A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization

Abstract

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.

Keywords

• linear combination
• stepwise algorithm
• Youden index
• biomarkers
• diagnosis