Analysis of longitudinal clinical trials with missing data using multiple imputation in conjunction with robust regression

In a typical randomized clinical trial, a continuous variable of interest (e.g., bone density) is measured at baseline and fixed postbaseline time points. The resulting longitudinal data, often incomplete due to dropouts and other reasons, are commonly analyzed using parametric likelihood-based methods that assume multivariate normality of the response vector. If the normality assumption is deemed untenable, then semiparametric methods such as (weighted) generalized estimating equations are considered. We propose an alternate approach in which the missing data problem is tackled using multiple imputation, and each imputed dataset is analyzed using robust regression (M-estimation; Huber, 1973, Annals of Statistics 1, 799-821.) to protect against potential non-normality/outliers in the original or imputed dataset. The robust analysis results from each imputed dataset are combined for overall estimation and inference using either the simple Rubin (1987, Multiple Imputation for Nonresponse in Surveys, New York: Wiley) method, or the more complex but potentially more accurate Robins and Wang (2000, Biometrika 87, 113-124.) method. We use simulations to show that our proposed approach performs at least as well as the standard methods under normality, but is notably better under both elliptically symmetric and asymmetric non-normal distributions. A clinical trial example is used for illustration.