The potential for bias in principal causal effect estimation when treatment received depends on a key covariate

TL;DR

This paper investigates how using a key covariate to predict principal strata in causal inference can introduce bias in estimating causal effects, especially when treatment received differs from treatment assigned, and proposes Bayesian methods to assess this bias.

Contribution

It highlights the bias risks in principal causal effect estimation when incorporating predictive covariates and develops Bayesian posterior checks to evaluate this bias in complex treatment scenarios.

Findings

Inclusion of covariates can bias CACE estimates when treatment received differs from assigned.

Bayesian posterior checks can diagnose the extent of bias introduced by covariate use.

Application to clinical trial data demonstrates practical implications of the method.

Abstract

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.