Statistical inference using large administrative data on multiple event times, with application to cancer survivorship research

Motivated by the breast cancer survivorship research program at BC Cancer Agency, this dissertation develops statistical approaches to analyzing right-censored multivariate event time data. Following the background and motivation of the research, we introduce the framework of the dissertation, and provide a literature review and a list of the research questions. A description of the motivating study data is then given together with a preliminary analysis before presenting the proposed approaches as follows. We consider firstly estimation of the joint survivor function of multiple event times when the observations are subject to informative censoring due to a terminating event. We formulate the potential dependence of the multiple event times with the time to the terminating event by the Archimedean copulas. This may account for the informative censoring and, at the same time, allow to adapt the commonly used two-step procedure for estimating the joint distribution of the multiple event times under a copula model. We propose an easy-to-implement pseudo-likelihood based estimation procedure under the model, which reduces computational intensity compared to its MLE counterpart. A more flexible approach is then proposed to handling informative censoring with particular attention to observations on bivariate event time potentially censored by a terminating event. We formulate the correlation of the bivariate event time with the censoring time by embedding the bivariate event time distribution in a bivariate copula model. This yields the convenience of inference under the conventional copula model. At the same time, the proposed model is more flexible, and thus potentially more appropriate in many practical situations than modeling the event times and the associated censoring time jointly by a single multivariate copula. Adapting the commonly used two-stage estimation procedure under a copula model, we develop an easy-to-implement estimator for the joint survivor function of the two event times. A by-product of the proposed approaches is an estimator for the marginal distribution of a single event time with semicompeting-risks data. Further, we extend the approach to regression settings to explore covariate effects in either parametric or nonparametric forms. In particular, adjusting for some covariates, we compare two populations based on an event time with observations subject to informative censoring. We conduct both asymptotic and simulation studies to examine the consistency, efficiency, and robustness of the proposed approaches. The breast cancer program that motivated this research is employed to illustrate the methodological development throughout the dissertation.