A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization
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...
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/8/1221 |
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| author | Rocío Aznar-Gimeno Luis M. Esteban Rafael del-Hoyo-Alonso Ángel Borque-Fernando Gerardo Sanz |
| author_facet | Rocío Aznar-Gimeno Luis M. Esteban Rafael del-Hoyo-Alonso Ángel Borque-Fernando Gerardo Sanz |
| author_sort | Rocío Aznar-Gimeno |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T04:25:59Z |
| format | Article |
| id | doaj.art-8da2e02c35204236bf51c4e8b9d32a4a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:25:59Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8da2e02c35204236bf51c4e8b9d32a4a2023-12-03T13:40:00ZengMDPI AGMathematics2227-73902022-04-01108122110.3390/math10081221A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index MaximizationRocío Aznar-Gimeno0Luis M. Esteban1Rafael del-Hoyo-Alonso2Ángel Borque-Fernando3Gerardo Sanz4Department of Big Data and Cognitive Systems, Instituto Tecnológico de Aragón (ITAINNOVA), 50018 Zaragoza, SpainDepartment of Applied Mathematics, Escuela Universitaria Politécnica de La Almunia, Universidad de Zaragoza, La Almunia de Doña Godina, 50100 Zaragoza, SpainDepartment of Big Data and Cognitive Systems, Instituto Tecnológico de Aragón (ITAINNOVA), 50018 Zaragoza, SpainDepartment of Urology, Hospital Universitario Miguel Servet and IIS-Aragón, Paseo Isabel La Católica 1-3, 50009 Zaragoza, SpainDepartment of Statistical Methods and Institute for Biocomputation and Physics of Complex Systems-BIFI, University of Zaragoza, 50009 Zaragoza, SpainCombining 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.https://www.mdpi.com/2227-7390/10/8/1221linear combinationstepwise algorithmYouden indexbiomarkersdiagnosis |
| spellingShingle | Rocío Aznar-Gimeno Luis M. Esteban Rafael del-Hoyo-Alonso Ángel Borque-Fernando Gerardo Sanz A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization Mathematics linear combination stepwise algorithm Youden index biomarkers diagnosis |
| title | A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization |
| title_full | A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization |
| title_fullStr | A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization |
| title_full_unstemmed | A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization |
| title_short | A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization |
| title_sort | stepwise algorithm for linearly combining biomarkers under youden index maximization |
| topic | linear combination stepwise algorithm Youden index biomarkers diagnosis |
| url | https://www.mdpi.com/2227-7390/10/8/1221 |
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