Incorporating a New Summary Statistic into the Min–Max Approach: A Min–Max–Median, Min–Max–IQR Combination of Biomarkers for Maximising the Youden Index

Rocío Aznar-Gimeno, Luis M. Esteban, Gerardo Sanz, Rafael del-Hoyo-Alonso and Ricardo Savirón-Cornudella
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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
Gerardo Sanz: Department of Statistical Methods and Institute for Biocomputation and Physics of Complex Systems-BIFI, University of Zaragoza, 50009 Zaragoza, Spain
Rafael del-Hoyo-Alonso: Department of Big Data and Cognitive Systems, Instituto Tecnológico de Aragón (ITAINNOVA), 50018 Zaragoza, Spain
Ricardo Savirón-Cornudella: Department of Obstetrics and Gynecology, Hospital Clínico San Carlos and Instituto de Investigación Sanitaria San Carlos (IdISSC), Universidad Complutense de Madrid, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 19, 1-17

Abstract: Linearly combining multiple biomarkers is a common practice that can provide a better diagnostic performance. When the number of biomarkers is sufficiently high, a computational burden problem arises. Liu et al. proposed a distribution-free approach (min–max approach) that linearly combines the minimum and maximum values of the biomarkers, involving only a single coefficient search. However, the combination of minimum and maximum biomarkers alone may not be sufficient in terms of discrimination. In this paper, we propose a new approach that extends that of Liu et al. by incorporating a new summary statistic, specifically, the median or interquartile range (min–max–median and min–max–IQR approaches) in order to find the optimal combination that maximises the Youden index. Although this approach is more computationally intensive than the one proposed by Liu et al, it includes more information and the number of parameters to be estimated remains reasonable. We compare the performance of the proposed approaches (min–max–median and min–max–IQR) with the min–max approach and logistic regression. For this purpose, a wide range of different simulated data scenarios were explored. We also apply the approaches to two real datasets (Duchenne Muscular Dystrophy and Small for Gestational Age).

Keywords: linear combination; biomarkers; classification; Youden index; summary statistic; min–max approach; logistic regression; median; interquartile range (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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