Nonparametric Methods for Stratified Two-Sample Designs with Application to Multiclinic Trials

Abstract

Motivated by some problems arising from multiclinic trials, we consider stratified two-sample designs. Nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment, centers (strata), and interactions are assumed to be fixed factors. The interpretation of the nonparametric effects and hypotheses is analyzed in two classes of semiparametric models: the linear models and models with Lehmann alternatives. The case where centers and interactions are assumed to be random factors, the so-called mixed model, is also considered. Nonparametric effects and hypotheses are defined for general models, and their properties are analyzed in corresponding linear models and in models with Lehmann alternatives. The nonparametric effects are estimated by linear rank statistics where the ranks over all centers are used. The mixed model for repeated (baseline and endpoint) observations is briefly considered, and rank procedures are also proposed for this model. All procedures are related to the nonparametric effects and are not restricted to the two classes of semiparametric models, which are used only for interpretation of the nonparametric effects. Moreover, we do not assume continuity of the underlying distribution functions of the observations, to be as general as possible. We exclude only the trivial case where the distribution function arises from a point mass; that is, a “one-point distribution.” Thus, not only data coming from continuous distribution functions, but also data with ties—especially discrete ordinal data—can be handled with the proposed procedures. In all cases, the results are derived for unbalanced designs so that there are no restrictions for practical applications. The small-sample properties of the proposed statistics are investigated by simulation studies, and the relevant asymptotic distribution theory is considered. Applications of the proposed procedures are demonstrated by means of examples related to multicenter clinical trials.

Key Words:

• Asymptotic normality
• Fixed-effect model
• Mixed model
• Rank tests
• Repeated measurements
• Ties
• Two-factor designs
• Unbalanced designs