Bias Analysis for The Principal Stratum Direct Effect in The Presence of Confounded Intermediate Variables

In epidemiological and clinical research, investigators often want to estimate the direct effect of a treatment on an outcome, which is not relayed by intermediate variables. Even if the total effect is unconfounded, the direct effect is not identifi ed when unmeasured variables affect the intermediate and outcome variables. This article focuses on the principal stratum direct effect (PSDE) of a randomized treatment, which is the difference between expectations of potential outcomes within latent subgroups of subjects for whom the intermediate variable would be constant, regardless of the randomized treatment assignment. Unfortunately, the PSDE will not generally be estimated in an unbiased manner without untestable conditions, even if monotonicity is assumed. Thus, we propose bounds and a simple method of sensitivity analysis for the PSDE under a monotonicity assumption. To develop them, we introduce sensitivity parameters that are defi ned as the difference in potential outcomes with the same value of the intermediate variable between subjects who are assigned to the treatment and those who are assigned to the control group. Investigators can use the proposed method without complex computer programming. The method is illustrated using a randomized trial for coronary heart disease.