  In clustered data setting, informative cluster size has been a focus of
recent research. In the nonparametric context, the problem has been considered
mainly for testing equality of distribution functions. The aim in this paper is
to develop inferential procedure for the Wilcoxon-Mann-Whintey effect (also
known as the nonprametric relative effect). Unbiased estimator is provided and
its asymptotic properties are investigated. The asymptotic theory is employed
to develop inferential methods. While the proposed method takes information in
the cluster sizes into consideration when constructing the estimator, it is
equally applicable for ignorable cluster size situation. Simulation results
show that our method appropriately accounts for informative cluster size and it
generally outperforms existing methods, especially those designed under
ignorable cluster sizes. The applications of the method is illustrated using
data from a longitudinal study of alcohol use and a periodontal study.
