Analyzing longitudinal data using random effects models

Longitudinal data have been collected in many medical studies. For this kind of data, observations within the same subject are modeled as correlated, and observations from different subjects are assumed to be independent. It is important for us to account for the within-subject correlations in the analysis for valid inferences, especially on the treatment effects. In this thesis, I am concerned with the exploration of random effects (frailty) models that model this correlation on three types of data: event time data, zero inflated count data, and discrete multi-stage data. ^ The first part is on the modeling of recurrent events times. We assume the underlying process for the recurring events to be an inhomogeneous Poisson counting process. The mean function of this process is expressed as a product of a subject specific frailty, treatment effect and a common baseline effect. We propose a new family of frailty models that are more flexible than existing models. We model the baseline intensity function as a time varying effect with an unknown number of change points. The subject specific frailty effects are modeled as latent variables. Implementation of Bayesian inference using a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is developed to handle the varying-dimension problems in the parameter space. ^ The second part is inspired by an alcoholism treatment study. Zero-inflated Poisson (ZIP) mixed models are explored for modeling the number of drinks taken by each subject each day. As a mixture distribution, ZIP model mixes a latent class 0 with a Poisson process. The covariates are related to the response by either a Poisson regression in the Poisson mean or a logistic regression in the probability of the latent class 0. Inference and model determination for various ZIP mixed models that include the random effects for handling within subject correlations are discussed and evaluated. ^ The third part is inspired by the Bronx ageing study. We are interested in the influence of risk factors on the transitions of three cognitive status: cognitive stability, cognitive impairment and dementia. Generalized logits and proportional odds models are considered to model the transitional probabilities. Random effects are incorporated into the generalized logits and proportional odds to account for the within-subject correlations.