Abstract

Health care interventions which use quality of life or health scores often provide data which are skewed and bounded. The scores are typically formed by adding up responses to a number of questions. Different questions might have different weights, but the score will be bounded, and might be scaled to the range 0 to 100. If improvement in health over time is measured, scores will tend to cluster near the ‘healthy’ or ‘good’ boundary as time progresses, leading to a skew distribution. Further, some patients will drop out as time progresses, so the scores reflect a selected population.

We fit multivariate skew normal distributions to data from a randomised controlled trial of four treatments for sprained ankles, in which scores were recorded at baseline and 1, 3 and 9 months. In these data, the scores at 3 and 9 months have skew marginal distributions, but the variance is similar across the four times points. We consider the extent to which variance and skewness can be explained by covariates including treatment and age. In order to address the effect of clustering at the boundary, we consider censored multivariate normal and skew model. The extended skew normal is used to model the selection due to drop-out.