Tackling Missing Data: Control-Based Quantile Imputation and Tipping Point Analysis
*Devan V Mehrotra, Merck Research Laboratories 

Keywords: control-based imputation, dropouts, incomplete data, least squares mean, longitudinal data analysis, missing at random, quantile imputation, tipping point analysis

In a typical randomized two-arm (test, control) longitudinal clinical trial, the endpoint of interest is not observed for dropouts. The resulting missing data problem is commonly tackled by invoking a missing at random (MAR) assumption and proceeding with a mixed model repeated measures (MMRM) analysis. If the MAR assumption is incorrect, the estimated treatment effect is biased for the primary estimand of interest, the latter defined as the true between-treatment difference in endpoint means in the entire study population based on complete or partial adherence to assigned treatment in the absence of rescue medication. Published methods that attempt to decrease the bias are somewhat complicated and involve additional assumptions. We propose a simple solution in which the implicitly imputed mean for test-arm dropouts in the MMRM analysis is explicitly replaced with a given quantile (default:50%) of the estimated endpoint distribution for the control arm. Systematically varying the level of the quantile leads to a spectrum of estimated treatment effects and corresponding p-values that can be used for (i) benchmarking the MMRM results, and (ii) assessing robustness of the study conclusions via the tipping point concept. Three real datasets are used to illustrate the proposed methodology.