A min–max combination of biomarkers to improve diagnostic accuracy

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Abstract
Diagnostic accuracy can be improved considerably by combining multiple biomarkers. Although the likelihood ratio provides optimal solution to combination of biomarkers, the method is sensitive to distributional assumptions which are often difficult to justify. Alternatively simple linear combinations can be considered whose empirical solution may encounter intensive computation when the number of biomarkers is relatively large. Moreover, the optimal linear combinations derived under multivariate normality may suffer substantial loss of efficiency if the distributions are apart from normality. In this paper, we propose a new approach that linearly combines the minimum and maximum values of the biomarkers. Such combination only involves searching for a single combination coefficient that maximizes the area under the receiver operating characteristic (ROC) curves and is thus computation‐effective. Simulation results show that the min–max combination may yield larger partial or full area under the ROC curves and is more robust against distributional assumptions. The methods are illustrated using the growth‐related hormones data from the Growth and Maturation in Children with Autism or Autistic Spectrum Disorder Study (Autism/ASD Study). Copyright © 2011 John Wiley & Sons, Ltd.

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