Physical activity and exercise capacity as composite versus single categorical endpoints for trials of exercise-based cardiac rehabilitation interventions: comparison of sample size requirements
Authors: Carrozzo E , Cornelissen V , Bathke A , Claes J , Niebauer J , Zimmermann G , Treff G , Kulnik S T 
Published: May 2023

Abstract

Funding Acknowledgements
Type of funding sources: None.

Introduction
A composite primary endpoint consists of two or more component endpoints, events or outcomes. If any one of these is observed, it is considered that the composite primary endpoint has been reached. A potential advantage of a composite over a single primary endpoint in a randomised controlled trial (RCT) is a reduction of the required sample size.

Purpose
The combined endpoint "major adverse cardiac events" (MACE) is well-established in cardiovascular research, but MACE is often unsuitable in trials of exercise-based cardiac rehabilitation interventions with short follow-up periods. We therefore explored the application of a composite primary endpoint incorporating exercise capacity and physical activity for parallel-group RCTs of exercise-based cardiac rehabilitation (CR) interventions.

Methods
Our composite endpoint combines two categorical (binary) single endpoints, i.e., exercise capacity (given as maximum mechanical power output of a graded exercise test) and physical activity. Thresholds for categorisation were defined on literature-based minimal clinically worthwhile changes and defined as an increase of 15 W or more for improving exercise capacity and an increase of 10 min/day or more for improving moderate to vigorous physical activity (MVPA). If the aim of an intervention is to avoid clinically meaningful deterioration (i.e., to achieve maintenance as opposed to improvement), the threshold is defined as deterioration in exercise capacity of less than 15 W and a reduction in MVPA of less than 10 min/day (figure 1).
To illustrate the impact of a single versus a composite primary end point on sample size requirements, we used real-world data from two completed phase 3 CR trials ([1] and [2]). We applied the commonly used formula for estimating sample sizes to detect the difference between the probabilities of an event in two independent groups [3].

Results
Sample size requirements for detecting a between-group difference of 5%, 10%, 15% and 20% under the different endpoint approaches are shown in table 1. If the aim of the intervention is to achieve improvement, the composite endpoint results in approximately equivalent sample size requirements to the single endpoint. If the aim of the intervention is to achieve maintenance, the composite endpoint results in markedly lower sample size requirements compared to the primary endpoint. Statistically, these differences are driven by the percentage of improvers or maintainers in the control group of the reference population.

Conclusion
The composite primary endpoint approach can be a useful alternative to the single primary endpoint in trials of exercise-based CR. Depending on the baseline probability, it may be possible to reduce the sample size requirement by applying a composite endpoint. In our examples, the composite endpoint results in smaller sample size requirements when the intervention aim is to avoid clinically meaningful deterioration.