Hutton, Jane (Statistician) 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
Volume:	Vol.2009
Number:	No.39
Number of Pages:	13
Status:	Not Peer Reviewed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)
References:	[1] Azzalini A, Capitanio A. Statistical application of the multivariate skew-normal distribution. Journal of the Royal Statistical Society, Series B, 1999; 61,3,579-602. [2] Skinner, CJ. Discussion on ”Informative drop-out in longitudinal data analysis” by PJ Diggle and MG Kenward. Journal of the Royal Statistical Society Series C, 1994; 43, 76-77. [3] Lamb SE, Marsh JL, Hutton JL, Nakash RA, Cooke MW. Mechanical supports for acute, severe ankle sprains: a pragmatic, multi-centre, randomised controlled trial. The Lancet, 2009; 373, 575–581. [4] Nakash RA, Hutton JL, Lamb SE, Gates S, Fisher J. Response and non-response to postal questionnaire follow-up in a clinical trial - a qualitative study of the patient’s perspective. BMC Med Res Meth. 2008; 14, 226-235. [5] Wetherill GB. Intermediate statistical methods. London: Chapman and Hall, 1981. [6] Heckman JJ. Sample bias as a specification error. Econometrica, 1979; 47, 153–61. [7] Copas, JB, Li HG. Inference for Non-random Samples (with discussion). Journal of the Royal Statistical Society, Series B, 1997; 59, 55-95. [8] Wooldridge JM. Econometrics Analysis of Cross Section and Panel data. Cambridge, MA: The MIT Press, 2003. [9] Marchetti GM, Stanghellini E. A note on distortions induced by truncation, with application to linear regression systems. Statistics & Probability Letters, 2008; 78, 824–829. [10] Diggle, PJ, Kenward MG. Informative drop-out in longitudinal data analysis. Journal of the Royal Statistical Society, Series C, 1994; 43, 49-93. [11] Goldberger AS. Linear regression after selection. Journal of Econometrics, 1981; 15, 357– 66.
URI:	http://wrap.warwick.ac.uk/id/eprint/35226

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