Nonparametric Methods for Incomplete Multivariate Data: Applications to Quality of Life Outcomes

In studies of efficacies of intervention modalities, outcomes measured in ordinal scales such as Quality of Life (QOL) outcomes 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 homoscedasticity can be severely violated in these cases. Furthermore, it is more challenging when there are missing values on some of the variables. In this chapter, 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 were 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.