Testing equality of correlations of two paired binary responses from two treated groups in a randomized trial

We explore measuring Scleroderma patient disease improvement at the paired body part level and account for their correlation with the long term goal of possibly redefining disease progression using a shorter clinical examination. We propose using a binary outcome to measure disease progression at each paired body part level, construct tests for assessing equality of the correlations between groups for each paired body part and determine sample size requirements for such tests in a two-arm randomized clinical trial. Simulations are performed to evaluate properties of the tests and the accuracy of our sample size formulae. We demonstrate our method with data from a multi-center two-arm randomized clinical trial.