Composite endpoints combine a number of outcomes to assess the efficacy of a treatment. They are used in situations where it is difficult to identify a single relevant endpoint, such as in complex multisystem diseases. Our focus in this thesis is on composite responder endpoints, which allocate patients as either ‘responders’ or ‘non-responders’ based on whether they cross predefined thresholds in the individual outcomes. These composites are often combinations of continuous and discrete measures and are typically collapsed into a single binary endpoint and analysed using logistic regression. However, this is at the expense of losing information on how close each patient was to the responder threshold. As well as being inefficient the analysis is sensitive to misclassification due to measurement error. The augmented binary method was introduced to improve the analysis of composite responder endpoints comprised of a single continuous and binary endpoint, by making use of the continuous information.

In this thesis we build on this work to address some of the existing limitations. We implement small sample corrections for the standard binary and augmented binary methods and assess the performance for application in rare disease trials, where the gains are most needed. We find that employing the small sample corrected augmented binary method results in a reduction of required sample size of 32%. Motivated by systemic lupus erythematosus (SLE), we consider the case where the composite has multiple continuous, ordinal and binary components. We adapt latent variable models for application to these endpoints and assess the performance in simulated data and phase IIb trial data in SLE. Our findings show reductions in required sample size of at least 60%, however the magnitude of the gains depends on which components drive response. Finally, we develop a method for sample size estimation so that the model may be used as a primary analysis method in clinical trials. We assess the impact of correlation structure and drivers of response on the sample size required.