Discrete -time survival mixture analysis for single and recurrent events using latent variables

Survival analysis refers to the general set of statistical methods developed specifically to model the timing of events. This dissertation concerns a subset of those methods that deals with events measured or occurring in discrete-time or grouped-time intervals. A method for modeling single event discrete-time data utilizing a latent class regression (LCR) framework, originally presented by Muthen and Masyn (2001), is further developed and detailed. It is shown that discrete-time data can be represented as a set of binary event indicators and observed risk indicators that allow estimation using a latent class regression specification under a missing-at-random assumption that corresponds to the assumption of noninformative right-censoring. The modeling of the effects of time-dependent and time-independent covariates with constant or time-varying effects is demonstrated along with approaches to model testing. The LCR framework also allows for the modeling of unobserved heterogeneity through finite mixture modeling, i.e., multiple latent classes. The problems of ignoring unobserved heterogeneity and the challenges of discrete-time mixture model identification and specification for single event data are discussed. The LCR model for single event data is extended to recurrent event survival data with a focus on recurrent event processes, with a low frequency of recurrences The gap time, counting process, and total time formulations in the continuous-time setting are all reformulated for discrete-time and model specification and estimation is demonstrated for all three. The proposed model accommodates event-specific baseline hazard probabilities as well as event-specific covariate effects. The model also allows for multiple event occurrences in a single time period for a single subject and accounts for within as well as between subject correlation of event times through the same mixture modeling approach given for single event data. All models are illustrated with data on the event times of domestic violence episodes perpetrated by sample of married men observed for 12 months after an alcohol treatment program. Opportunities for future methodology developments for discrete-time models are discussed.