Grant: Discovery Grants Program - Individual

Statistical methods and models have been instrumental to making inferences about longitudinal processes generating some specific events and related outcomes over time in a random way. Event history analysis is a general term to define studies of such processes focusing on the occurrence times and types of events. Examples of event history data include survival and competing risks data, recurrent event data and data obtained from illness-death studies or more general life history processes. Dynamic modeling of event history processes is of interest in many research fields, including engineering, medicine and epidemiology. Dynamic models are intensity based stochastic processes, in which the effects of past of a process on its present state or future evolution are examined so that enhanced inferences about important process features can be made. Dynamic models include functions of the past of a process as covariates, called dynamic covariates. Models and methods that ignore dynamic covariates may not provide a comprehensive understanding of the processes unless strong independence assumptions are imposed, which are unrealistic in many studies. Although dynamic modeling of event history processes provides excellent opportunities to address many important scientific issues that arise in natural sciences and engineering, it also poses important methodological challenges. The inherent nature of dynamic covariates and their complex relations with interventions, treatment effects, complicated observation schemes and unexplained heterogeneity make modeling and inference challenging when dynamic modeling of event history processes is of interest. The overarching goal of this research program is to enhance statistical inference procedures for event history processes, and to develop novel methods for the analysis of complex event history data. I will achieve this goal under three specific objectives. Objective 1 is to develop tools and formal goodness-of-fit tests for testing the adequacy of the assumed dynamic models under dependent event times settings. Quantile regression is an emerging method that provides a complete understanding of the effects of covariates on the distribution of lifetime variables in event history processes. In the second objective, I will explore the quantile regression methodology in the dynamic event history context. Objective 3 is to develop inference procedures to distinguish direct and indirect effects of exposure variables on event history processes. Research carried out through this program will have direct impact on important application areas in Canada. Data sets from system reliability, epidemiology and medicine will be analyzed. The anticipated outcomes of this research will be instrumental in understanding event history processes in reliability of repairable systems, health services and cancer studies.