In this thesis we propose a joint model for competing risks and longitudinal data. Our joint model provides a flexible approach to handle longitudinal data with complicated structures. Our model consists of a multi-state model for the competing risks and a general mixed model for the longitudinal outcomes, linked together by some latent random effects. For the joint model of one longitudinal outcome, we obtain the estimates of the parameters by maximising the marginal likelihood. We also extend the joint model to take into account multiple longitudinal outcomes simultaneously. To alleviate the ‘curse of dimensionality’ in integration, we propose to use Bayesian inference and use the posterior means as the estimates of the parameters. The joint models are applied to two datasets, the English Longitudinal Study of Ageing (ELSA) and the clinical data from the PhysioNet/Computing in Cardiology Challenge 2019. For the second dataset, we also propose a two-stage framework for disease early diagnosis. We construct a time-dependent loss function, and make diagnosis by minimising the expected loss.