A Novel Sensitivity Maximization at a Given Specificity Method for Binary Classifications

In the cancer early detection field, logistic regression (LR) is a frequently used approach to establish a combination rule that differentiates cancer from noncancer. However, the application of LR relies on a maximum likelihood approach, which may not yield optimal combination rules for maximizing sensitivity at a clinically desirable specificity and vice versa. In this article, we have developed an improved regression framework, sensitivity maximization at a given specificity (SMAGS), for binary classification that finds the linear decision rule, yielding the maximum sensitivity for a given specificity or the maximum specificity for a given sensitivity. We additionally expand the framework for feature selection that satisfies sensitivity and specificity maximizations. We compare our SMAGS method with normal LR using two synthetic datasets and reported data for colorectal cancer from the 2018 CancerSEEK study. In the colorectal cancer CancerSEEK dataset, we report 14% improvement in sensitivity at 98.5% specificity (0.31 vs. 0.57; P value <0.05). The SMAGS method provides an alternative to LR for modeling combination rules for biomarkers and early detection applications. Prevention Relevance: This study introduces a new machine learning methodology that identifies the optimal features and combination rules to maximize sensitivity at a fixed specificity, making it applicable to many existing biomarker prevention studies.