Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (-1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.