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Nonparametric Bayesian covariate‐adjusted estimation of the Youden index

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  • Vanda Inácio de Carvalho
  • Miguel de Carvalho
  • Adam J. Branscum

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.

Suggested Citation

  • Vanda Inácio de Carvalho & Miguel de Carvalho & Adam J. Branscum, 2017. "Nonparametric Bayesian covariate‐adjusted estimation of the Youden index," Biometrics, The International Biometric Society, vol. 73(4), pages 1279-1288, December.
    • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1279-1288
    DOI: 10.1111/biom.12686
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    References listed on IDEAS

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    1. GonzAlez-Manteiga, Wenceslao & Pardo-FernAndez, Juan Carlos & Van Keilegom, Ingrid, 2011. "ROC Curves in Non-Parametric Location-Scale Regression Models," LIDAM Reprints ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Leonidas E. Bantis & Christos T. Nakas & Benjamin Reiser, 2014. "Construction of confidence regions in the ROC space after the estimation of the optimal Youden index-based cut-off point," Biometrics, The International Biometric Society, vol. 70(1), pages 212-223, March.
    3. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    4. Wenceslao González‐Manteiga & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2011. "ROC Curves in Non‐Parametric Location‐Scale Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 169-184, March.
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    1. Fanjul-Hevia, Arís & González-Manteiga, Wenceslao & Pardo-Fernández, Juan Carlos, 2021. "A non-parametric test for comparing conditional ROC curves," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Yingli Pan & Zhan Liu & Guangyu Song, 2021. "Outlier detection under a covariate-adjusted exponential regression model with censored data," Computational Statistics, Springer, vol. 36(2), pages 961-976, June.

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