Correlated binary data from a cross-sectional study frequently arise in the health sciences. In a randomized trial, patients with multiple myeloma from the same institution were randomly assigned to one of the two chemotherapy treatment groups, and it is often of interest in comparing overall success rates between the two chemotherapy treatment groups. Due to a cross-sectional design, the success rates between the two chemotherapy treatment groups are no longer independent. Moreover, due to cluster effect, post-treatment responses from each cluster (institution) for each treatment group can be highly correlated. By taking both correlation structures into account, we develop three efficient methods for the above inference problem. An extensive simulation study is conducted for the purpose of evaluating and comparing the performance of the proposed methods. An application to a chemotherapy study is used to illustrate the proposed methods.