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

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).