Date on Master's Thesis/Doctoral Dissertation
Survival analysis; Hypothesis testing; Multi-stage models; Regression; Nonparametric inference
Nonparametric statistics; Statistical hypothesis testing; Statistics
Marginal inference for waiting times in multi-stage time-to-event models is complicated by right censoring of observations as well as the prior history of events in the model. In general, complications arise due to the evolution of the censoring process in so called "calendar time", contrasted with the evolution of the waiting time process conditional upon entry into a given stage. Developments in inference for survival data under dependent censoring have been extended to the multi-stage framework, and non parametric estimators for the cumulative hazard function and survival function for waiting times analogous of the classical Nelson-Aalen and Kaplan-Meier estimators for survival data have been developed. These estimators were derived under the principle of weighting the basic at-risk and event counting processes by the inverse probability of censoring. We extend this concept to K-sample hypothesis testing and non parametric regression, and define test statistics and regression coefficient estimators analogous to the log-rank test and Aalen's nonparametric linear regression estimators for survival data. We examine the asymptotic distribution of these statistics, and justify their use via simulation studies and analyses of real data sets.
Lorenz, Douglas J., "Marginal nonparametric inference for waiting times in multistage models : hypothesis testing and regression." (2011). Electronic Theses and Dissertations. Paper 856.