A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization

Rocío Aznar-Gimeno, Luis M. Esteban, Rafael del-Hoyo-Alonso, Ángel Borque-Fernando and Gerardo Sanz
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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

Mathematics, 2022, vol. 10, issue 8, 1-26

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.

Keywords: linear combination; stepwise algorithm; Youden index; biomarkers; diagnosis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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