Selection bias in the treatment effect for a principal stratum

TL;DR

This paper discusses how selection bias can cause the true treatment effect for a principal stratum to differ from zero, even when treatments have identical effects at the individual level, highlighting challenges in hypothesis testing.

Contribution

It introduces the phenomenon where principal stratum treatment effects may be biased due to selection bias, emphasizing the need for proper hypothesis formulation.

Findings

True treatment effect may not be zero despite equal individual effects.

Selection bias influences principal stratification estimands.

Highlights the need for further research on null hypothesis formulation.

Abstract

Estimation of treatment effect for principal strata has been studied for more than two decades. Existing research exclusively focuses on the estimation, but there is little research on forming and testing hypotheses for principal stratification-based estimands. In this brief report, we discuss a phenomenon in which the true treatment effect for a principal stratum may not equal zero even if the two treatments have the same effect at patient level which implies an equal average treatment effect for the principal stratum. We explain this phenomenon from the perspective of selection bias. This is an important finding and deserves attention when using and interpreting results based on principal stratification. There is a need to further study how to form the null hypothesis for estimands for a principal stratum.