Seminário no âmbito do Mestrado em Bioestatística, por Carmen Armero (Department of Statistics and Operations Research, Universitat de València).

A Bayesian joint model for longitudinal and survival data is a joint distribution for a survival process and for a longitudinal process as well as for all relevant sets of random effects, parameters and hyperparameters. Joint models allow to model longitudinal data with non-ignorable missing data mechanisms with the help of survival tools as well as to model survival models with internal time- dependent covariates with the help of longitudinal models. We introduce two Bayesian joint models for two different studies within the medical setting, one for a longitudinal analysis and one for a survival scenario. The longitudinal study is defined in terms of a linear mixed-effects model that accounts for heterogeneity between the subjects, serial correlation, and measurement error. Dropout is modeled in terms of a survival model with competing risks and left truncation. The survival study uses an ordinal longitudinal marker modeled in terms of a proportional-odds cumulative logit model and a Cox proportional hazard model with left truncation for the time to the event of interest. Prediction and estimation for generic and particular individuals from the population is discussed in both studies.