  Quality of Life (QOL) outcomes are important in the management of chronic
illnesses. In studies of efficacies of treatments or intervention modalities,
QOL scales multi-dimensional constructs are routinely used as primary
endpoints. The standard data analysis strategy computes composite (average)
overall and domain scores, and conducts a mixed-model analysis for evaluating
efficacy or monitoring medical conditions as if these scores were in continuous
metric scale. However, assumptions of parametric models like continuity and
homoscedastivity can be violated in many cases. Furthermore, it is even more
challenging when there are missing values on some of the variables. In this
paper, we propose a purely nonparametric approach in the sense that meaningful
and, yet, nonparametric effect size measures are developed. We propose
estimator for the effect size and develop the asymptotic properties. Our
methods are shown to be particularly effective in the presence of some form of
clustering and/or missing values. Inferential procedures are derived from the
asymptotic theory. The Asthma Randomized Trial of Indoor Wood Smoke data will
be used to illustrate the applications of the proposed methods. The data was
collected from a three-arm randomized trial which evaluated interventions
targeting biomass smoke particulate matter from older model residential wood
stoves in homes that have children with asthma.
