Identifying Treatment Effects using Trimmed Means when Data are Missing Not at Random

Patients often discontinue treatment in a clinical trial because their health condition is not improving. Consequently, the patients still in the study at the end of the trial have better health outcomes on average than the initial patient population would have had if every patient had completed the trial. If we only analyze the patients who complete the trial, then this missing data problem biases the estimator of a medication's efficacy because study outcomes are missing not at random (MNAR). One way to overcome this problem - the trimmed means approach for missing data - sets missing values as slightly worse than the worst observed outcome and then trims away a fraction of the distribution from each treatment arm before calculating differences in treatment efficacy (Permutt 2017, Pharmaceutical statistics 16.1:20-28). In this paper we derive sufficient and necessary conditions for when this approach can identify the average population treatment effect in the presence of MNAR data. Numerical studies show the trimmed means approach's ability to effectively estimate treatment efficacy when data are MNAR and missingness is strongly associated with an unfavorable outcome, but trimmed means fail when data are missing at random (MAR) when the better approach would be to multiply impute the missing values. If the reasons for discontinuation in a clinical trial are known analysts can improve estimates with a combination of multiple imputation (MI) and the trimmed means approach when the assumptions of each missing data mechanism hold. When the assumptions are justifiable, using trimmed means can help identify treatment effects notwithstanding MNAR data.