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Diagnostic Accuracy of Biomarkers with a Continuous Gold Standard Open Access

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The receiver operating characteristic (ROC) curve is a very useful tool for describing and comparing the diagnostic accuracy of biomarkers when the binary-scale gold standard is available.There are, however, many examples of diagnostic tests whose gold standards are continuous. Hence, several extensions are proposed to evaluate the diagnostic potential of biomarkers when the gold standard is continuous-scale, such as the modified area under ROC curve (AUC)-type measure defined by Obuchowski. Also, diagnostic accuracy can be improved by effectively combining biomarkers. Some methods of maximizing diagnostic accuracy via linear combination of biomarkers are proposed. But there is no explicit form of the ROC-type measure and the best linear combination. In practice, the performances of biomarkers are affected by various factors beyond the disease status, for example, the characteristics of patients or test settings. In our research, we focused on the situations where the gold standard is continuous. For multiple biomarkers' test, an explicit form of ROC-type measure of diagnostic accuracy is derived under the elliptical distributions, a more general distribution than normal distribution, and so is the best linear combination. We also propose a linear combination by fitting regression of the gold standard on the biomarkers. It is the estimate of the best linear combination and much easier to compute. For the single biomarker's test, we proposed regression methods for adjusting the ROC-type measure with covariate effect. We discussed the regression modeling framework for categorical covariates and continuous covariates.

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