Confidence intervals for correlated proportion differences from paired data in a two-arm randomised clinical trial

Many key outcome measures for monitoring disease progression are based on summing across several paired domains. The scores from the paired domain in an individual are likely to be correlated and we present here an analysis of treatment effect at each domain that accounts for the correlation. We use the profile likelihood method, asymptotic score method, and three simple asymptotic methods and construct confidence intervals to compare proportions of responders in a two-arm randomised trial. We evaluate the performance of these confidence interval estimators with respect to their mean coverage probabilities, mean left-tail and right-tail non-coverage rates, and mean confidence widths. These methods are then applied to analyse a multi-centre randomised clinical trial for scleroderma patients.