Non‐parametric bootstrap confidence intervals for the intraclass correlation coefficient

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Abstract
The intraclass correlation coefficient ρplays a key role in the design of cluster randomized trials. Estimates of ρ obtained from previous cluster trials and used to inform sample size calculation in planned trials may be imprecise due to the typically small numbers of clusters in such studies. It may be useful to quantify this imprecision. This study used simulation to compare different methods for assigning bootstrap confidence intervals to ρfor continuous outcomes from a balanced design. Data were simulated for combinations of numbers of clusters (10, 30, 50), intraclass correlation coefficients (0.001, 0.01, 0.05, 0.3) and outcome distributions (normal, non‐normal continuous). The basic, bootstrap‐t, percentile, bias corrected and bias corrected accelerated bootstrap intervals were compared with new methods using the basic and bootstrap‐t intervals applied to a variance stabilizing transformation of ρ. The standard bootstrap methods provided coverage levels for 95 per cent intervals that were markedly lower than the nominal level for data sets with only 10 clusters, and only provided close to 95 per cent coverage when there were 50 clusters. Application of the bootstrap‐t method to the variance stabilizing transformation of ρimproved upon the performance of the standard bootstrap methods, providing close to nominal coverage. Copyright © 2003 John Wiley & Sons, Ltd.