This thesis consists of three papers on multivariate frailty models and one paper on the use of latent class models in genetic association studies. The common theme through the four papers is the use of latent variables to capture complex dependence structures in the data. The multivariate frailty models define a hazard regression framework to describe general dependence structures in survival data. In the first three papers, three different estimation strategies for multivariate frailty models are presented: (i) an approximate maximum likelihood method leading to estimation equations based on penalized partial likelihood, (ii) a stochastic approximation of the marginal likelihood function using the MCEM algorithm, and (iii) a fully Bayesian frailty model with smoothed baseline hazard. The multivariate frailty models are illustrated with data on hip endoprosthesis, rat carcinogenesis, rose vase lifetime and age at dementia onset in twins.

In Paper IV, a latent class model is used to capture unmeasured heterogeneity due to two unknown underlying populations in a genetic population based case-control study. The information about the underlying populations is drawn from additional unlinked genetic markers genotyped from different chromosomes. Association between the candidate gene and the disease is tested with two nested latent class models.

In the summary of the thesis, parallel developments in multivariate extensions of the generalized linear model and the multiplicative hazard model are reviewed. The focus is on the estimation and computational aspects of fitting random effects models and on the relative merits of the different methods.