  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.
