Cost-effectiveness analysis (CEA) models, used to make health policy decisions, are usually subject to uncertainty. This thesis aims to develop statistical methods to quantify uncertainty and target where reducing uncertainty is most beneficial in a CEA. This enables policy decisions, based on the models, to be better informed. There is a focus on two areas: adherence to interventions and heterogeneity in treatment effects, which are often not modelled due to a lack of good data. A case study of treatment for patients with sleep apnoea is used to illustrate these methods and techniques.

Value of Information measures can help prioritise where to focus further research and estimate the expected benefits from a study of particular design and size. Until recently, it has been difficult to evaluate these quantities due to computational complexity. Various recently developed methods to calculate the expected value of information are summarised. Through an application to the case study, the importance of an adequate number of simulations to gain reliable results is highlighted.

Adherence to interventions is often neglected in CEAs due to limited and sparse data. Data on adherence to interventions for sleep apnoea is collected. Through Bayesian model-based meta-analyses, implemented by Markov Chain Monte Carlo simulation, the impact of modelling adherence to interventions on the CEA results is explored. Additionally, the value of collecting further information on adherence to interventions is calculated, indicating value in collecting data even at few time points, and in the early period of follow-up.

Another under explored area within CEAs is stratification of the optimal treatment decision. Here, the focus is on stratification based on continuous measures of disease severity, which may be associated with differential cost-effectiveness through variations in treatment effects. Aggregate and individual participant data on the impact of baseline covariates and treatment effects is summarised. Bayesian model-based meta-regression is used to explore stratification on one or two measure of treatment severity. The value of collecting further data on factors relating to stratification has been explored by using and extending recent non-parametric regression methods.

By using evidence synthesis methods, to make use of all available data, this thesis has found it is possible to incorporate uncertainty due to adherence to interventions and stratifications of treatment decisions into CEA models, allowing future research priorities to be assessed through value of information methods.