A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve.

The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.

Relationship of Socioeconomic Status Indicators to Obesity in Hispanic and Non-Hispanic White Middle-Aged Women: A Population Study.

BACKGROUND: Obesity rates differ between Hispanic and White (non-Hispanic) women in the United States, with higher rates among Hispanic women. Socioeconomic processes contribute to this disparity both at the individual and the environmental level. Understanding these complex relationships requires multilevel analyses within cohorts of women that have a shared environment. In population-based samples of Hispanic and White (non-Hispanic) women from the same neighborhoods, we evaluated within each ethnic group a) The association of individual-level socioeconomic status (SES) with body mass index (BMI); and b) The additional contribution of neighborhood-level measures of SES. METHODS: Using population-based multi-stage sampling methods, we oversampled low SES and Hispanic block groups. During household screening, we identified women aged 30 to 50 years. Among White women, we specifically oversampled women with low educational levels. 515 Hispanic and 503 White women completed baseline. Height and weight were measured. Baseline surveys, in Spanish and English, included four measures of SES. Three measures of area-level SES were examined. Analysis of loge BMI on each SES measure used linear mixed models, incorporating design effects. RESULTS: Among White women, low education, social status, and neighborhood SES were associated with higher BMI (p < 0.001, p < 0.0001, and p < 0.05, respectively), independent of other SES measures. Although the highest grouped category of education, income and subjective social status within the Hispanic cohort had the lowest mean estimated BMI, the point estimates across categories were not monotonic, and had wide confidence intervals. As a result, in contrast to the findings among White women, no statistically significant associations were found between BMI and measures of SES among Hispanic women. DISCUSSION: Neighborhood and individual measures of SES operate differently in Hispanic compared with White women. We had assumed the measures we included to be most salient and operate similarly for both groups of women. Rather the salient factors for Hispanic women have yet to be identified. Improved understanding may ultimately inform the design of culturally-relevant multilevel obesity prevention strategies.