Missing data and sensitivity analysis for binary data with implications for sample size and power of randomized clinical trials

Despite our best efforts, missing outcomes are common in randomized controlled clinical trials. The National Research Council's Committee on National Statistics panel report titled The Prevention and Treatment of Missing Data in Clinical Trials noted that further research is required to assess the impact of missing data on the power of clinical trials and how to set useful target rates and acceptable rates of missing data in clinical trials. In this article, using binary responses for illustration, we establish that conclusions based on statistical analyses that include only complete cases can be seriously misleading, and that the adverse impact of missing data grows not only with increasing rates of missingness but also with increasing sample size. We illustrate how principled sensitivity analysis can be used to assess the robustness of the conclusions. Finally, we illustrate how sample sizes can be adjusted to account for expected rates of missingness. We find that when sensitivity analyses are considered as part of the primary analysis, the required adjustments to the sample size are dramatically larger than those that are traditionally used. Furthermore, in some cases, especially in large trials with small target effect sizes, it is impossible to achieve the desired power.