  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.
