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Estimation of ROC Curve with Complex Survey Data Open Access

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Receiver Operating Characteristic (ROC) curve analysis has gained an increased interest in past decades. It has been widely used to evaluate the performance of diagnostic tests. The area under the ROC curve (denoted by AUC) is the most commonly used summary index of a ROC curve. A larger AUC value for a diagnostic test usually means that the test has better discriminating ability between diseased and non-diseased populations. Both parametric and nonparametric methods have been developed to estimate and compare AUCs. However, these methods are standardly used for simple random sample, not complex samples.In surveys, complex sample designs with cluster sampling are commonly implemented. The Hispanic Health and Nutrition Examination Survey (HHANES) was conducted to assess the health and nutritional status the population of Hispanic individuals aged 6 months to 74 years in specific areas in U.S. by using a multistage, stratified, probability design with complex weight calculation. Analyses without accounting for weighting and clustering effect that is induced by the complex survey sampling can be biased. Thus, standard statistical methods of estimation of AUC for the population and its variance are not applicable to complex survey data.In this dissertation, we propose an extension of the nonparametric method in the estimation of the population AUC that accounts for sample weighting under differing complex survey designs. We provide and study the accuracy of a jackknife method, along with balanced repeated replication (BRR), for variance estimation of our proposed estimator of AUC. We also discuss informative sample designs where the selection probabilities are related to the parameter of interest, so that the standard analyses that ignore the sample weights can be seriously biased. Finally, our proposed methods are then applied to the Mexican-American portion of the HHANES to compare the classification accuracy of three predictors for overweight/obese using measured BMI as a gold standard.

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