Impact of correlation structure on sample size requirements of statistical methods for multiple binary outcomes: A simulation study

Background: In randomized clinical trials, multiple-testing procedures, composite endpoints, and prioritized outcome approaches are increasingly used to analyze multiple binary outcomes. Previous studies have shown that correlations between outcomes influence their sample size requirements. Although sample size is an important factor affecting the choice of statistical methods, the power and required sample sizes of methods for analyzing multiple binary outcomes have yet to be compared under the influence of outcome correlations.

Methods: We conducted simulations to evaluate the power of co-primary and multiple primary endpoints, composite endpoints, and prioritized outcome approaches based on generalized pairwise comparisons with varying correlations, marginal proportions, treatment effects, and number of outcomes. We then conducted a case study on sample size using a clinical trial of a migraine treatment as an example.

Results: The correlations significantly affected the statistical power and sample size of composite endpoints. The power and sample size of co-primary endpoints remained relatively stable across different correlations, though their power declined substantially when treatment effects were opposite on some components or more than two components were present. While the correlations influenced the power and sample size of all methods assessed, their direction and degree of influence varied between methods. Notably, the method with the greatest power and smallest sample size also differed depending on the correlations. When the correlations were the same between arms, prioritized outcome approaches usually had higher power and smaller sample sizes than other methods.

Conclusions: Anticipated correlations and their uncertainty should be considered when selecting statistical methods. Overall, co-primary endpoints remain a reliable option for evaluating the superiority of all components, although they are unsuitable for assessing the balance between treatment effects pointing in different directions. Generalized pairwise comparisons offer a useful alternative to deal with multiple prioritized outcomes, often providing the smallest sample sizes when the correlation structures are shared between the arms.