Nonparametric and Semiparametric Inference for Treatment Efficacy in Randomized Clinical Trials with a Time-to-event Outcome and Non-compliance

We consider a subgroup comparison problem in randomized clinical trials when the subgroup status cannot be identified in some study arms. One well-known example is a two-arm randomized clinical trial with non-compliance. To evaluate the biological efficacy of treatment (as opposed to intent-to-treat effect) in the presence of all-or-none compliance, one often needs to assess the treatment effect relative to a control in the subgroup of study participators who would always comply with their assigned treatment regimen. In practice, however, the subgroup status is usually unobservable in one or both study arms. The main objective of our research is to develop nonparametric and semiparametric statistical methodology and inference procedures for assessing biological treatment efficacy in randomized clinical trials with a right-censored time-to-event outcome and unknown subgroup status in the control arm. In our study, the treatment efficacy is measured in terms of the difference in subgroup survival probabilities between treatment and control subjects. Specifically, we propose nonparametric and semiparametric estimation procedures, derive the large sample theory, construct asymptotic pointwise confidence intervals and simultaneous confidence bands, and develop a procedure for estimating the onset and duration of the treatment efficacy. Simulation studies are conducted to investigate the performance of our methods. The proposed methods are also applied to the real data from the Multicenter Selective Lymphadenectomy Trial I, an NIH-funded Phase III randomized clinical trial for melanoma. Finally, we extend our semiparametric maximum likelihood method to a more general subgroup comparison problem in which the subgroup status is fully missing in both treatment and control arms.