A Bayesian Analysis of Body Mass Index Data From Small Domains Under Nonignorable Nonresponse and Selection

Here we analyze body mass index (BMI) data for children and adolescents from the Third National Health and Nutrition Examination Survey (NHANES III). Because of the lack of BMI values for a considerable number of the children and adolescents, and the differential probabilities of selection of these individuals, serious nonresponse and selection bias in inference can be present. To analyze the NHANES III BMI data, a nonignorable nonresponse model has been proposed to estimate the finite population means of small domains formed by crossing age, race and sex within counties. In this approach, the log-BMI values are used to obtain more normally distributed data, and the model includes a spline regression of log-BMI on age, adjusted for race, sex, and the interaction of race and sex. In this work, to assess the status of overweight and obesity in children and adolescents, our new model predicts the more informative finite population percentiles of BMI for these small domains, incorporating additional measures to minimize possible biases. These measures are the most appropriate transformation for the skewed BMI data, incorporation of an intraclass correlation within the households, and inclusion of selection probabilities into the nonignorable nonresponse model to reflect the higher probabilities of selection among black non-Hispanics and Hispanic-Americans. We also consider robustness and sensitivity to the assumptions of the nonignorable nonresponse model by fitting several versions of our proposed model, as well as a very different ignorable nonresponse model that uses a mixture of Student t densities, selection probabilities, and BMI values. It is noteworthy that in the likelihood-based inference literature, we have seen no work by others that includes both nonignorable nonresponse and nonignorable selection. Based on NHANES III data, we show that there are differences in the 85th or 95th percentile for overweight by county, race, and particularly age, and a small difference in sex.

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