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.