Statistical Inferences For Two-stage Treatment Regimes for Time-to-Event and Longitudinal Data

Adaptive treatment regime is a set of rules that governs the assignment of time-varying treatment based on observed covariates and intermediate response. Treatment choices are made sequentially as patients make transition from one health state to another. Specifically, in two stage randomization designs, patients are randomized to one of the initial treatments, and at the end of the first stage, they are randomized to one of the second stage treatments depending on the outcome of the initial treatment. The goal is to find the best treatment regime which produces the best terminal outcome. For time-to-event data, the best outcome is the longest survival time, and for longitudinal data, the best outcome is greatest reduction (or increase) in some scores such as reduction 24-item Hamilton Rating Scale of Depression (HRSD24) score. For time-to-event data, we propose a weighted Kaplan-Meier estimator based on the method of inverse-probability weighting and compare its properties to that of the standard Kaplan-Meier estimator, and two other existing methods such as marginal mean model based estimator and weighted risk set estimator. For longitudinal data, outcome such as HRSD24 scores are collected repeatedly to monitor the progress of the subject. We propose three methods incorporating inverse probability weighting, mixed models, multiple imputations, and pattern mixture models to assess the effect of treatment regimes on the longitudinal HRSD24 scores. Methods are compared through simulation studies with an application to a depression study. Assessing the effect of treatment regimes on longitudinally observed outcome data is important in Public Health since clinicians will be able to identify effective treatment regimes for treating chronic diseases. Proposed statistical methods provide useful tools for unbiased estimation of the effects of treatment regimes from sequentially randomized designs. Availability of these methods will help advance the research in AIDS, cancer, depression, hepatitis and other disease areas.