) by performing
baseline comparison, ablation study, and interpretability analysis.

##  2\. Related Work

In this section, we provide an overview of key contributions and advancements
in the survival analysis field, concentrating on relevant methodologies and
techniques in the literature.

One of the most widely used statistical methods in survival analysis is the
Kaplan-Meier (KM) estimator (Kaplan and Meier, 1958) which is a non-parametric
survival analysis method, calculating the survival probability by dividing the
number of individuals who have survived up to a given time by the number of
patients at risk just before that time. However, KM does not take into account
the covariates of patients. Early works in survival analysis primarily
revolved around the Cox proportional hazards (CPH) model (Cox, 1972b), which
assumes a proportional relationship between covariates and the hazard
function. Due to the advantages of CPH, such as simplicity and
interpretability, many survival analysis models have been proposed based on
CPH, such as incorporation of time-varying covariates (Lin and Zelterman,
2002), accounting for competing risks (Fine and Gray, 1999), and CoxTime
(Kvamme et al., 2019) which expands upon Cox model by extending its
capabilities beyond the assumption of proportional hazards.

In recent years, there has been an increasing interest in applying machine
learning techniques to survival analysis. Random Survival Forests (Ishwaran et
al., 2008), Deep Exponential Families (Ranganath et al., 2016, 2015), and
semi-parametric Bayesian models based on Gaussian Processes (Fernández et al.,
2016), offer flexibility in capturing complex survival patterns and handling
non-linear relationships. As for deep learning-based approaches, DeepSurv
(Katzman et al., 2018) introduced the application of deep neural networks for
survival prediction, capturing complex relationships between covariates and
survival outcomes using the Cox partial likelihood loss function. This has
opened up many doors for utilizing deep learning in survival analysis, leading
to the development of models like DeepHit (Lee et al., 2018), which is a
multitask deep learning model capable of handling competing risks, DRSA (Ren
et al., 2019) and RNN-SURV (Giunchiglia et al., 2018), both of which
exploiting a recurrent neural network (RNN) to handle sequential data, and
N-MTLR (Fotso, 2018) which leverages deep neural networks to replace the
linear core of the MTLR (Yu et al., 2011).

Some more recent state-of-the-art deep learning-based SA models are Dynamic-
DeepHit (Lee et al., 2019), Survtrace (Wang and Sun, 2022), and Deep-CSA (Hong
et al., 2022). An extension of DeepHit is Dynamic-DeepHit which instead of the
simple neural network, uses a recurrent neural network to dynamically capture
longitudinal dependencies in the presence of competing risks. Survtrace
proposes a transformer-based SA model that handles competing risks and
benefits from a multi-task learning framework to learn a strong shared
representation. Transformer-Based Deep Survival Analysis (Hu et al., 2021)
tries to make a trade-off between time predictive power and risk ranking power
using both the absolute error as well as ranking evaluation metrics.

Generally, the existing architectures suffer from multiple limitations. Some
works, such as Cox-based survival models, show suboptimal performances due to
certain assumptions for the underlying stochastic process. Violations of these
assumptions can lead to incorrect conclusions. Some of the deep learning
methods are black boxes and do not offer sufficient interpretability. Also,
many works only employ ranking methods to reach survival rate concordance and,
to the best of our knowledge, there is no exploration of the use of
contrastive methods based on the temporality for healthcare survival analysis.
OTCSurv managed to mitigate the aforementioned challenges and support
interpretable, data- efficient, and discriminative survival analysis. As
demonstrated in the following sections, OTCSurv exhibits an enhanced
performance compared to its predecessors.

##  3\. Proposed Method

In this section, we first describe the notations and formulate the EHR
survival analysis problem. We then present the overview of the model. Last, we
introduce each module in detail.

Figure 1. Architecture of the proposed OTCSurv model. There are three main
components: 1) Sequential attention-based ontological encoder, which mainly
consists of an ontological encoder, two attention-pooling blocks, and a
transformer encoder to learn the ultimate instance-level representations of
patients. 2) Contrastive Learning, which uses an intermediary transformation
to transfer the ultimate representations to another latent space where SupWCon
is functioning. 3) Survival prediction, which is a fully connected neural
network and outputs the probabilities necessary for survival analysis
calculation.

###  3.1. Problem Formulation

Electronic healthcare records (EHRs) usually contain comprehensive information
about a patient’s medical history. Each patient normally has multiple hospital
visits where diagnoses, prescriptions, and procedures are recorded using
standardized codes in the hospital’s database. EHRs can be exploited in three
sets of information to be used in survival analysis: 1) covariates, 2) time to
the event, and 3) a label indicating the type of the event
(censored/observed). A discrete and finite time window with a maximum length
of $T_{\text{max}}$ is considered for the time prediction. Therefore, our goal
is to predict in which time interval $t\in\\{0,\ldots,T_{\text{max}}\\}$ the
event of interest is most likely to happen, or to determine the probability of
survival in each time interval. We show the event label by a binary variable
$k$. If the instance is observed $k=1$, otherwise (censored) $k=0$. We can
consider each instance (i.e., patient) as a triple of $(V,t,k)$ where
$V=\\{v_{n}\\}_{n=1}^{N}$ is a sequence of covariates showing $N$ visits, and
$v_{n}=\\{c_{1},c_{2},\ldots,c_{|C|},d_{1},d_{2},\ldots,d_{|\mathcal{D}|}\\}$
indicating the existence of both binary and continuous features. Binary
medical codes are denoted by $c_{i}$, and continuous features such as
demographics are denoted by $d_{j}$ where $|C|$ and $|\mathcal{D}|$ represent
the sizes. For each medical code $c_{i}$, we extract the set of its ancestor
codes (higher level concepts) in the hierarchy of the medical ontology,
represented as a directed acyclic graph (DAG).

We denote the probability by $P$, the hazard function by $\lambda(t)$, the
probability density function by $f(t)$, and the survival probability by
$S(t)$. By adding the caret symbol to each notation, we indicate their
estimated forms, e.g., $\hat{S}(t)$ is the estimated survival probability.

Task: Given the patient’s sequential medical history in terms of longitudinal
hospital visits containing medical codes, we aim to build a model to estimate
the survival probability of patients in each time interval inside the
prediction time window in the future.

###  3.2. Model Overview

In this subsection, we introduce an overview of our proposed OTCSurv model
architecture. As shown in Figure 1, the model consists of three main
components. The first component is Sequential attention-based ontological
encoder that consists of two main blocks. The first one is the ontological
encoder which effectively utilizes the inherent valuable information within
the medical ontologies to generate informed embedding vectors for medical
codes. Next is the sequential attention encoder which consists of three
attention-based parts: visit-level attention-pooling, transformer encoder, and
instance-level attention-pooling. The visit-level attention-pooling uses the
attention mechanism to reduce the dimension of the visit representations.
Then, the output of the visit-level attention-pooling integrates with
demographic information inside a data integration block to produce a
representation containing all the patient’s information. This representation
along with positional encoding of visits is fed to the transformer encoder.
The multi-head attention of the transformer will extract the interactions of
medical visits to produce a rich representation of a patient that encompasses
all the meaningful information. Instance-level attention-pooling is
implemented on the output of the transformer encoder, to compress and combine
the information of different visits of an instance using the attention
mechanism and produce the ultimate instance representation. This ultimate
instance representation will go through the second and the third main
components of OTCSurv parallelly. One is Contrastive Learning component (the
second main component) where a projection head which is a nonlinear
transformation, e.g., a simple multilayer perceptron (MLP) with a nonlinear
activation function, transfers the ultimate instance representation to a
different latent space. This is where our proposed SupWCon loss comes into
play, adding temporal distinctive refinements to the ultimate representations.
In parallel, the ultimate representation is fed into the Survival Prediction
component (the third main component) which consists of a fully connected
neural network. This neural network predicts $T_{\text{max}}$ number of
probabilities, which are the complement of the hazard rates, for each of the
$T_{\text{max}}$ predefined time intervals. To train this model, combined with
SupWCon, three loss functions of Loglikelihood Loss, Pairwise Ranking Loss,
Mean Squared Error loss are implemented to guide the model towards an optimum
point regarding predictive, discriminating, and ranking ability in survival
analysis.

###  3.3. Sequential Attention-based Ontological Encoder

The sequential attention-based ontological encoder is responsible for
generating instance representations using attention-based components which are
explained hereunder.

####  3.3.1. Ontological Encoder

In order to address the challenge of data limitation in the healthcare domain,
acquire comprehensive representations of medical codes, and increase
predictability, we utilize the attention-based graph representation approach
known as GRAM (Choi et al., 2017). First, an initial embedding vector
$h_{j}\in\mathbb{R}^{d_{c}}$ is assigned to each medical code as well as its
ancestors (higher lever concepts) in the medical ontology, where $d_{c}$ is
the code embedding dimension. Then, each code’s final representation
$q_{i}\in\mathbb{R}^{d_{c}}$ is calculated as a convex combination of the
initial embeddings of itself and its ancestors using the attention mechanism:

(1) $q_{i}=\sum_{j\in A(i)}\alpha_{ij}h_{j},\ \ \sum_{j\in
A(i)}\alpha_{ij}=1,\ \ \alpha_{ij}\geq 0\ \ for\ \ j\in A(i)$

where $A(i)$ is the set containing the indices of the code $c_{i}$ and its
ancestors. $\alpha_{ij}\in\mathbb{R}^{+}$ shows the attention weight given to
ancestor code embedding $c_{j}$ when calculating $q_{i}$, which is the final
representation of $c_{i}$. Using a Softmax function, $\alpha_{ij}$ is
formulated as:

(2) $\alpha_{ij}=\frac{\exp(f(h_{i},h_{j}))}{\sum_{k\in
A(i)}\exp(f(h_{i},h_{k})}$ (3)
$f(h_{i},h_{k})=\omega^{T}_{\alpha}\tanh({W_{\alpha}Concat(h_{i};h_{k})+b_{\alpha}})$

where $Concat(h_{i};h_{k})$ is the concatenation of $h_{i}$ and $h_{j}$ in a
child-ancestor order. $f(\cdot)$ is an MLP operator with learnable parameters
of $\omega_{\alpha},W_{\alpha},b_{\alpha}$.

####  3.3.2. Attention-Pooling

We used two attention-pooling components in our architecture, one after the
ontological encoder, which is the visit-level attention-pooling, and one after
the transformer encoder, which is the instance-level attention-pooling, to
compress the information flow using the attention mechanism.

Assumes that the input of visit-level attention-pooling for a patient $i$ is a
tensor $E_{i}\in\mathbb{R}^{N\times M\times d_{c}}$, where $N$, $M$, $d_{c}$
are the number of visits, the specified maximum number of possible codes
inside each visit, and the dimension for the code embedding111We omit the
patient index $i$ in the following notation for easier demonstration.,
respectively. Using the attention mechanism, we assign a weight to each code
in a visit and use those weights to calculate the weighted average of medical
code vectors. Thus instead of having a vector of size $(N\times M\times
d_{c})$ for each patient, we reduce its dimension to a vector of size
$(N\times d_{c})$. So, given the $n$-th visit representation
$v_{n}\in\mathbb{R}^{M\times d_{c}}$, which is the concatenation of M code
embeddings $q^{n}_{m}$ ($1\leq m\leq M$), we calculate an attention energy
$e^{n}_{m}\in\mathbb{R}$ for each of $M$ medical code embedding:

(4) $e^{n}=l(v_{n})=W_{2}\sigma(v_{n}W_{1}+\beta_{1}),\ \ 1\leq n\leq N$

where $e^{n}\in\mathbb{R}^{M\times 1}$ contains M attention energies for the
codes within $n$-th visit, and $l(\cdot)$ is a MLP operater with a ReLU
activation function $\sigma$ and learnable parameters of $W_{1}$, $W_{2}$,
$\beta_{1}$. Using softmax on attention energies, we calculate attention
weights $\alpha^{n}\in\mathbb{R}^{M\times 1}$:

(5) $\alpha^{n}=\text{softmax}(e^{n})$

where $\alpha^{n}$ is the concatenation of M attention weights
$\alpha_{m}^{n}$ ($1\leq m\leq M$). Finally, we have

(6) $p^{n}=\sum_{i=1}^{M}\alpha^{n}_{m}q_{m}^{n}$

where $p^{n}\in\mathbb{R}^{d_{c}}(1\leq n\leq N)$ represents the $n$-th visit
of the patient. So, for each patient, we have $P\in\mathbb{R}^{N\times d_{c}}$
as the concatenation of $N$ visit representations
$p^{n}\in\mathbb{R}^{d_{c}}$. The output of the visit-level attention block
$P\in\mathbb{R}^{N\times d_{c}}$ is concatenated with each patient demographic
embedding $s\in\mathbb{R}^{N\times d_{s}}$ ($d_{s}$ is the dimension for the
demographic feature embedding) to obtain
$F=\text{Concat}(P,s)\in\mathbb{R}^{N\times d}$ where $d=d_{c}+d_{s}$.

For the instance-level attention-pooling which is implemented on the output of
the transformer encoder, we use the same technique described above to reduce
the dimensionality. The output of the transformer encoder for a patient is
$U\in\mathbb{R}^{N\times D}$, where $D$ is the transformer dimension. $U$ is
fed to the instance-level attention-pooling, where using the attention
mechanism, $N$ attention weights for each of the visit representations are
generated. These weights are used to calculate the weighted average of visit
representations, thereby reducing the dimension of $U$, outputting
$u\in\mathbb{R}^{D}$ as the ultimate instance (patient) representation to be
used in both the contrastive task and the survival prediction downstream task.

####  3.3.3. Transformer Encoder

The encoder of the transformer architecture serves as the primary block for
obtaining representations for survival analysis. For each patient, the input
to the encoder of the transformer is a sequence of final visits’ embeddings.
The transformer’s multihead-attention mechanism captures complex relationships
among different hospital visits of a patient, enabling the model to encode
comprehensive information about their dependencies over time. This results in
rich representations that can capture survival patterns and time-dependent
features.

###  3.4. Temporal Distinctiveness with Supervised Weighted Contrastive
Learning

Contrastive learning aims to learn meaningful representations by maximizing
agreement between similar examples while minimizing agreement between
dissimilar examples. One technique to measure the similarity between two
vectors is the cosine similarity, which can be calculated by the dot product
of two vectors. It calculates the cosine of the angle between two vectors,
representing their similarity by assessing how closely the two vectors align
in the vector space. In this study, we formulate a contrastive learning loss
function featuring an adaptive temperature parameter, referred to as
Supervised Weighted Contrastive (SupWCon) loss. SupWCon is an extended version
of the method proposed in (Khosla et al., 2020) and has been tailored for
survival analysis, particularly for handling censored data. We formulate

(7) $L^{\text{SupWCon }}=\sum_{i\in I}\frac{-1}{|P(i)|}\sum_{p\in
P(i)}\log\frac{\exp\left(\boldsymbol{z}_{i}\cdot\boldsymbol{z}_{p}/\tau\right)}{\sum_{a\in
A(i)}\exp\left(\boldsymbol{z}_{i}\cdot\boldsymbol{z}_{a}/\tau_{ia}\right)}$

where $I$ is the set of indices of all the instances, $P(i)$ is the set of
indices of the instances that make a positive pair with the instance $i$, and
$A(i)\equiv I$ \$\\{i\\}$. The dot ($\cdot$) operator in the formulation
represents the dot product of two vectors. $\tau\in\mathbb{R}^{+}$ is the
constant scalar temperature parameter for positive pairs and
$\tau_{ia}\in\mathbb{R}^{+}$ is the adaptive scalar temperature parameter for
negative pairs which will be explained shortly. The instance with the index
$i$ is called the anchor. Positive and negative pairs were particularly
generated considering both the survival duration times and the labels of
instances (observed/censored). For anchor $i$, which is an observed instance,
any other observed instance with the survival duration time $t$ (which is the
duration from day one to the day before the event time) inside the time window
of $T_{i}-T/2\leq t<T_{i}+T/2$ (referred to as positive window) makes a
positive pair with the anchor and belongs to $P(i)$. Time window length $T$ is
a hyperparameter that needs to be tuned with respect to the $T_{\text{max}}$,
data distribution, and the nature of the problem. Any observed instance with a
survival duration time $t$ outside the positive window ($t<T_{i}-T/2$ or
$T_{i}+T/2\leq t$) plus any censored instance with the survival duration time
(which is the duration from day one to the day of censoring) greater or equal
to $T_{i}+T/2$ ($T_{i}+T/2\leq t$) makes a negative pair with the anchor. We
do not consider censored instances with a censoring time smaller than
$T_{i}+T/2$ for both positive and negative pair generation because what
happened to the patient after censoring is unknown (whether they were
diagnosed with AKI or not, and if so when that happened). In fact, if, after
censoring, the event (AKI) happens inside the positive window of the anchor,
making a negative pair is wrong. Conversely, for patients with a censoring
time greater or equal to $T_{i}+T/2$, we are sure that their survival duration
is outside of the positive window of the anchor, so they are safe to be
considered for negative pair generation.

The temperature parameter for positive pairs $\tau$ is a constant positive
scalar for all positive pairs and will be chosen by hyperparameter tuning.
However, we adjusted the temperature parameter for each negative pair to
encourage our model to regulate the amount of dissimilarity between the
representations of negative pairs that exhibit various differences in survival
duration. Hence, the model can better capture the distinction for negative
pairs of various hardness. For example, if patient $i$ and patient $j$ make a
negative pair, the adjusted temperature parameter for this negative pair is
calculated as follows:

(8) $\tau_{ij}=|T_{i}-T_{j}|^{-1}$

which is the inverse of their difference in survival duration. The more
distant their survival duration is, the more SupWCon pulls their
representations apart in the latent space. This is the first time in the
context of survival analysis, to the best of our knowledge, that contrastive
learning is used to make hardness-aware temporal distinctiveness based on the
known survival duration of subjects.

We used two more tricks that have been established as effective in the
literature regarding contrastive learning. First, introducing a learnable
nonlinear transformation, such as a simple two-layer fully connected neural
net with a nonlinear activation function, between the ultimate instance
representation and where the SupWCon loss performs. This trick substantially
improves the quality of the ultimate instance representations compared to when
the SupWCon performs directly on them (Chen et al., 2020)222The work in (Chen
et al., 2020) conjectures that the importance of using the representation
before the nonlinear projection is due to loss of information induced by the
contrastive loss on the direct vectors that contrastive loss is working on..
Second, we normalized the vector representations of instances onto the unit
sphere ($l_{2}$ normalization) prior to using them in SupWCon, which also
experimentally proved to be effective (Chen et al., 2020).

It is noteworthy that the contrastive learning component is only used during
training to add hardness-aware distinctive refinements to the ultimate
representations and is discarded during inference.

###  3.5. Survival Prediction

For continuous survival models, the hazard function, denoted as $\lambda(t)$,
represents the instantaneous probability of an event occurring at time $t$,
given that the individual has survived up to time $t$. However, in the
discrete setting, where time is considered as a sequence of distinct points,
the hazard function is defined differently. Instead of dealing with
infinitesimal intervals, the hazard function represents the conditional
probability that the patient dies at a specific time $t$, given he/she was
alive before $t$. Given that training data consists of pairs of covariates and
time $(x,t)$, our goal is to model the distribution of event times. The
probability density function $f(t|x)$, the survival function $S(t|x)$, and the
hazard function $\lambda(t|x)$ respectively are defined as:

(9) $f(t|x)=P_{x}(T=t)$

which represents the probability mass assigned to an event occurring exactly
at time $t$,

(10) $S(t|x)=P_{x}(T>t)$

which gives the probability that an event has not occurred up to and including
time $t$, and finally the hazard function formulation,

(11) $\begin{split}\lambda(t|x)&=P_{x}(t=T|T>t-1)\\\
&=\frac{f(t|x)}{S(t-1|x)}=\frac{S(t-1|x)-S(t|x)}{S(t-1|x)}\end{split}$

Using the above formulation, we can rewrite the survival function formulation
as follows:

(12) $S(t|x)=(1-\lambda(t|x))S(t-1|x)$

If we show the complement of hazard function by $r(t|x)=1-\lambda(t|x)$, we
have:

(13) $S(t|x)=r(t|x)S(t-1|x)$

By recursively expanding on equation 13, the survival function can be
expressed as:

(14) $S(t|x)=\prod_{s=1}^{t}r(s|x)$

A feed-forward neural network (FFN) is the core of the survival prediction
component, which predicts the complement of the hazard function $r(t|x)$ for
all times up to $T_{max}$. Thus, the output of the survival prediction
component for a patient $i$ is a vector of size $T_{max}$ as follows:

(15) $\hat{y_{i}}=[\hat{r_{i}}(t|x)]_{t=1}^{T_{\text{max}}}$

In continuous-time survival analysis, the mean lifetime of a patient or the
expected value of the random variable $T$, which represents the average time
until an event occurs, can be calculated by integrating the survival function
over time. Mathematically, the mean lifetime $\mu$ (also known as the expected
lifetime or average survival time) is derived in the following manner:

(16) $\hat{\mu}=\int_{0}^{\infty}t\cdot
f(t|x)\,dt=\int_{0}^{\infty}t\cdot(S(t|x).\lambda(t|x))\,dt$

Using the technique of integration by parts, we arrive at,

(17) $\hat{\mu}=\int_{0}^{\infty}S(t|x)\,dt$

which is the area under the survival curve. In the discrete-time formulation,
we can approximate it by the sum of the survival probabilities up to $T_{max}$
as follows:

(18)
$\hat{\mu}\approx\sum_{t=1}^{T_{\text{{max}}}}\hat{S}(t|x)=\sum_{t=1}^{T_{\text{{max}}}}\prod_{s=1}^{t}\hat{r}(s|x)$

We consider $\hat{\mu}$ as our predicted survival time duration.

###  3.6. Loss Functions

In this section, we will expand upon different loss functions implemented to
train our model. Besides the SupWCon loss which was explained in 3.4, we have
three more losses working in combination with SupWCon. The motivation is to
optimize the model with respect to the two important objectives of survival
analysis: 1) accuracy in the prediction of survival duration for observed
data, and 2) accurately ranking patients (both observed and censored) in terms
of their risk and survival rate in different time points.

####  3.6.1. Loglikelihood Loss

Loglikelihood loss is the main loss used to train the survival task. For
observed data points, we minimize the following loss:

(19)
$L^{\text{Loglikelihood}}_{\text{ob}}=-\sum_{t=1}^{T-1}\log\hat{S}(t|x)-\sum_{t=T}^{T_{\text{{max}}}}\log(1-\hat{S}(t|x))$

and for censored data, the loss is defined as follows:

(20) $L^{\text{Loglikelihood}}_{\text{cen}}=-\sum_{t=1}^{T}\hat{S}(t|x)$

(21)
$L^{\text{Loglikelihood}}=L^{\text{Loglikelihood}}_{\text{cen}}+L^{\text{Loglikelihood}}_{\text{ob}}$

where $T$ is either event time or censoring time. In other words, for observed
data points, we maximize the summation of the survival probabilities for
$1\leq t<T$ (since the patient has survived in this time window) and minimize
the summation of the survival probabilities for $t\geq T$ (which means there
is no survival starting from the occurrence of the event). For censored data
points, we only maximize the summation of the survival probabilities for
$1\leq t\leq T$. In essence, for observed instances, the survival
probabilities of all the time intervals are optimized, whereas for censored
data, only the survival probabilities up to $T$, which is the time of
censoring, are optimized. This is because, after censoring time, we do not
have any information about the survival of the patients.

####  3.6.2. Pairwise Ranking Loss

We employ a pairwise ranking loss function that incorporates the concept of
concordance and is based on the method used in (Hu et al., 2021). Such ranking
losses have been widely used in the literature (Lee et al., 2018, 2019) for
survival analysis. According to this idea, a patient who experiences an event
at time $s$ should have a shorter predicted survival duration time (a higher
risk) at time s compared to a patient who survives beyond time s. In other
words, we want to penalize the discordant pairs. Let $T_{i}$ and $T_{j}$
represent the observed event times for patients i and j, and respectively,
$T_{i}<T_{j}$. The predicted survival durations $\hat{T}_{i}$ and
$\hat{T}_{j}$ (obtained from Eq. 18) are considered discordant if
$\hat{T}_{i}>\hat{T}_{j}$. Our aim is to minimize the number of such
discordant pairs. For every observed patient $i$ in the training set, we
randomly select (with replacement) another patient $j$, ensuring that
$T_{i}<T_{j}$. we only compare them with one other randomly selected data
point since comparing with all the possible data points is too computationally
expensive. As $T_{j}$ can be subject to censoring, the actual survival
duration for patient $j$ cannot be smaller than $T_{j}$. Consequently, the
difference between the predicted durations $\hat{T}_{i}$ and $\hat{T}_{j}$
should be at least $T_{j}-T_{i}$. Hence, the ranking loss formulation is as
follows:

(22)
$L^{\text{Ranking}}=\text{max}(0,(T_{j}-T_{i})-(\hat{T}_{j}-\hat{T}_{i}))$

####  3.6.3. Mean Squared Error (MSE) Loss

MSE Loss penalizes wrong predicted survival duration times for only observed
data points. This loss ensures that the proposed model performs well at
accurate time prediction for observed patients instead of only being able to
rank patients in terms of their risk. Therefore, for observed patients, MSE is
calculated as follows:

(23)
$\text{MSE}=\frac{1}{N_{\text{ob}}}\sum_{i=1}^{N_{\text{ob}}}(T_{i}-\hat{T}_{i})^{2}$

where $N_{\text{ob}}$ is the number of observed instances, $T_{i}$ is the true
survival duration, and $\hat{T}_{i}$ is the predicted survival duration
obtained as $\hat{\mu}$ from equation 18.

##  4\. Experiments

###  4.1. Dataset and Preprocessing

We test our model on a real-world EHR dataset acquired from the University of
Kansas Medical Center (KUMC) gathered from early 2009 to late 2021 for the
purpose of the Acute Kidney Injury (AKI) study. In this dataset, each patient
has a history of one year of hospital visits before the final hospital visit,
called the onset visit, which was monitored for the occurrence of AKI. Each
hospital visit comprises a collection of documented medical codes. Diagnosis
codes were recorded using the International Classification of Diseases system
in both the ninth and tenth Revisions (ICD-9 & ICD-10). The prescription codes
follow the RxNorm format, which provides standardized names for clinical
drugs. After preprocessing, we acquired a dataset with the statistics
demonstrated in table 1. Since the dataset is highly imbalanced, we balance
the training dataset by duplicating the observed data so we have a 50%
censored-50% observed train set. For implementing the GRAM method, we used the
hierarchical ontology of ICD-9333In preprocessing, all the ICD-10 codes were
converted to ICD-9. and the Anatomical Therapeutic Chemical (ATC)
classification system respectively for diagnosis codes and prescription codes.

Table 1.  Dataset Statistics

Number of patinets 56779 Number of censored patients 47773 (84.1%) Number of
observed patients 9006 (15.8%) The average age of patients 59.47 Sex of
patients distribution (52% M, 48% F) Average number of medical codes in a
visit 13.29 Average number of medical codes in a patient 66.46

###  4.2. Experimental Setting

Conducting a hyperparameter tuning, we chose $128$ as the dimension of code
embeddings for the ontological encoder. Two layers of transformer encoder each
with two heads of multihead-attention are selected for the main encoder with a
hidden dimension of $512$, which outputs a representation vector of size
$256$. The survival prediction part is a three-layered fully connected neural
network with hidden dimensions of $[256,128,9]$ which outputs 9 probabilities
for each instance ($T_{\text{max}}=9$). Every probability is for a unit of
time interval as one day. $T_{\text{max}}$ was chosen $9$ because $96\%$ of
hospitalized patients were diagnosed with AKI or discharged (censored) in $9$
days. RMSprop optimizer with a learning rate of $1e-3$ and weight decay of
$2e-5$ was employed for training the proposed model. For implementing SupWCon,
after a thorough hyperparameter search, we chose a time window length of $2$
as the positive contrastive pairing criteria. As for the training strategy, We
let the model first run for $40$ epochs with loglikelihood, ranking, and MSE
losses, and then add the SupWCon loss and train for $50$ more epochs. This
strategy gives us the best performance. As mentioned earlier, the contrastive
component is discarded during inference. We released the GitHub implementation
code of OTCSurv.444https://github.com/mohsen-nyb/OTCSurv.git

###  4.3. Evaluation Metrics

The model was evaluated with two main metrics: the time-dependent
discrimination index $C^{td}$(Antolini et al., 2005), and the Mean Absolute
Error (MAE). The time-dependent discrimination index $C^{td}$, which is one of
the most widely used evaluation metrics in survival analysis, is an extension
of Harrell’s concordance index (C-index). $C^{td}$, unlike the conventional
c-index, assesses the model’s discriminatory ability at specific time points,
capturing changing predictive performance over time. Also, we used the MAE of
the predicted survival duration to express the model’s performance in
estimating the exact survival duration for observed data.

###  4.4. Results and Discussion

Figure 2. Comparison of the mean survival curves of proposed model and
baselines with Kaplan-Meier curve (for all patients). Figure 3. Comparison of
the mean survival curves of proposed model and baselines with Kaplan-Meier
curve (only for observed patients).

####  4.4.1. Baselines

We compare the results of our model with various popular baselines, which are
introduced below briefly. Table 2 shows the performance of each model on the
AKI survival analysis task. It is evident that our proposed model outperforms
all of the baselines regarding both evaluation metrics. Also, Figure 2 and
Figure 3 exhibit the comparison of the mean survival curves of each model with
the Kaplan-Meier curve, which is the survival curve based on true data. Our
proposed model’s mean survival curve is the closest to the Kaplan-Meier curve
considering all the data as well as only observed data, indicating that our
model accurately captures the survival behavior and provides survival
predictions that are more consistent with the actual outcomes.

  * •

Nnet-survival (Gensheimer and Narasimhan, 2019): Nnet-survival which is
trained with stochastic gradient descent employs parameterization of discrete
hazards and optimization of survival likelihood and allows for non-
proportional hazards.

  * •

N-MTLR (Fotso, 2018): The Neural Multi-Task Logistic Regression uses the
Multi-Task Logistic Regression (MTLR) (Yu et al., 2011) model as its base and
a deep learning architecture as its core.

  * •

DeepHit (Lee et al., 2018): DeepHit is a deep learning-based survival analysis
that uses a multi-task learning framework to simultaneously estimate the
survival time and the event type probabilities, thereby handling competing
risks.

  * •

CoxTime (Kvamme et al., 2019): Cox-Time is an extension of Cox regression that
goes beyond the proportional hazards assumption and incorporates the concept
of relative risk.

  * •

DeepSurv (CoxPH) (Katzman et al., 2018): DeepSurv, a personalized treatment
recommender system, is a Cox proportional hazards deep neural network,
modeling interactions between a patient’s covariates and treatment
effectiveness.

Table 2. Evaluation based on $C^{td}$ and MAE for AKI survival prediction

Model Name $C^{td}$ MAE Nnet-survival 0.6332 3.165 MTLR (N-MTLR) 0.6712 4.081
DeepHit 0.6929 3.012 CoxTime 0.6912 2.980 DeepSurv (CoxPH) 0.6898 3.007 Our
model 0.6990 1.890

###  4.5. Ablation Study

The ablation study was conducted to determine the contribution of each
component in the model to the performance. We experimented with different
combinations of loss components and show the results in Table 3. Training the
model with $L^{{\text{Loglikelihood}}}$ alone performs relatively poor,
particularly in $C^{td}$. Having only ranking loss makes the model much
stronger in terms of $C^{td}$, but the accurate time predictive ability of the
model is reduced since MAE increases by $0.5$ compared to training only with
$L^{{\text{Loglikelihood}}}$. Using $L^{\text{SupWCon}}$ along with
$L^{{\text{Loglikelihood}}}$ increases the $C^{td}$ by $0.0161$ and decreases
the MAE by $0.4$, demonstrating the prominent effectiveness of our SupWCon
loss on improving both evaluation metrics. We also tried adding
$L^{\text{Ranking}}$ to $L^{{\text{Loglikelihood}}}$ which results in a
substantial increase in $C^{td}$ by $0.026$ but an undesired increase in MAE
by $0.13$. The last two combinations bring the best performances. With
$L^{\text{Loglikelihood}}$, $L^{\text{Ranking}}$, and $L^{\text{SupWCon}}$, we
achieve the highest $C^{td}$. With all four loss components, we achieve the
best trade-off in the performance with a small compromise on $C^{td}$ but an
improvement to the lowest MAE. Eventually, we utilized a weighted summation of
these four losses as follows:

(24)
$L^{\text{Total}}=\lambda_{1}L^{\text{Loglikelihood}}+\lambda_{2}L^{\text{Ranking}}+\lambda_{3}L^{\text{SupWCon}}+\lambda_{4}L^{\text{MSE}}$

where $\lambda_{1}$, $\lambda_{2}$, $\lambda_{3}$, $\lambda_{4}$ are
hyperparameters.

From Table 4, which is the ablation study of the ontological encoder and the
attention-pooling blocks, we can realize that they play a significant role in
improving the final results. We first, remove the ontological encoder from the
architecture, which leads to a drop in the $C^{td}$ index and an increase in
MAE, indicating the effectiveness of incorporating the knowledge domain from
medical ontologies in the overall model performance. The same result happens
when we remove both attention-pooling parts, which results in increasing the
number of the model’s parameters, making the model complex and less
generalizable, and also losing the advantage of attention’s performance
boosting and Interpretability.

Table 3. Contributions of loss functions

Loss functions $C^{td}$ MAE $L^{\text{Loglikelihood}}$ 0.6647 2.30
$L^{\text{Ranking}}$ 0.6907 2.80 $L^{\text{Loglikelihood}},L^{\text{SupWCon}}$
0.6808 1.90 $L^{\text{Loglikelihood}},L^{\text{Ranking}}$ 0.6951 2.43
$L^{\text{Loglikelihood}},L^{\text{Ranking}},L^{\text{SupWCon}}$ 0.7030 1.91
$L^{\text{Loglikelihood}},L^{\text{Ranking}},L^{\text{SupWCon}},L^{\text{MSE}}$
0.6990 1.89

Table 4. Ontological encoder and attention-pooling contributions

Window size $C^{td}$ MAE w/o ontology 0.6888 2.11 w/o attention-pooling 0.6795
2.21 Full model 0.6990 1.89

##  5\. Interpretability

Our proposed model can be interpreted by analyzing the attention weights
learned in each of the model’s components. In the ontological encoder, we can
find the attention weights assigned to each medical code and its ancestors to
realize their importance in generating the medical code embeddings. The
weights learned in the visit-level attention-pooling determine the relative
significance of each diagnosis or prescription code in calculating the visit-
level representations. Also, by examining the attention weights learned in the
instance-level attention-pooling, we can infer the relative importance of each
of the visits inside the patient’s medical history in composing the instance
(patient) representations that will be used in the SA downstream task.

Figure 4. Analysis of the attention weights of the visits and the medical
codes (ICD-9) inside each visit. The height of each stacked bar is the
attention weight of the corresponding visit and each bar inside the stacked
bars presents a medical code inside the visit and its attention weight.

To illustrate the interpretability of our model, we select a random patient
diagnosed with AKI on the second day of hospitalization from the test set.
Extracting the visits’ attention weights from the instance-level attention-
pooling and codes’ attention weights from the visit-level attention-pooling,
we plot Figure 4. Therefore, we can realize the most important visits and the
medical codes inside each visit for the model’s decision-making. In Figure 4,
we have five stacked bars representing the five hospital visits of the
patient. The height of each stacked bar shows the attention weight assigned to
each visit. Each stacked bar associated with a visit has some bars indicating
different codes and their attention weights. It is clear that visit 5 has the
highest attention weight and consequently is the most important hospital visit
for this patient. Among all the codes in this visit, ”572”, ”410”, and ”287”
have the highest attention weights. ”572” is the ICD-9 code associated with
liver abscess and sequelae of chronic liver disease, which can potentially
lead to AKI (Duah et al., 2022; Chancharoenthana and Leelahavanichkul, 2019;
Parikh et al., 2008). ICD-9 code ”410” is for acute myocardial infarction
(AMI), commonly known as a heart attack. AMI also can be closely associated
with the onset of AKI which is discussed carefully in the medical literature
(Shacham, 2019; Wang et al., 2019). ICD-9 code ”287” represents purpura and
other hemorrhagic conditions. Some hemorrhagic conditions, including certain
types of purpura and other bleeding disorders, can potentially result in acute
kidney injury (AKI) as a complication (Wang et al., 2017; Kelleher et al.,
1987). Furthermore, in Figure 5, we demonstrate how the ontological encoder
learns code representations and refers to higher-level medical concepts when
it comes to a rare medical code. Clearly, the ”460-519” ICD-9 code which is
the most general ancestor of the ”514” ICD-9 code, receives the highest
attention weight because first, the ”514” code is not a frequent code across
the train set and second, there are enough samples with the children of
”460-519” (as their parent) in the train set.

##  6\. Conclusion

This paper introduces a novel survival model on the basis of longitudinal
healthcare data, termed Ontology-aware Temporality-based Contrastive Survival
analysis (OTCSurv), which combines the benefits of a contrastive learning
approach adapted for survival analysis as well as attention-based methods.
Specifically, we designed a supervised weighted contrastive learning (SupWCon)
loss function which is specifically formulated to handle data censoring and
improve patients’ representations using the time labels as the contrastive
pairing criteria. SupWCon regulates the weights (temperature parameters)
assigned to each negative pair by considering their differences in survival
duration. Also, we used a sequential attention-based ontological encoder,
which consists of an ontological encoder block to incorporate domain knowledge
through medical ontologies, and a sequential attention encoder to capture
temporal dependencies while making the model interpretable. Along with
SupWCon, three other losses are employed to guide the training towards two
goals of survival analysis which are risk ranking ability and precise time
prediction capability. Experimental results, including baseline comparison and
ablation study, on a real-world EHR dataset, showcase the superiority of the
proposed model compared to existing approaches regarding both mentioned goals.
Also, an attention analysis study was conducted to demonstrate the
interpretability of the OTCSurv.

Figure 5. Attention weights which GRAM assigned to the ICD-9 diagnosis code
$c_{1}$: 514 and its ancestors ($c_{2}$: 510-519, $c_{3}$: 460-519). The size
of each node as well as the height of their bar plots show the amount of
attention they received.

## Acknowledgments

This work is partially supported by University of Kansas New Faculty Research
Development (NFRD) Award, National Science Foundation Grant CNS-2125958, and
WVHEPC Grant HEPC.dsr.23.7.

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