| In biomedical and social science research studies, the outcome variables of interest are often in the form of count or time-to-event data. Appropriate models for such data are Poisson regression models for count data and survival models (e.g., the Weibull regression model) for time-to-event data. However, in many studies subjects are often clustered or have repeated measurements on the outcome variables of interest, resulting in correlated observations. As a result, the usual Poisson and Weibull regression models assuming independent observations are inappropriate. To include the clustering effect in the analysis, Poisson random-effects regression and Weibull random-effects regression models are proposed in this dissertation.;Various distributions for the random effects can be considered, for example, normal, gamma, and extreme value distributions. Currently, gamma and extreme value distributions have been considered for random effects in the Poisson and Weibull regression models. Although normally distributed random effects are common in many other models, this is not the case in Poisson and Weibull random-effects regression models, primarily due to computational complexity. In this dissertation, the normal distribution is considered for random effects in the Poisson and Weibull regression models. Simulations for both of the proposed models are presented showing that the model parameters are accurately estimated.;The proposed Poisson random-effects and Weibull random-effects regression models are then used to determine the significant predictors of current level of smoking (number of cigarettes smoked in the last seven days) and age of onset of smoking in a school-based smoking prevention study. In these models, students are considered clustered within classrooms, and the degree of variation attributable to classrooms is estimated in addition to the model covariates. Regarding the covariates, the Poisson random-effects regression model indicates that race, gender, peer approval of smoking, and parental approval of smoking had significant main and interaction effects on current level of adolescent smoking. The Weibull random-effects regression model reveals that race, peer approval, and parental approval had significant main effects on age of onset of smoking, but their interaction effects were not significant. For both models, the classroom variance was also observed to be statistically significant, indicating the importance of appropriately accounting for the clustering of students within classrooms.;In conclusion, this dissertation demonstrates that normally distributed random effects for the Poisson and Weibull regression models represent a useful generalization, and the methods have direct applicability in the analysis of clustered data. |
