A method for the analysis of repeated binary outcomes in randomized clinical trials with non-compliance

When analysing repeated binary data from randomized trials, the model-based approaches, such as generalized estimating equations, are frequently used. Such methods ignore compliance information and give the model-based intention-to-treat estimate of treatment effect. In this paper, the design-based (randomization-based) semi-parametric estimation procedure is given in the estimation of causal risk difference. The resulting risk difference estimator is interpreted as an extension of the instrumental variables estimator for a binary outcome which has the causal interpretation. Extension of the proposed method to stratified analysis is given for data from stratified randomization or meta-analysis. It yields a Mantel-Haenszel type risk difference estimator. As a special case of stratified analysis, the pattern mixture model which stratifies the data by pattern of missing data is performed. Application of the proposed method to a trial in which endpoints were the occurrences of fever over three courses is provided. The same ideas are applied to the causal risk ratio estimation.