Imperfect reference standards cause biased likelihood ratios

In a study of the diagnostic accuracy of a quantitative biomarker, the researcher compares the concentration of the biomarker in patients with and without the disease in question. The diagnosis must be set without knowledge of the biomarker concentration, using the best reference standard available. If the reference standard is not perfect, the estimates of the receiver operating characteristic (ROC) curves will be biased. The likelihood ratio (LR) for the biomarker concentration, the measure connecting pretest and posttest probability, will also be biased when imperfect reference standards are used. In this work, we used simulated datasets to study how much the LRs were affected in different scenarios of prevalence of disease and correlation between the biomarker and the imperfect reference standard. Using the diagnosis of iron deficiency as an example, we showed that the estimated likelihood ratios for S-transferrin saturation may be biased in a clinically significant way.