Estimation of Causal Effect on Treatment on Longitudinal Binary Outcomes in Randomized Clinical Trials with Non-compliance

摘要

In this paper, we focus on estimating the complier average causal effect for longitudinal binary outcomes in randomized clinical trials with non-compliance. Sato[3] proposed a simple addictive risk model for repeated binary outcomes in randomized clinical trials with non-compliance and extended the instrumental variable estimator to repeated binary outcomes based on a randomization-based approach. Matuyama[5] extended Sato's result to a general case of repeated binary data. Sato[3] and Matuyama[5] gave the point and interval estimators for the risk difference. Lui[6] derived variances of these point estimators. But all of these results were derived under the very strong addictive risk model assumption. In order to relax the assumption, we focus on a special case of Sato's; that is, the treatments patients received at the different time points are the same. We proposed the potential outcomes model, defined the parameters of average causal effects in Rubin's causal models of three repeated binary outcomes, and discussed parameter identifiability and derived the simple ML likelihood (ML) estimators of average causal effects in different time points under stable unit treatment values, monotonicity and exclusion restriction assumptions. Then we conducted simulation study to evaluate the finite-sample performance for the proposed ML estimators.