Adjustment for measurement error in evaluating diagnostic biomarkers by using an internal reliability sample

Abstract

Biomarkers are often measured with error due to imperfect lab conditions or temporal variability within subjects. Using an internal reliability sample of the biomarker, we develop a parametric bias-correction approach for estimating a variety of diagnostic performance measures including sensitivity, specificity, the Youden index with its associated optimal cut-point, positive and negative predictive values, and positive and negative diagnostic likelihood ratios when the biomarker is subject to measurement error. We derive the asymptotic properties of the proposed likelihood-based estimators and show that they are consistent and asymptotically normally distributed. We propose confidence intervals for these estimators and confidence bands for the receiver operating characteristic curve. We demonstrate through extensive simulations that the proposed approach removes the bias due to measurement error and outperforms the naïve approach (which ignores the measurement error) in both point and interval estimation. We also derive the asymptotic bias of naïve estimates and discuss conditions in which naïve estimates of the diagnostic measures are biased toward estimates produced when the biomarker is ineffective (i.e., when sensitivity equals 1 - specificity) or are anticonservatively biased. The proposed method has broad biomedical applications and is illustrated using a biomarker study in Alzheimer's disease. We recommend collecting an internal reliability sample during the biomarker discovery phase in order to adequately evaluate the performance of biomarkers with careful adjustment for measurement error.