NONPARAMETRIC METHODS FOR STRATIFIED 2-SAMPLE DESIGNS WITH APPLICATION TO MULTICLINIC TRIALS

Motivated by some problems arising from multiclinic trials, we conside r 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. Th e interpretation of the nonparametric effects and hypotheses is analyz ed in two classes of semiparametric models: the linear models and mode ls with Lehmann alternatives. The case where centers and interactions are assumed to be random factors, the so-called mixed model, is also c onsidered. Nonparametric effects and hypotheses an defined for general models, and their properties are analyzed in corresponding linear mod els and in models with Lehmann alternatives. The nonparametric effects are estimated by linear rank statistics where the ranks over all cent ers are used, The mixed model for repeated (baseline and endpoint) obs ervations is briefly considered, and rank procedures are also proposed for this model, All procedures are related to the nonparametric effec ts and are not restricted to the two classes of semiparametric models which are used only for interpretation of the nonparametric effects. M oreover, we do not assume continuity of the underlying distribution fu nctions of the observations, to be as general as possible. We exclude only the trivial case when the distribution function arises from a poi nt mass; that is, a ''one-point distribution.'' Thus, not only data co ming from continuous distribution functions, but also data with ties-e specially discrete ordinal data-can be handled with the proposed proce dures. In all cases the results are derived for unbalanced designs so that there are no restrictions for practical applications. The small-s ample properties of the proposed statistics are investigated by simula tion studies, and the relevant asymptotic distribution theory is consi dered. Applications of the proposed procedures are demonstrated by mea ns of examples related to multicenter clinical trials.