Send to

Choose Destination
Stat Methods Med Res. 2015 Dec;24(6):657-74. doi: 10.1177/0962280211421840. Epub 2011 Oct 3.

Assessing the sensitivity of methods for estimating principal causal effects.

Author information

Departments of Mental Health and Biostatistics, Johns Hopkins Bloomberg School of Public Health, 624 N Broadway, 8th Floor, Baltimore, MD, USA.
Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, CA 94305-5795, USA.


The framework of principal stratification provides a way to think about treatment effects conditional on post-randomization variables, such as level of compliance. In particular, the complier average causal effect (CACE) - the effect of the treatment for those individuals who would comply with their treatment assignment under either treatment condition - is often of substantive interest. However, estimation of the CACE is not always straightforward, with a variety of estimation procedures and underlying assumptions, but little advice to help researchers select between methods. In this article, we discuss and examine two methods that rely on very different assumptions to estimate the CACE: a maximum likelihood ('joint') method that assumes the 'exclusion restriction,' (ER) and a propensity score-based method that relies on 'principal ignorability.' We detail the assumptions underlying each approach, and assess each methods' sensitivity to both its own assumptions and those of the other method using both simulated data and a motivating example. We find that the ER-based joint approach appears somewhat less sensitive to its assumptions, and that the performance of both methods is significantly improved when there are strong predictors of compliance. Interestingly, we also find that each method performs particularly well when the assumptions of the other approach are violated. These results highlight the importance of carefully selecting an estimation procedure whose assumptions are likely to be satisfied in practice and of having strong predictors of principal stratum membership.


complier average causal effect; intermediate outcomes; non-compliance; principal stratification; propensity scores

[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for Atypon Icon for PubMed Central
Loading ...
Support Center