A framework for longitudinal latent factor modelling of treatment response in clinical trials with applications to Psoriatic Arthritis and Rheumatoid Arthritis

Objective: Clinical trials involve the collection of a wealth of data, comprising multiple diverse measurements performed at baseline and follow-up visits over the course of a trial. The most common primary analysis is restricted to a single, potentially composite endpoint at one time point. While such an analytical focus promotes simple and replicable conclusions, it does not necessarily fully capture the multi-faceted effects of a drug in a complex disease setting. Therefore, to complement existing approaches, we set out here to design a longitudinal multivariate analytical framework that accepts as input an entire clinical trial database, comprising all measurements, patients, and time points across multiple trials. Methods: Our framework composes probabilistic principal component analysis with a longitudinal linear mixed effects model, thereby enabling clinical interpretation of multivariate results, while handling data missing at random, and incorporating covariates and covariance structure in a computationally efficient and principled way. Results: We illustrate our approach by applying it to four phase III clinical trials of secukinumab in Psoriatic Arthritis (PsA) and Rheumatoid Arthritis (RA). We identify three clinically plausible latent factors that collectively explain 74.5% of empirical variation in the longitudinal patient database. We estimate longitudinal trajectories of these factors, thereby enabling joint characterisation of disease progression and drug effect. We perform benchmarking experiments demonstrating our method's competitive performance at estimating average treatment effects compared to existing statistical and machine learning methods, and showing that our modular approach leads to relatively computationally efficient model fitting. Conclusion: Our multivariate longitudinal framework has the potential to illuminate the properties of existing composite endpoint methods, and to enable the development of novel clinical endpoints that provide enhanced and complementary perspectives on treatment response.