Abstract: When informative dropouts exist for longitudinal studies, ignoring the informative dropout will result in biased results. Joint modeling of the outcome and dropout time can take into account some information from informative dropouts and correct some biases. In this dissertation, we introduce a random pattern mixture model to jointly model the longitudinal non-gaussian outcomes and the dropout time. The random pattern effects are defined as the latent effects linking the dropout process and the longitudinal outcome. Conditional on the random pattern effects, longitudinal non-gaussian outcome and dropout time are assumed independent. EM algorithm is used for estimation. We also apply the random pattern concept into a joint modeling of non-gaussian outcome and survival time to analyze the effects of treatment on both longitudinal and survival responses simultaneously. In the first part of the dissertation, the random pattern mixture model is applied to a dataset of the Prevention of Suicide in Primary Care Elderly Collaborative Trial (PROSPECT) to estimate the intervention effect on the binary depression outcome compared with an independent generalized linear mixed model and a shared parameter model linking the depression outcome and dropout time at subject level. We model the longitudinal binary outcome using a generalized linear mixed model with logit link function with random subject and pattern effects, and joint with the dropout model at the pattern level. The baseline Hamilton 23 Depression (HAMD) score is found to be a good surrogate for the dropout process because of its relationship to both the dropout time and the depression outcome, and is used to stratify the data into patterns. The random pattern mixture model estimates an increased and significant intervention effect compared to the generalized linear mixed model and the shared parameter model. The sensitivity of the random pattern mixture model is explored through simulations with two true underlying models. In the second part of the dissertation, we apply random pattern mixture model to a sample of end-stage renal disease (ESRD) study to estimate the baseline iron effect on the ordinal anemia outcome. A proportional odds model is used for the longitudinal ordinal anemia outcome. Age is used as a pattern variable because of its relationship with the dropout time and the ordinal anemia outcome. The random pattern mixture model estimates an increased and significant iron effect compared to an independent proportional odds model and a shared parameter model. Simulations are performed to study the robustness of the random pattern mixture model. In the third part of the dissertation, joint modeling of longitudinal outcome and survival time is applied to a sample of ESRD study. The iron effects on both longitudinal anemia and survival responses are estimated simultaneously. The longitudinal binary anemia outcome is fitted with a generalized linear mixed model with site and subject level random effects. The survival time is fitted with Cox proportional hazard model with random site level effect. The two response models are linked at site level due to data clustering by site. The joint model shows that baseline iron exposure does not significantly reduce the odds of having anemia but significantly reduce the relative risk of death, as compared to a naive approach with two independent submodels and a two-stage model.