Sample size estimation using a latent variable model for mixed outcome co‐primary, multiple primary and composite endpoints

Abstract

Mixed outcome endpoints that combine multiple continuous and discrete components are often employed as primary outcome measures in clinical trials. These may be in the form of co‐primary endpoints, which conclude effectiveness overall if an effect occurs in all of the components, or multiple primary endpoints, which require an effect in at least one of the components. Alternatively, they may be combined to form composite endpoints, which reduce the outcomes to a one‐dimensional endpoint. There are many advantages to joint modeling the individual outcomes, however in order to do this in practice we require techniques for sample size estimation. In this article we show how the latent variable model can be used to estimate the joint endpoints and propose hypotheses, power calculations and sample size estimation methods for each. We illustrate the techniques using a numerical example based on a four‐dimensional endpoint 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 in the multiple primary case is similar to that needed for the outcome with the largest effect size. We show that the empirical power is achieved for each endpoint and that the FWER can be sufficiently controlled using a Bonferroni correction if the correlations between endpoints are less than 0.5. Otherwise, less conservative adjustments may be needed. We further illustrate empirically the efficiency gains that may be achieved in the composite endpoint setting.

Sample size calculation in clinical trials with two co‐primary endpoints including overdispersed count and continuous outcomes

“…20 For clinical trials evaluating co-primary endpoints, outcomes are obtained on the same patients; therefore, the required sample size can be reduced to account for the correlation between outcomes during sample size calculation. Some researchers have proposed sample size calculation methods in the context of co-primary endpoints for various outcomes, including continuous outcomes, 21 binomial outcomes, 22 mixed continuous and binomial outcomes, 23 and survival outcomes. 24 These methodologies have also been extended to more complex trial designs, such as a sequential parallel comparison design with two co-primary continuous endpoints 25 and group-sequential trials with two co-primary continuous endpoints.…”