Inference On Diagnostic Accuracy When The Gold Standard Is Measured With Error

ROC curve is an instrument for describing and comparing the diagnostic accuracy of the biomarker,it is initially used when the gold standard is binary-scale,and then extended to the continuous-scale.However,for the restriction of cost and operability,the reference standard was chosen to replace the gold standard in application.By this time,there was a bias that could not be ignored between the diagnostic accuracy based on the reference standard and the true diagnostic accuracy.So the problem of how to estimate the biomarker of diagnostic accuracy based on the reference standard is concerned by statisticians and in pharmaceutical field.In this article,we considered the estimation of diagnostic accuracy when the gold standard is measured with error under elliptically contoured distribution.The diagnostic accuracy we used for the research is the index proposed by Obuchowski based on non-parametric method.Under this assumption of the additive error model,we proposed the point estimations and interval estimations of the diagnostic accuracy of biomarker(in univariate and multivariate cases).In Chapter 2,we considered the situation of univariate biomarker.Firstly,we gave the explicit form(only depends on the correlation coefficient)of Obuchowski's diagnostic accuracy under elliptically contoured distribution,and got the method of estimating the diagnostic accuracy of biomarker.Then,in the situation of the reliability coefficient is known and the variance of additive error is known,we proposed the methodology of bias-corrected for reference standard,and derived the asymptotic properties of estimators under the normal hypothesis.Finally,based on the estimators proposed in this article,we constructed Jackknife confidence intervals of the estimators.The results of simulation showed that even the sample size is not large,the coverage probabilities of the confidence intervals were very close to the nominal confidence level.In Chapter 3,we studied the problem of estimating the synthetical diagnostic accuracy with multiple biomarkers.Under elliptically contoured distribution,we applied the linear combination of biomarkers for dimension reduction to get the explicit form(only depends on the multiple correlation coefficient)of diagnostic accuracy by combining multiple biomarkers.Similar to the chapter 2,we proposed the estimators of diagnostic accuracy with combining multiple biomarkers and Jackknife confidence intervals.The simulation's results showed that the coverage probabilities of the confidence intervals were very close to the nominal level,and the Jackknife confidence intervals possessed the robustness.