A Multiple Imputation Approach for the Evaluation of Surrogate Markers in the Principal Stratification Causal Inference Framework

The concept of principal surrogate developed in the causal inference framework (Frangakis and Rubin (Biometrics 58:21–29, 2002); Gilbert and Hudgens (Biometrics 64:1146–1154, 2008)) has drawn much attention in the field of biomarker research. Principal surrogates are defined based on the causal treatment effects in principal strata, which are constructed based on the joint distribution of the potential surrogate markers when a patient receives either the placebo or the treatment. The challenge of evaluating principal surrogates lies in the fact that half of these potential surrogate markers cannot be observed in most clinical trials. Therefore assessing the principal surrogacy of biomarkers is essentially a missing data problem. In this article, we propose a multiple imputation approach to evaluate candidate principal surrogate markers. The proposed method employs baseline variables to impute the missing potential surrogate markers. The stratum-specific causal treatment effects on the clinical endpoint are then estimated for each imputed dataset and the inference for surrogacy of a biomarker is based on the combined results over multiple imputations. Simulation studies are performed to evaluate the performance of the proposed method and the implementation of the method is illustrated using a vaccine study.