E. Brunner et al., NONPARAMETRIC METHODS FOR STRATIFIED 2-SAMPLE DESIGNS WITH APPLICATION TO MULTICLINIC TRIALS, Journal of the American Statistical Association, 90(431), 1995, pp. 1004-1014
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.