Selection bias in the treatment effect for a principal stratum

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.