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Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of biomarkers, which is computationally tractable and has been shown to be optimal in certain scenarios. We developed the Min–Max–Median/IQR algorithm under Youden index optimisation which, although more computationally intensive, is still approachable and includes more information. The aim of this work is to compare the performance of these algorithms with well-known Machine Learning algorithms, namely logistic regression and XGBoost, which have proven to be efficient in various fields of applications, particularly in the health sector. This comparison is performed on a wide range of different scenarios of simulated symmetric or asymmetric data, as well as on real clinical diagnosis data sets. The results provide useful information for binary classification problems of better algorithms in terms of performance depending on the scenario. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]