Semi-Markov Multi-State Models for Cardiovascular Outcomes: Beyond Composite Time-to-First Endpoints

Abstract

In cardiovascular trials, composite endpoints are typically analysed with time-to-first (TTF) methods. The composite endpoints under TTF ignore subsequent events and associations with different event types, which can overlook disease burden and treatment benefit. This thesis proposes a Multi-state Model (MSM) as an alternative for cardiovascular trials, providing detailed insights into transitions among states representing different types of disease. We develop three semi-Markov MSM structures from the cardiovascular composite used in the ORIGIN (Outcome Reduction with an Initial Glargine Intervention) trial: 3-state illness–death model, 5-state irreversible model, and 5-state reversible model. We then conduct Monte Carlo simulations to compare MSMs with TTF Cox models in terms of Type I error, power, confidence interval width, and hazard ratio estimation. In the simulation, we demonstrate the ability to detect a treatment effect among intermediate states while maintaining a 5% Type I error rate for other states showing no effect. In contrast, none of the TTF estimates detect any treatment effect. As more states and transitions are added, the precision of the estimates and the power to detect any treatment effect for subsequent transitions become increasingly limited by the availability of events. We apply these MSMs to ORIGIN to re-analyse cardiovascular outcomes between the treatment groups. Key outputs include the treatment effect for each transition, cumulative incidence, state occupation probabilities over the follow-up period, and the restricted mean time spent in each state, providing insights beyond TTF analysis. Semi-Markov MSMs complement traditional TTF analyses by decomposing composite endpoints into clinically interpretable transitions in cardiovascular trials. This is particularly useful in studies with higher rates of non-fatal events allowing for deeper exploration of disease burden from subsequent transitions.