Diagnostic tests usually need to operate at a high sensitivity or specificity level in practice. Accordingly, specificity at the controlled sensitivity, or vice versa, is a clinically sensible performance metric for evaluating continuous biomarkers. Meanwhile, the performance of a biomarker may vary across sub-populations as defined by covariates, and covariate-specific evaluation can be informative. In this article, we develop a novel modeling and estimation method for covariate-specific specificity at a controlled sensitivity level. Unlike existing methods which typically adopt elaborate models of covariate effects over the entire biomarker distribution, our approach models covariate effects locally at a specific sensitivity level of interest. We also extend our proposed model to handle the whole continuum of sensitivities via dynamic regression and derive covariate-specific ROC curves. We provide the variance estimation through bootstrapping. The asymptotic properties are established. We conduct extensive simulation studies to evaluate the performance of our proposed methods in comparison with existing methods, and further illustrate the applications in two clinical studies for aggressive prostate cancer.
Keywords: continuous biomarker; dynamic regression; logistic regression; quantile regression; receiver operating characteristic curve; sensitivity; specificity; specificity at controlled sensitivity.
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