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A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization

Author

Listed:
  • Rocío Aznar-Gimeno

    (Department of Big Data and Cognitive Systems, Instituto Tecnológico de Aragón (ITAINNOVA), 50018 Zaragoza, Spain)

  • Luis M. Esteban

    (Department of Applied Mathematics, Escuela Universitaria Politécnica de La Almunia, Universidad de Zaragoza, La Almunia de Doña Godina, 50100 Zaragoza, Spain)

  • Rafael del-Hoyo-Alonso

    (Department of Big Data and Cognitive Systems, Instituto Tecnológico de Aragón (ITAINNOVA), 50018 Zaragoza, Spain)

  • Ángel Borque-Fernando

    (Department of Urology, Hospital Universitario Miguel Servet and IIS-Aragón, Paseo Isabel La Católica 1-3, 50009 Zaragoza, Spain)

  • Gerardo Sanz

    (Department of Statistical Methods and Institute for Biocomputation and Physics of Complex Systems-BIFI, University of Zaragoza, 50009 Zaragoza, Spain)

Abstract

Combining multiple biomarkers to provide predictive models with a greater discriminatory ability is a discipline that has received attention in recent years. Choosing the probability threshold that corresponds to the highest combined marker accuracy is key in disease diagnosis. The Youden index is a statistical metric that provides an appropriate synthetic index for diagnostic accuracy and a good criterion for choosing a cut-off point to dichotomize a biomarker. In this study, we present a new stepwise algorithm for linearly combining continuous biomarkers to maximize the Youden index. To investigate the performance of our algorithm, we analyzed a wide range of simulated scenarios and compared its performance with that of five other linear combination methods in the literature (a stepwise approach introduced by Yin and Tian, the min-max approach, logistic regression, a parametric approach under multivariate normality and a non-parametric kernel smoothing approach). The obtained results show that our proposed stepwise approach showed similar results to other algorithms in normal simulated scenarios and outperforms all other algorithms in non-normal simulated scenarios. In scenarios of biomarkers with the same means and a different covariance matrix for the diseased and non-diseased population, the min-max approach outperforms the rest. The methods were also applied on two real datasets (to discriminate Duchenne muscular dystrophy and prostate cancer), whose results also showed a higher predictive ability in our algorithm in the prostate cancer database.

Suggested Citation

  • Rocío Aznar-Gimeno & Luis M. Esteban & Rafael del-Hoyo-Alonso & Ángel Borque-Fernando & Gerardo Sanz, 2022. "A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization," Mathematics, MDPI, vol. 10(8), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1221-:d:789432
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    References listed on IDEAS

    as
    1. Hua Ma & Susan Halabi & Aiyi Liu, 2019. "On the Use of Min-Max Combination of Biomarkers to Maximize the Partial Area under the ROC Curve," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-13, February.
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    5. Luis Mariano Esteban & Gerardo Sanz & Angel Borque, 2011. "A step-by-step algorithm for combining diagnostic tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 899-911, February.
    6. Yin, Jingjing & Tian, Lili, 2014. "Joint inference about sensitivity and specificity at the optimal cut-off point associated with Youden index," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 1-13.
    7. Rota, Matteo & Antolini, Laura, 2014. "Finding the optimal cut-point for Gaussian and Gamma distributed biomarkers," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 1-14.
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    1. Haneen Hamam & Ali Raza & Manal M. Alqarni & Jan Awrejcewicz & Muhammad Rafiq & Nauman Ahmed & Emad E. Mahmoud & Witold Pawłowski & Muhammad Mohsin, 2022. "Stochastic Modelling of Lassa Fever Epidemic Disease," Mathematics, MDPI, vol. 10(16), pages 1-17, August.

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