R Estimates and Associated Inferences for Mixed Models With Covariates in a Multicenter Clinical Trial

Abstract

Robust rank-based methods are proposed for the analysis of data from multicenter clinical trials using a mixed model (including covariates) in which the treatment effects are assumed to be fixed and the center effects are assumed to be random. These rank-based methods are developed under the usual mixed-model structure but without the normality assumption of the random components in the model. For this mixed model, our proposed estimation includes R estimation of the fixed effects, robust estimation of the variance componets, and studentized residuals. Our accompanying inference includes estimates of the standard errors of the fixed-effects estimators and tests of general linear hypotheses concerning fixed effects. While the development is for general scores function, the Wilcoxon linear scores are emphasized. A discussion of the relative efficiency results shows that the R estimates are highly efficient compared to the traditional maximum likelihood (ML) estimates. A small Monte Carlo study confirms the validity of the analysis and its gain in power over the ML analysis for heavy-tailed distributions. We further develop a rank-based test for center by treatment interactions. We discuss the results of our analysis for an example of a multicenter clinical trial which shows the robustness of our procedure.