There has been an increasing interest in using cell and gene therapy (CGT) to treat/cure difficult diseases. The hallmark of CGT trials are the small sample size and extremely high efficacy. Due to the innovation and novelty of such therapies, when there is missing data, more scrutiny is exercised, and regulators often request for missing data handling strategy when missing data occurs. Often, multiple imputation (MI) will be used. MI for continuous endpoint is well established but literature of MI for binary endpoint is lacking. In this work, we compare and develop 3 new methods to handle missing data using MI for binary endpoints when the sample size is small and efficacy extremely high. The parameter of interest is population proportion of success. We show that our proposed methods performed well and produced good 95% coverage. We also applied our methods to an actual clinical study, the Clinical Islet Transplantation (CIT) Protocol 07, conducted by National Institutes of Health (NIH).

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