A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

The relationship between supermarket nutrient movements and the mortality rates from fat-associated and non-fat-associated cardiovascular disease: Development of an ecologic method for determining community food patterns

Supermarket nutrient movement, a community food consumption measure, aggregated 1,023 high-fat foods, representing 100% of visible fats and approximately 44% of hidden fats in the food supply (FAO, 1980). Fatty acid and cholesterol content of foods shipped from the warehouse to 47 supermarkets located in the Houston area were calculated over a 6 month period. These stores were located in census tracts with over 50% of a given ethnicity: Hispanic, black non-Hispanic, or white non-Hispanic. Categorizing the supermarket census tracts by predominant ethnicity, significant differences were found by ANOVA in the proportion of specific fatty acids and cholesterol content of the foods examined. Using ecological regression, ethnicity, income, and median age predicted supermarket lipid movements while residential stability did not. No associations were found between lipid movements and cardiovascular disease mortality, making further validation necessary for epidemiological application of this method. However, it has been shown to be a non-reactive and cost-effective method appropriate for tracking target foods in populations of groups, and for assessing the impact of mass media nutrition education, legislation, and fortification on community food and nutrient purchase patterns. ^