Sensitivity to missing not at random dropout in clinical trials: use and interpretation of the Trimmed Means Estimator

Abstract

Outcome values in randomized controlled trials (RCTs) may be missing not at random (MNAR), if patients with extreme outcome values are more likely to drop out (e.g., due to perceived ineffectiveness of treatment, or adverse effects). In such scenarios, estimates from complete case analysis (CCA) and multiple imputation (MI) will be biased. The trimmed means (TM) estimator operates by setting missing values to the most extreme value, and then "trimming" away equal fractions of both treatment groups, estimating the treatment effect using the remaining data. The TM estimator relies on two assumptions, which we term the "strong MNAR" and "location shift" assumptions. In this article, we derive formulae for the bias resulting from the violation of these assumptions for normally distributed outcomes. We propose an adjusted estimator, which relaxes the location shift assumption and detail how our bias formulae can be used to establish the direction of bias of CCA, MI and TM estimates under a range of plausible data scenarios, to inform sensitivity analyses. The TM approach is illustrated with simulations and in a sensitivity analysis of the CoBalT RCT of cognitive behavioural therapy (CBT) in 469 individuals with 46 months follow-up. Results were consistent with a beneficial CBT treatment effect. The MI estimates are closer to the null than the CCA estimate, whereas the TM estimate was further from the null. We propose using the TM estimator as a sensitivity analysis for data where it is suspected that extreme outcome values are missing.