Search

Times between successive events (i.e., gap times) are of great importance in survival analysis. Although many methods exist for estimating covariate effects on gap times, very few allow for comparisons between gap times themselves. Motivated by the comparison of primary and repeat transplantation, our interest is specifically in contrasting the gap times. In the first chapter of this thesis, we propose methods to contrast gap time survival functions and their integration (restricted mean gap time). Specifically, we use Cox regression to estimate the (conditional) survival distributions of each gap time (given the previous gap times). Combining fitted survival functions based on those models, along with multiple imputation applied to censored gap times, we then contrast the first and second gap times with respect to average survival and restricted mean lifetime. Large-sample properties are derived, with simulation studies carried out to evaluate finite-sample performance. We apply the proposed methods to kidney transplant data obtained from a national organ transplant registry. In the second chapter, we aim at contrasting gap time hazard functions, assuming that the hazard ratio between two hazard functions is constant over time. In particular, we propose a two-stage procedure, wherein the first stage involves a Cox regression model on the first gap time. Weighted estimating equations are then solved at the second stage to compare the first and second gap time hazard functions. We derive the asymptotic properties of the proposed estimators, and investigate their performance in simulated finite samples. The proposed methods are applied to liver transplant data obtained from a national organ transplant registry. The third chapter can be viewed as an extension of the second one, recognizing that the hazard ratio could be time-dependent. We propose semiparametric methods to estimate the gap time hazard functions, where the correlation between gap times are directly built into the model. Time-dependent hazard ratios and an average overall hazard ratio can therefore be estimated. Simulation studies are conducted under different scenarios. The proposed methods are applied to liver transplant data to compare the hazard functions of post-transplant graft survival for first and second liver transplant.