Testing equality of correlation coefficients for paired binary data from multiple groups

Paired binary data arise naturally when paired body parts are investigated in clinical trials. One of the widely used models for dealing with this kind of data is the equal correlation coefficients model. Before using this model, it is necessary to test whether the correlation coefficients in each group are actually equal. In this paper, three test statistics (likelihood ratio test, Wald-type test, and Score test) are derived for this purpose. The simulation results show that the Score test statistic maintains type I error rate and has satisfactory power, and therefore is recommended among the three methods. The likelihood ratio test is over conservative in most cases, and the Wald-type statistic is not robust with respect to empirical type I error. Three real examples, including a multi-centre Phase II double-blind placebo randomized controlled trial, are given to illustrate the three proposed test statistics.