Evaluations and comparisons of treatment effects based on best combinations of biomarkers with applications to biomedical studies.

Many clinical and biomedical studies evaluate treatment effects based on multiple biomarkers that commonly consist of pre- and post-treatment measurements. Some biomarkers can show significant positive treatment effects, while other biomarkers can reflect no effects or even negative effects of the treatments, giving rise to a necessity to develop methodologies that may correctly and efficiently evaluate the treatment effects based on multiple biomarkers as a whole. In the setting of pre- and post-treatment measurements of multiple biomarkers, we propose to apply a receiver operating characteristic (ROC) curve methodology based on the best combination of biomarkers maximizing the area under the receiver operating characteristic curve (AUC)-type criterion among all possible linear combinations. In the particular case with independent pre- and post-treatment measurements, we show that the proposed method represents the well-known Su and Liu's (1993) result. Further, proceeding from derived best combinations of biomarkers' measurements, we propose an efficient technique via likelihood ratio tests to compare treatment effects. We show an extensive Monte Carlo study that confirms the superiority of the proposed test in comparison with treatment effects based on multiple biomarkers in a paired data setting. For practical applications, the proposed method is illustrated with a randomized trial of chlorhexidine gluconate on oral bacterial pathogens in mechanically ventilated patients as well as a treatment study for children with attention deficit-hyperactivity disorder and severe mood dysregulation.