Estimation of Optimally Combined-Biomarker Accuracy in the Absence of a Gold Standard Reference Test

Abstract

The reference diagnostic test used to establish the discriminative properties of a combination of biomarkers could be imperfect. This may lead to a biased estimate of the accuracy of the combination. A Bayesian latent-class mixture model is proposed to estimate the Area Under the ROC Curve (AUC) of a combination of biomarkers. The model allows selecting the combination that maximizes the AUC and takes possible errors in the reference test into account. A simulation study was performed based on 400 data sets. Sample sizes from 100 to 600 observations were considered. Informative as well as non-informative prior information for the diagnostic accuracy of the reference test was considered. In addition, a controlled prior specification is proposed. The obtained average estimates for all parameters were close to the true values; some differences in efficiency were observed. Results indicate an adequate performance of the model-based estimates.