Nonparametric and semiparametric censored survival analysis of correlated times to event and their sequelae.

The main goal of this dissertation is to construct nonparametric or semiparametric methods for analyzing correlated failure times. Landmark events such as cancer occurrence, time to severe vision loss or HIV infection are intimately tied to patient quality-of-life (QOL) and they are both of capital scientific interest in this dissertation. In Chapter II we develop testing methods for the group sequential monitoring of paired censored survival data, as in the Early Treatment Diabetic Retinopathy Study. With independent groups, the log-rank is most powerful under proportional hazards (PH), while the Pepe-Fleming test might be more powered in non-PH situations. However, the paired versions of the weighted log-rank (PWLR) and the weighted Pepe-Fleming (PWKM) tests are not known to be optimal, under general standard assumptions. We propose monitoring methods based on PEMAX, the largest, in absolute value, of PWLR and PWKM. With correlation properly accounted for in the asymptotic variance of PEMAX, type I error is properly maintained and power robustness is observed in PH and non-PH scenarios, under stochastic ordering. Methods for correlated QOL-adjusted successive failure times are developed in Chapter III. Attempting to reconcile the quantitative and the qualitative aspects of individual survival during successive life events, we propose the concept of QOL-adjusted gap time (QAGT), in anticipation of a scenario when deteriorating QOL accompanies a series of successive adverse events. We develop estimators of joint and conditional distributions of QAGTs, prove consistency and characterize their asymptotic distributional properties. Applications to the International Breast Cancer Study Group (IBCSG) Trial V are presented. In Chapter IV, we develop methods for incorporating prognostic covariates via generalized linear regression models on pseudo-values for the restricted mean of the quality-of-life-adjusted survival time (RMQAST). Existing methods model QOL-adjusted lifetime through Cox models for the QOL-adjusted hazard function. The coefficient estimates thus obtained do not have clinically meaningful interpretations. By modeling covariate effects on RMQAST directly, we facilitate the interpretability of the regression coefficients. At the modeling stage, which involves the pseudo-observations, generalized estimating equations (GEE) are used. We present applications to the IBCSG Trial V. Comments and interesting directions for future research conclude this dissertation.PhDBiological SciencesBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125009/2/3186564.pd