Modelling complex survey data with population level information: an empirical likelihood approach.

Survey data are often collected with unequal probabilities from a stratified population. In many modelling situations, the parameter of interest is a subset of a set of parameters, with the others treated as nuisance parameters. We show that in this situation the empirical likelihood ratio statistic follows a chi-squared distribution asymptotically, under stratified single and multi-stage unequal probability sampling, with negligible sampling fractions. Simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation, linearization or resampling.

Body mass index and common mental disorders: exploring the shape of the association and its moderation by age, gender and education.

BACKGROUND: Obesity is known to be associated with increased prevalence of common mental disorders (for example, depression and anxiety), and there is evidence of age and gender differences in this relationship. However, categorisation of body mass index (BMI) and age has limited our ability to understand the nature of these differences. This study used continuous values of BMI and age to explore the shape of the association between common mental disorders and BMI and whether it varied with age, gender and education. METHOD: The analysis used cross-sectional data on 7043 adults from the English 2007 Adult Psychiatric Morbidity Survey. Common mental disorders were assessed using the revised Clinical Interview Schedule (CIS-R). Cubic splines allowed BMI and age to have non-linear effects in the logistic regression analysis. RESULTS: BMI was strongly associated with the presence of common mental disorders, and there was clear evidence that this association varied with gender and age. In young women the probability of having a disorder increased as BMI increased, whereas in young men the relationship was U-shaped-probabilities were higher for both underweight and obese men. These associations diminished in older age groups, particularly when potential confounders such as physical health were taken into account. There was no evidence that the relationship varied with education. CONCLUSIONS: Age and gender differences must be taken into account when investigating the link between BMI or obesity and common mental disorders. Furthermore, results of studies that categorise BMI may be highly sensitive to the width of the 'normal weight' reference category.