Analysis of the short form-36 (SF-36): the beta-binomial distribution approach

Abstract

Health-related quality of life (HRQoL) is an important indicator of health status and the Short Form-36 (SF-36) is a generic instrument to measure it. Multiple linear regression (MLR) is often used to study the relationship of HRQoL with patients' characteristics, though HRQoL outcomes tend to be not normally distributed, skewed and bounded (e.g. between 0 and 100). A sample of 193 patients with eating disorders has been analysed to assess the performance of the MLR under non-normality conditions. Normal distribution was rejected for seven out of the eight domains. A beta-binomial distribution is suggested to fit the SF-36 scores. The beta-binomial distribution is not rejected for five out of the eight domains. Thus, a beta-binomial regression (BBR) is suggested to analyse the SF-36 scores. Results using MLR and BBR have been compared for real and simulated data. Performance of the BBR is shown to be better than MLR in the HRQoL domains with few ordered categories and very similar to MLR in the more continuous domains. Moreover, the interpretation of the estimates obtained with BBR is clinically more meaningful. A common technique of statistical analysis is preferable for all the HRQoL dimensions. Therefore, the BBR approach is recommended not only to detect significant predictors of HRQoL when SF-36 is used, but also to analyse and interpret the effect of several explanatory variables on HRQoL. Further work is required to test the better performance of BBR against standard methods for other HRQoL outcomes, populations or interventions.