Model Specification and Prediction in Joint Modelling

This thesis explores several methodological aspects of joint modelling of longitudinal outcomes and recurrent and terminal events, including variable selection, description, prediction, causal inference and model specification. The methods we discuss were motivated by the Community Ageing Research study (CARE75+) to investigate the relationships between frailty, falls and mortality. These outcomes have previously been analyzed with marginal models, but not as joint outcomes.
We propose a variable selection strategy to optimize prediction of joint models for longitudinal and time-to-event outcomes. This strategy combines penalized likelihood with the LASSO penalty and cross-validation methods to select the fixed effects that optimize simultaneously the mean-squared error (MSE) and the Integrated Brier Score (IBS). Our simulation studies suggest that it is not always possible to optimize simultaneously MSE and IBS, but there seems to be a region defined by the constraints close to an optimal solution. In such a case a small compromise between MSE and IBS is required, depending on which outcome is the priority.
Joint modelling has been an area of active research for description and prediction, but causal inference has received less attention. Using Direct Acyclic Graphs, we state our hypotheses about the paths between frailty, falls and mortality and confounders to formulate joint models adjusting for confounders. Via simulation studies we assessed the consequences of model misspecification, finding that even when link of the joint model and some features of the mean structure are not the correct ones, the fixed effects can still be correctly estimated.