Over recent decades, medical interventions and advances have become important drivers of health and morbidity trends. In this project we will consider statistical predictive models for such trends, relating to particular major conditions such as heart disease and cancer. The principal aim will be to address the timely need to develop robust predictive models for rapidly changing morbidity risks and relevant impact on health-related insurance, such as long-term care, disability and critical illness insurance. Bayesian model diagnostics, assessment and selection will be considered for a range of models including machine learning-based approaches.