Hutton, Jane and Stanghellini, E. (2009) Modelling health scores with the skew-normal distribution. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.39).

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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 scores
will be bounded, and are often 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 models based on the skew-normal distribution to data from a randomised controlled trial of treatments for sprained ankles, in which scores were recorded at baseline
and 1, 3 and 9 months. We consider the extent to which skewness in the data can be
explained by the 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 distortion of
the treatment effects due to informative drop-out is given. This allows us to assess under
which conditions the conclusions drawn on the complete data may be either reinforced or
reversed, when the informative drop-out process is taken into account.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Medical care -- Statistics
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.2009
Number:	No.39
Number of Pages:	13
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Great Britain. Dept. of Health (DoH), University of Warwick. Centre for Research in Statistical Methodology, Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR)
Grant number:	01/14/10 (DoH), PRIN 2007XECZ7L−003 (MIUR)

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