In cluster randomized trials (CRTs), clusters of individuals are randomized rather than the individuals themselves. For such trials, power depends in part on the degree of similarity among responses within a cluster, which is quantified by the intaclass correlation coefficient (ICC). Thus, for a fixed sample size, power decreases with increasing ICC. In reliability studies with two observers, dichotomizing a continuous outcome variable has been shown to reduce the ICC. We checked (by a simulation study) that this property still applies to CRTs, in which cluster sizes are variable and usually greater than in reliability studies and observations (within clusters) are exchangeable. Then, in a CRT, dichotomizing a continuous outcome actually induces two antagonistic effects: decreased power because of loss of information and increased power induced by attenuation of the ICC. Therefore, we aimed to assess the impact of dichotomizing a continuous outcome on power in a CRT. We derived an analytical formula for power based on a generalized estimating equation approach after dichotomizing a continuous outcome. This theoretical result was obtained by considering equal cluster sizes, and we then assessed its accuracy (by a simulation study) in the more realistic situation of varying cluster sizes. We showed that dichotomization is associated with decreased power: attenuation of the ICC does not compensate for the loss of power induced by loss of information. Loss of power is reduced with increased initial continuous-outcome ICC and/or prevalence of success for the dichotomized outcome approaching 50%.
Copyright © 2012 John Wiley & Sons, Ltd.