Modelling bounded health scores with censored skew-normal distributions
Article first published online: 5 NOV 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 30, Issue 4, pages 368–376, 20 February 2011
How to Cite
Hutton, J. L. and Stanghellini, E. (2011), Modelling bounded health scores with censored skew-normal distributions. Statist. Med., 30: 368–376. doi: 10.1002/sim.4104
- Issue published online: 10 JAN 2011
- Article first published online: 5 NOV 2010
- Manuscript Accepted: 9 SEP 2010
- Manuscript Received: 22 SEP 2009
- bounded scores;
- ceiling effect;
- informative drop-out;
- skew-normal distribution
Health care interventions that use quality of life or health scores often provide data which are skewed and bounded. The scores are typically formed by adding up numerical responses to a number of questions. Different questions might have different weights, but the scores will be bounded, and are often scaled to the range 0–100. 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, hence the scores reflect a selected population.
We fit models based on the skew-normal distribution to data from a randomized controlled trial of treatments for sprained ankles, in which scores were recorded at baseline and at 1, 3 and 9 months after injury. We consider the extent to which skewness in the data can be explained by clustering at the boundary via a comparison between a censored normal and a censored skew-normal model.
As this analysis is based on the complete data only, a formula for the bias of the treatment effects due to informative drop-out is given. This allows us to assess under what conditions the conclusions drawn from the complete data might be either reinforced or reversed, when the informative drop-out process is taken into account. Copyright © 2010 John Wiley & Sons, Ltd.