Abstract

The method of principal stratification is a unifying framework for modelling cause and effect which is applicable to adjusting for treatment noncompliance in multiple arms of a trial. Baseline covariates which predict compliance with treatment are useful in addressing parameter identification problem associated with principal stratification. Roy, Hogan and Marcus (RHM) (2008) proposed a principal stratification framework in which they used baseline covariates to adjust for imperfect compliance in both arms of a two-active treatments trial. Key to the application of this method is a defining but untestable distributional assumption whose robustness is unknown. The present work uses statistically designed simulation studies in the framework of a clinical trial comparing two active treatments as applied to survival data under both homogeneous and heterogeneous treatment effect assumptions to evaluate the performance of the RHM method in terms of bias and $95\%$ credible intervals. We first apply the standard proportional hazard model to obtain the ITT estimate and evaluate resulting bias if viewed as estimating a causal hazard ratio. We then compare the method's performance in terms of stratum-specific causal relative risk for different specifications of a user-defined spectrum parameter. The results showed no effect of the spectrum parameter on the ITT estimates. The RHM method performed poorly by producing significantly biased efficacy estimates in all strata with wider corresponding $95\%$ credible intervals under heterogeneous treatment effect assumption. The resulting efficacy estimates varied a lot depending on the value of the unknown (user-defined) spectrum parameter.

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