NON-PARAMETRIC INFERENCE AND REGRESSION ANALYSIS FOR CUMULATIVE INCIDENCE FUNCTION UNDER TWO-STAGE RANDOMIZATION

In recent years, personalized medicine and dynamic treatment regimes have drawn considerable attention and two-stage randomization is commonly used to gather data for making inference on dynamic treatment regimes. Meanwhile, more and more practitioners become aware of competing risk censoring, where subjects are exposed to more than one possible failure and the event of interest may be dependently censored by the occurrence of competing events. We aim to compare several treatment regimes from a two-stage randomized trial on survival outcomes that are subject to competing-risk censoring. With the presence of competing risks, cumulative incidence function (CIF) has been widely used to quantify the cumulative probability of occurrence of the target event by a specific time point. In the first part of this dissertation, we propose non-parametric estimators for the CIF using inverse weighting, and provide inference procedures based on the asymptotic linear representation to help compare the CIFs from two different treatment regimes. Through simulation, we show the practicality and advantages of the proposed estimators and apply them to data from the Cancer and Leukemia Group B (CALGB) trial. Next, we propose a pattern-mixture type estimator for the CIF. Pattern-mixture models stratify data according to dropout patterns, make estimates of a certain parameter on each stratum, and obtain the final estimate by taking a weighted average of these estimates. We show that this approach can be borrowed for estimating the CIF under a two-stage randomization. We investigate its properties using simulation and apply it to the CALGB data. In the third part, we focus on regression analysis under a two-stage randomization setting. Even though extensive research is being carried out by researchers on the regression problem for dynamic treatment regimes, no research has been done on modeling the CIF when a two-stage randomization has been carried out. We extend the multi-state (Cheng et al., 1998), Fine and Gray (1999) and Scheike et al. (2008) regression models for modeling the CIF of dynamic treatment regimes and provide ways to implement the proposed models in R using the existing packages. We show the improvement our methods provide by simulation