This project aims to develop novel statistical methods for the analysis of dependent multivariate count and survival data from epidemiology. First, tools for structured factor analysis in Bayesian hierarchical Poisson and competing risk regression models will be developed. Emphasis will be on designing efficient Markov chain Monte Carlo (MCMC) algorithms based on auxiliary variables, enabling automatic model selection via reversible jump MCMC. The methodology will be applied to joint spatial, temporal and spatio-temporal analyses of multivariate area-level cancer registry data as well as to multivariate individual-level survival data. Secondly, statistical methods for the analysis of multivariate infectious disease surveillance data will be developed. Appropriate time-series models to adjust for possible local outbreaks will be modified and extended to incorporate multivariate and, in particular, spatio-temporal dependencies. One particular area of application of the methodology is outbreak detection for multivariate surveillance data.