Sample Size Estimation using a Latent Variable Model for Mixed Outcome Co-Primary, Multiple Primary and Composite Endpoints

TL;DR

This paper develops methods for sample size estimation in clinical trials with mixed outcome endpoints using a latent variable model, demonstrating how to optimize trial design for co-primary, multiple primary, and composite endpoints.

Contribution

It introduces a novel application of latent variable models for sample size calculation tailored to different joint endpoint types in clinical trials.

Findings

Sample size for co-primary endpoints is larger than for the smallest effect size endpoint.

Sample size for multiple primary endpoints is smaller than for the largest effect size endpoint.

Sample size depends mainly on component response and correlation, less on individual treatment effects.

Abstract

Mixed outcome endpoints that combine multiple continuous and discrete components to form co-primary, multiple primary or composite endpoints are often employed as primary outcome measures in clinical trials. There are many advantages to joint modelling the individual outcomes using a latent variable framework, however in order to make use of the model in practice we require techniques for sample size estimation. In this paper we show how the latent variable model can be applied to the three types of joint endpoints and propose appropriate hypotheses, power and sample size estimation methods for each. We illustrate the techniques using a numerical example based on the four dimensional endpoint in the MUSE trial and find that the sample size required for the co-primary endpoint is larger than that required for the individual endpoint with the smallest effect size. Conversely, the sample size required for the multiple primary endpoint is reduced from that required for the individual outcome with the largest effect size. We show that the analytical technique agrees with the empirical power from simulation studies. We further illustrate the reduction in required sample size that may be achieved in trials of mixed outcome composite endpoints through a simulation study and find that the sample size primarily depends on the components driving response and the correlation structure and much less so on the treatment effect structure in the individual endpoints.