Strategies for handling normality assumptions in multi-level modeling: a case study estimating trajectories of Health Utilities Index Mark 3 scores.

BACKGROUND: With longitudinal data, lifetime health statusŏ dynamics can be estimated by modeling trajectories. Health status trajectories measured by the Health Utilities Index Mark 3 (HUI3) modeled as a function of age alone and also of age and socio-economic covariates revealed non-normal residuals and variance estimation problems. The possibility of transforming the HUI3 distribution to obtain residuals that approximate a normal distribution was investigated. DATA AND METHODS: The analysis is based on longitudinal data from the first six cycles of the National Population Health Survey (NPHS). The data pertain to 7,784 individuals, who, in 1994/1995, were aged 40 to 99, were living in private households, and had complete information on HUI3. A multilevel growth model was used to examine the hierarchical structure of NPHS data (repeated measurements nesting within respondents). The transformation of arcsine [2 x (HUI + 0.36) / (1 + 0.36)-1] was used to improve the distribution of the residuals at both levels and limit the conditional mean to the -0.36 to 1.00 interval. A model was estimated using socio-economic determinants. Analyses were performed with SAS and MLwiN. RESULTS: After the transformation of HUI3, the model was satisfactory and allowed for inclusion of new socio-demographic and health variables in order to estimate their impact on the health-related quality of life of aging populations. Because of the complex transformation of the arcsine model, the regression coefficients were not interpreted. Instead, the estimation results were summarized graphically.