title: Analysis of SF-6D index data: is beta regression appropriate?
abstract: BACKGROUND
  Preference-weighted index scores of health-related quality of life are commonly skewed to the left and bounded at one. Beta regression is used in various disciplines to address the specific features of bounded outcome variables such as heteroscedasticity, but has rarely been used in the context of health-related quality of life measures. We aimed to examine if beta regression is appropriate for analyzing the relationship between subject characteristics and SF-6D index scores.
  
  
  METHODS
  We used data from the population-based German KORA F4 study. Besides classical beta regression, we also fitted extended beta regression models by allowing a regression structure on the precision parameter. Regression coefficients and predictive accuracy of the models were compared to those from a linear regression model with model-based and robust standard errors.
  
  
  RESULTS
  The beta distribution fitted the empirical distribution of the SF-6D index better than the normal distribution. Extended beta regression performed best in terms of predictive accuracy but confidence intervals of the fit measures suggested that no model was superior to the others. Age had a significant negative effect on the precision parameter indicating higher variation of health utilities in older age groups. The observations reporting perfect health had a high influence on model results.
  
  
  CONCLUSIONS
  Beta regression, especially with precision covariates is a possible supplement to the methods currently used in the analysis of health utility data. In particular, it accounted for the boundedness and heteroscedasticity of the SF-6D index. A pitfall of the beta regression is that it does not work well in handling one-valued observations.
authors.affiliation: Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Health Economics and Health Care Management, Neuherberg, Germany. matthias.hunger@helmholtz-muenchen.de
authors.forename: Matthias
authors.initials: M
authors.lastname: Hunger
authors.forename: Jens
authors.initials: J
authors.lastname: Baumert
authors.forename: Rolf
authors.initials: R
authors.lastname: Holle
mesh_terms: D000328:Adult; D000367:Age Factors; D000368:Aged; D000369:Aged, 80 and over; D005260:Female; D005858:Germany; D006304:Health Status; D006305:Health Status Indicators; D006306:Health Surveys; D006801:Humans; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D011788:Quality of Life; D012044:Regression Analysis; D011795:Surveys and Questionnaires