On the use of propensity scores in principal causal effect estimation.

We examine the practicality of propensity score methods for estimating causal treatment effects conditional on intermediate posttreatment outcomes (principal effects) in the context of randomized experiments. In particular, we focus on the sensitivity of principal causal effect estimates to violation of principal ignorability, which is the primary assumption that underlies the use of propensity score methods to estimate principal effects. Under principal ignorability (PI), principal strata membership is conditionally independent of the potential outcome under control given the pre-treatment covariates; i.e. there are no differences in the potential outcomes under control across principal strata given the observed pretreatment covariates. Under this assumption, principal scores modeling principal strata membership can be estimated based solely on the observed covariates and used to predict strata membership and estimate principal effects. While this assumption underlies the use of propensity scores in this setting, sensitivity to violations of it has not been studied rigorously. In this paper, we explicitly define PI using the outcome model (although we do not actually use this outcome model in estimating principal scores) and systematically examine how deviations from the assumption affect estimates, including how the strength of association between principal stratum membership and covariates modifies the performance. We find that when PI is violated, very strong covariate predictors of stratum membership are needed to yield accurate estimates of principal effects.