Recurrent event studies: efficient panel designs and joint modeling of events and severities

Recently there has been tremendous growth in the use and interest of longitudinal data, particularly because of the development of large scale investigations which are conducted to study different aspects of the dynamics of a population over time (for instance, the Canadian National Longitudinal Study of Children and Youth (Statistics Canada, 1996)). Recurrent event data are a type of longitudinal data which occur in many fields. Such data arise when an event repeats over time, and are common especially in medicine and reliability. Sometimes, in addition to the occurrence of the event, there is also information which reflects the severity of the event; this is called a mark. In this thesis, we develop efficient designs for longitudinal recurrent event studies, and we also develop methods to model recurrent events with marks. In longitudinal recurrent event studies, sometimes partial information on the counting process, such as the number of events occurring in specific intervals, called panel data, provides nearly the same precision for estimation of treatment effects as full information based on data from continuous observation of the process. We compare the efficiency of the analysis of such panel data with respect to the analysis of data recorded as times of recurrences, and we articulate conditions for efficient panel designs where the focus is on estimation of a treatment effect when adjusting for other covariates. We model the recurrent intensity through the common proportional intensity framework, with the treatment effect modeled flexibly as piecewise constant over panels, or groups of panels. We provide some important considerations for the design of efficient panel studies. The thesis also develops methods for situations where marks, denoting a measure of prognostic factors or severity of the event, are also recorded. Often, there is an association between the recurring processes of events and their marks. We model these outcomes jointly through the use of shared or linking random effects, and investigate biases resulting in analyses of the outcomes when they are not modeled jointly. This analysis of joint outcomes is motivated by a study of healthy menstruating women prior to hysterectomy/ovariectomy for benign disease.