Test-dependent sampling design and semi-parametric inference for the ROC curve

Horton, Bethany Jablonski

Test-dependent sampling design and semi-parametric inference for the ROC curve Public Deposited

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March 22, 2019

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Horton, Bethany Jablonski
- Affiliation: Gillings School of Global Public Health, Department of Biostatistics

Abstract

The receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) are used to describe the ability of a screening test to discriminate between diseased and non-diseased subjects. As evaluating the true disease status can be costly, researchers can increase study efficiency by allowing selection probabilities to depend on the screening test. We consider a test dependent sampling (TDS) design where TDS inclusion depends on a continuous screening test measure. Disease status is validated only for those in the SRS and TDS components. To improve efficiency, this sampling design incorporates three components: the simple random sample (SRS) component, TDS component, and the un-sampled subjects. We propose semi-parametric empirical likelihood estimators for the AUC, partial AUC, and the covariate-specific ROC curve. First, the AUC estimator allows us to summarize the ability of the screening test to distinguish between diseased and non-diseased subjects. Empirical likelihood methods are used to avoid making distributional assumptions for the screening test variable. Second, the AUC estimator is adapted to estimate partial AUC when a subset of false positive rates is more clinically relevant. Third, the covariate-specific ROC curve is estimated using a binormal model for the screening test variable. Although parametric assumptions are made for the screening test, distributional assumptions are avoided for the covariates by using empirical likelihood methods. This ROC curve estimator allows us to assess the influence covariates have on the accuracy of the diagnostic test. This cost-effective sampling design allows for a more powerful study on the same budget. Efficiency is gained in all three estimators by incorporating information from both the sampled and un-sampled portions of the population.

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