Nonparametric Bayesian Covariate-Adjusted Estimation of the Youden Index

Abstract

A novel nonparametric regression model is developed for evaluating the covariate-specific accuracy of a continuous biological marker. Accurately screening diseased from nondiseased individuals and correctly diagnosing disease stage are critically important to health care on several fronts, including guiding recommendations about combinations of treatments and their intensities. The accuracy of a continuous medical test or biomarker varies by the cutoff threshold (c) used to infer disease status. Accuracy can be measured by the probability of testing positive for diseased individuals (the true positive probability or sensitivity, Se(c), of the test), and the true negative probability (specificity, Sp(c)) of the test. A commonly used summary measure of test accuracy is the Youden index, YI=max{Se(c)+Sp(c)-1:c∈ℝ}, which is popular due in part to its ease of interpretation and relevance to population health research. In addition, clinical practitioners benefit from having an estimate of the optimal cutoff that maximizes sensitivity plus specificity available as a byproduct of estimating YI. We develop a highly flexible nonparametric model to estimate YI and its associated optimal cutoff that can respond to unanticipated skewness, multimodality, and other complexities because data distributions are modeled using dependent Dirichlet process mixtures. Important theoretical results on the support properties of the model are detailed. Inferences are available for the covariate-specific Youden index and its corresponding optimal cutoff threshold. The value of our nonparametric regression model is illustrated using multiple simulation studies and data on the age-specific accuracy of glucose as a biomarker of diabetes.

Discrimination surfaces with application to region‐specific brain asymmetry analysis

“…A natural possibility for future work entails building alternative IMDs from other measures assessing discrimination between groups such as the Youden index—which has links with the Kolmogorov‐Smirnov statistic—or a standardized log‐rank statistic—which has links with the Wilcoxon rank statistic. Specifically, in a similar way that we argue here that discrimination surfaces have connections with the area under conditional ROC curves (cf Section 3.2), it would be naturally modeling our applied setting of interest with an analogue of the covariate‐adjusted Youden index, , with c t being a function of t ; the corresponding IMD would in this case result from maximizing YI t . In addition, a similar approach would entail developing standardized log‐rank statistics for random fields, , whose corresponding IMD would result from maximizing the discrimination surface over t in T .…”

Affinity-based measures of biomarker performance evaluation

“…In model fitting, the patients' ages were first rescaled from the interval [46.75,80.83] to the interval [-1,1], and, following numerical evidence from Inácio de Carvalho et al. 39 (Section 3), we elected not to include any additional knots in the cubic B-splines.…”

“…With this in mind, we obtained conditional density estimates for each biomarker in each population to estimate (age) and AUC(age) by fitting the conditional model and collecting 1 800 MCMC iterates after a burn in of 20 000 and thinning of 100 and using the same specifications as before. In model fitting, the patients' ages were first rescaled from the interval [46.75, 80.83] to the interval [ 1, 1], and, following numerical evidence from Inácio de Carvalho et al 39 (Section 3), we elected to not to include any additional knots in the cubic B-splines. Figure 9 displays the posterior mean and pointwise 95% credible intervals for  and AUC as a function of age.…”

Bayesian bootstrap inference for the receiver operating characteristic surface

“…Moreover, point estimates and credible intervals for the ROC surface and its corresponding VUS are obtained in a single integrated framework. Recent developments of flexible Bayesian models that have been successfully applied in medical diagnostic testing research abound (e.g., Branscum, Johnson, Hanson, & Gardner, ; Branscum, Johnson, & Baron, ; Branscum, Johnson, Hanson, & Baron, ; Erkanli, Sung, Jane Costello, & Angold, ; Hwang & Chen, ; Inácio de Carvalho, Jara, Hanson, & de Carvalho, ; Inácio de Carvalho, de Carvalho, & Branscum, ; Inácio de Carvalho & Branscum, ; Rodríguez & Martínez, ; Zhao, Feng, Chen, & Taylor, ).…”