Estimation of the odds ratio from multi‐stage randomized trials

A multi‐stage design for a randomized trial is to allow early termination of the study when the experimental arm is found to have low or high efficacy compared to the control during the study. In such a trial, an early stopping rule results in bias in the maximum likelihood estimator of the treatment effect. We consider multi‐stage randomized trials on a dichotomous outcome, such as treatment response, and investigate the estimation of the odds ratio. Typically, randomized phase II cancer clinical trials have two‐stage designs with small sample sizes, which makes the estimation of odds ratio more challenging. In this paper, we evaluate several existing estimation methods of odds ratio and propose bias‐corrected estimators for randomized multi‐stage trials, including randomized phase II cancer clinical trials. Through numerical studies, the proposed estimators are shown to have a smaller bias and a smaller mean squared error overall.