Adjusted intraclass correlation coefficients for binary data: methods and estimates from a cluster-randomized trial in primary care

Abstract

Background: Accurate estimates of the intraclass correlation coefficient (ICC) are important for calculating appropriate sample sizes for cluster-randomized trials. The ICC and hence the sample size may be reduced through adjustment for baseline covariates. A method exists for calculating adjusted ICCs for binary outcomes based on the logit link, used to calculate odds ratios. Recent interest in presenting relative risks rather than odds ratios indicates that a method based on the log link is needed. Purpose: To determine and evaluate a method for calculating adjusted ICCs based on the log link, and to provide and compare unadjusted and adjusted ICCs from a cluster-randomized trial in primary care based on the logit and log link. Methods: Two methods are proposed for calculating adjusted ICCs for the log link based on a first-order Taylor series expansion and properties of the lognormal distribution. The methods are evaluated by simulation. Unadjusted and adjusted ICCs are calculated for binary outcomes from the Point of Care Testing (PoCT) Trial using the logit and log link. Results: The methods for calculating adjusted ICCs for the log link produced similar results unless the between cluster variance was large. Unadjusted ICCs for the PoCT Trial ranged from 0.001 to 0.048. The impact of adjustment on the ICC varied between outcomes and link functions, ranging from a 59% reduction to an 89% increase. Limitations: The true ICC was unknown for the simulation study. Adjustment was made for age and gender only for the PoCT Trial. Conclusions: The method for calculating adjusted ICCs for binary outcomes depends on the link function. For the log link, the method based on the lognormal distribution is recommended. This method will be useful for cluster-randomized trials where the relative risk, rather than the odds ratio, is the effect measure of interest.