Dynamic Survival Transformers for Causal Inference with Electronic Health Records Prayag Chatha

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Dynamic Survival Transformers for Causal Inference

with Electronic Health Records

Prayag Chatha

Department of Statistics

University of Michigan

pchatha@umich.edu

Yixin Wang

Department of Statistics

University of Michigan

Zhenke Wu

Department of Biostatistics

University of Michigan

Jeffrey Regier

Department of Statistics

University of Michigan

Abstract

In medicine, researchers often seek to infer the effects of a given treatment on

patients’ outcomes. However, the standard methods for causal survival analysis

make simplistic assumptions about the data-generating process and cannot capture

complex interactions among patient covariates. We introduce the Dynamic Survival

Transformer (DynST), a deep survival model that trains on electronic health records

(EHRs). Unlike previous transformers used in survival analysis, DynST can make

use of time-varying information to predict evolving survival probabilities. We

derive a semi-synthetic EHR dataset from MIMIC-III to show that DynST can

accurately estimate the causal effect of a treatment intervention on restricted mean

survival time (RMST). We demonstrate that DynST achieves better predictive and

causal estimation than two alternative models.

1 Introduction

Medical practitioners are often interested in the effect of a treatment on a patient’s survival time

until an event of interest. For instance, if a patient is prescribed a certain antibiotic, how will that

affect their risk of experiencing sepsis in the next 24 hours? The ﬁeld of causal survival analysis is

concerned with estimating treatment effects on time-to-event outcomes given incomplete (censored)

data; classical techniques such as the Kaplan-Meier curves [1] and the Cox regression model [2]

are extensively used despite their limitations. Kaplan-Meier curves are a descriptive tool that do

not model individual survival trajectories, while the Cox model assumes proportionality of hazard

functions, which may be unrealistic. Meanwhile, the rise of electronic health records (EHRs) has led

to an abundance of multi-concept longitudinal data: a setting for observational causal inference, if

randomized controlled trials prove impractical or unethical.

With this observational setting in mind, we propose the Dynamic Survival Transformer (DynST), a

deep-learning survival model that estimates individual survival probabilities over time from EHR

data. DynST is built on the Transformer [3], a recent neural network architecture that has achieved

state-of-the-art results in sequence-to-sequence learning, particularly in NLP [4]. Transformers can

ﬂexibly model individual survival trajectories without making simplifying parametric assumptions

about the data-generating process. Unlike previous survival transformers [5, 6, 7] DynST exploits

both static and time-varying features to capture how a patient’s event risk evolves over time. Several

works have applied transformers to prediction problems in EHR data [8, 9, 10, 11], motivated by

similarities between EHRs and text, but DynST is the ﬁrst transformer used to estimate the average

effect of a treatment intervention on survival outcomes. Using a semi-synthetic dataset derived from

Accepted to the NeurIPS 2022 Workshop on Learning from Time Series for Health.

arXiv:2210.15417v1 [cs.LG] 25 Oct 2022

Figure 1: A diagram of DynST modeling the hazard function from a single patient’s EHR data.

MIMIC-III [12], we show that DynST can improve on baseline methods in survival time prediction

and causal inference.

2 Problem setup

We observe survival data taking the form

(Xi, Oi, δi)n

i=1

, where

represents the

-th patient’s

features,

is the observed (and possibly censored) time to the event, and

δi

is a binary variable

indicating whether the event was observed or not, due to censoring. If

δi= 0,

the

-th patient is

right-censored, so the event takes place after

Oi.

Let

represent the uncensored survival time and let

be the censoring time. Then,

Oi= min{Ti, Ci},

and

δi=1(Ti≤Ci).

In this paper, we assume

conditionally independent censoring, i.e.,

Ti⊥⊥ Ci|Xi.

We also assume a discrete survival setup,

where Ti∈ {1,2, . . . , ...tmax}and time steps are evenly spaced. The hazard function

h(t|X) = PX(T=t|T≥t)(1)

is the risk of failure at time

given that the patient has survived thus far. The survival probability

time tis

S(t|X) = PX(T > t) =

τ=1

(1 −h(τ|X)).(2)

The expected survival time is deﬁned as

E[T|X] =

tmax

t=1

S(t|X).(3)

Lastly, given a cutoff time τ, the restricted mean survival time (RMST) [13, 14] is deﬁned as

Yτ=EX[min{T, τ}] = 1

i=1 τ

t=1

S(t|Xi)!.(4)

RMST can be thought of as the expected survival time up to time

τ,

averaged over the population of

all patients.

3 Methods

3.1 Model architecture

Let

denote the features of a single patient; we suppress the patient index for readability.

consists

static features

Z1,...Zp,

collectively denoted as

and

time-varying features,

V1,...Vq,

collectively denoted as

Here each feature

is a time series vector

(V(1)

j, V (2)

j, . . . , V (tmax )

j).

Static variables may include initial diagnoses, whereas a sequence of lab measurements is an example

of a time-varying feature. Let

V(t)= (V(1)

j,· · · V(t)

j).

At each time step

the Dynamic Survival

Transformer models

q(t;Z, V (t))=1−h(t|Z, V (t)).

That is, DynST predicts the complement of

each patient’s hazard function using static features and the available history of time-varying features.

Figure 1 illustrates DynST’s architecture. The model transforms each patient’s medical records

through the following procedure:

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DynamicSurvivalTransformersforCausalInferencewithElectronicHealthRecordsPrayagChathaDepartmentofStatisticsUniversityofMichiganpchatha@umich.eduYixinWangDepartmentofStatisticsUniversityofMichiganZhenkeWuDepartmentofBiostatisticsUniversityofMichiganJeffreyRegierDepartmentofStatisticsUniversityofMichig...

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Dynamic Survival Transformers for Causal Inference with Electronic Health Records Prayag Chatha

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