Multi-state processes with duration-dependent transition intensities: statistical methods and applications

Multi-state processes provide a convenient framework for analysis of event history data, which arise in many fields including public health, biomedical and health services research, reliability, business, and social sciences. This thesis develops methods for statistical analyses with various Markov processes in particular, and presents applications of the methodology. Starting with the homogeneous semi-Markov (HSM) process, a generalization of the classical homogeneous Markov processes, we propose an alternative estimation procedure with right-censored data to the existing approaches to avoid their possible inconsistency in estimating the transition probabilities. Two simulation based algorithms are implemented to construct confidence bands for the HSM kernel and the sojourn time distributions. The modulated semi-Markov (MSM) process extends the HSM process to a Cox regression setting, allowing for general time-dependent covariates but invalidating the usual martingale methods to derive asymptotics. We consider estimation of the regression parameters in the MSM model and establish the consistency, asymptotic normality and efficiency of the estimators, applying the modern empirical process theory. As a further generalization, the nonhomogeneous semi-Markov (NHSM) process assumes its transition intensity involving two time scales, the individual study time since the onset of the process and the duration time in the current state. We provide estimation procedures for the parameters in four model specifications with the NHSM process. The last topic of the thesis is to deal with dependent censoring in event history data analysis. We focus on a particular informative censoring scheme with the observation of a NHSM process, and adapt a copula-based approach for dependent competing risks. Finite sample properties of all the proposed methods are examined via simulation. In addition, with the proposed methods, we conduct analyses of two real data sets, the human sleep data presented in Kneib and Hennerfeind (2008) and the hospitalization data collected by the CAYACS program (PI: M. McBride) with BC Cancer Centre.