The Annals of Applied Statistics

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

Corwin M. Zigler and Thomas R. Belin

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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.

Article information

Source
Ann. Appl. Stat. Volume 5, Number 3 (2011), 1876-1892.

Dates
First available: 13 October 2011

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1318514288

Digital Object Identifier
doi:10.1214/11-AOAS477

Zentralblatt MATH identifier
1228.62153

Mathematical Reviews number (MathSciNet)
MR2884925

Citation

Zigler, Corwin M.; Belin, Thomas R. The potential for bias in principal causal effect estimation when treatment received depends on a key covariate. The Annals of Applied Statistics 5 (2011), no. 3, 1876--1892. doi:10.1214/11-AOAS477. http://projecteuclid.org/euclid.aoas/1318514288.


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Supplemental materials

  • Supplementary material: Simulation study. A detailed exposition of the potential for bias using a richer set of simulations.