## The Annals of Applied Statistics

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

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

Corwin M. Zigler and Thomas R. Belin

#### 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 in Project Euclid: 13 October 2011

**Permanent link to this document**

http://projecteuclid.org/euclid.aoas/1318514288

**Digital Object Identifier**

doi:10.1214/11-AOAS477

**Mathematical Reviews number (MathSciNet)**

MR2884925

**Zentralblatt MATH identifier**

1228.62153

**Keywords**

Complier average causal effect noncompliance principal effect principal stratification

#### Citation

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

#### Supplemental materials

- Supplementary material: Simulation study. A detailed exposition of the potential for bias using a richer
set of simulations.Digital Object Identifier: doi: 10.1214/11-AOAS477SUPP