Estimation of an accuracy index of a diagnostic biomarker when the reference biomarker is continuous and measured with error

Abstract

New biomarkers continue to be developed for the purpose of diagnosis, and their diagnostic performances are typically compared with an existing reference biomarker used for the same purpose. Considerable amounts of research have focused on receiver operating characteristic curves analysis when the reference biomarker is dichotomous. In the situation where the reference biomarker is measured on a continuous scale and dichotomization is not practically appealing, an index was proposed in the literature to measure the accuracy of a continuous biomarker, which is essentially a linear function of the popular Kendall’s tau. We consider the issue of estimating such an accuracy index when the continuous reference biomarker is measured with errors. We first investigate the impact of measurement errors on the accuracy index, and then propose methods to correct for the bias due to measurement errors. Simulation results show the effectiveness of the proposed estimator in reducing biases. The methods are exemplified with hemoglobin A1c measurements obtained from both the central lab and a local lab to evaluate the accuracy of the mean data obtained from the metered blood glucose monitoring against the centrally measured hemoglobin A1c from a behavioral intervention study for families of youth with type 1 diabetes.

Error‐corrected estimation of a diagnostic accuracy index of a biomarker against a continuous gold standard

“…This is because under additive measurement models, Y o has larger variation than Y . As demonstrated by Wu et al, 33 the difference between these two indexes can be substantially large.…”

“…In this article, we established asymptotic normality of the error‐corrected estimator of Wu et al 33 with known reliability (or variance of measurement error) and the two newly proposed adaptive estimators with unknown reliability for the accuracy index of a continuous biomarker against a continuous gold standard that is measured with errors. For relatively small sample sizes, the confidence intervals based on the corresponding estimators lead to better precision.…”

“…Noting that the estimator is asymptotically unbiased for , and hence biased for , Wu et al 33 proposed an error‐corrected estimator of given by when r is known. They demonstrated via simulation that the proposed error‐corrected estimator substantially reduces both the biases and root mean square errors.…”

“…To the best of our knowledge, little work has been done in the literature on the impact of measurement errors and on how to correct the errors to reduce or eliminate the biases in estimating the accuracy index (Obuchowski index). To fill the gap, Wu et al 33 proposed an error‐corrected estimator for the accuracy index under the elliptical distribution assumption. The error‐corrected estimator requires the accuracy index known.…”