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Mixed outcome endpoints that combine multiple continuous and discretecomponents to form co-primary, multiple primary or composite endpoints areoften employed as primary outcome measures in clinical trials. There are manyadvantages to joint modelling the individual outcomes using a latent variableframework, however in order to make use of the model in practice we requiretechniques for sample size estimation. In this paper we show how the latentvariable model can be applied to the three types of joint endpoints and proposeappropriate hypotheses, power and sample size estimation methods for each. Weillustrate the techniques using a numerical example based on the fourdimensional endpoint in the MUSE trial and find that the sample size requiredfor the co-primary endpoint is larger than that required for the individualendpoint with the smallest effect size. Conversely, the sample size requiredfor the multiple primary endpoint is reduced from that required for theindividual outcome with the largest effect size. We show that the analyticaltechnique agrees with the empirical power from simulation studies. We furtherillustrate the reduction in required sample size that may be achieved in trialsof mixed outcome composite endpoints through a simulation study and find thatthe sample size primarily depends on the components driving response and thecorrelation structure and much less so on the treatment effect structure in theindividual endpoints.

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