Comparing intraclass correlation coefficient estimators for binary outcomes in sample size calculations in twin pregnancies

Intraclass correlation coefficients (ICCs) can be used to adjust for clustering in sample size calculations, but different ICC estimators for binary outcomes can return different estimates. We assessed the ability of five common ICC estimators to calculate sample sizes that achieve the desired power, for studies that compare binary outcomes in treated and untreated twin pregnancies.

We simulated studies in twin pregnancies with varying levels of clustering and outcome prevalence. We used ICC estimators derived from logistic generalized estimating equations (GEE), analysis of variance (ANOVA), linear mixed modelling (LMM), and logistic generalized linear mixed modelling (GLMM). We calculated the required sample size to obtain 80 % power (5 % Type I error) using a standard formula and used simulation to estimate the empirical power.

ICC estimates from GEE, ANOVA, and LMM were similar to each other, constant across outcome prevalence, and yielded required sample sizes that achieved the desired power. ICC estimators using logistic GLMM varied across outcome prevalence and yielded required sample sizes that were larger than necessary (power >80 %) when clustering was high or when outcome prevalence was low.

Investigators using ICCs in sample size calculations including twin pregnancies should consider avoiding estimates from logistic GLMMs.