Statistics in Medicine

Modelling bounded health scores with censored skew‐normal distributions

Journal Article


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.

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Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.