Maximum smoothed likelihood method for the combination of multiple diagnostic tests, with application to the ROC estimation

2026-01-07

AI Summary

This work proposes a semiparametric density ratio model to improve the accuracy of joint diagnosis using multiple biomarkers and to enable robust estimation of the receiver operating characteristic (ROC) curve. The method models the density ratio between diseased and healthy populations as a function of an unknown monotonic transformation applied to a linear combination of biomarkers, thereby relaxing restrictive assumptions such as exponential tilting commonly imposed in existing approaches. By integrating maximum smoothed likelihood estimation with nonparametric modeling of the monotonic function, the proposed framework achieves both computational efficiency and statistical precision under weaker assumptions. Theoretical analysis and numerical experiments demonstrate that the method substantially outperforms current techniques in estimating both the ROC curve and the area under the curve (AUC), offering a flexible and reliable tool for diagnostic biomarker evaluation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In medical diagnostics, leveraging multiple biomarkers can significantly improve classification accuracy compared to using a single biomarker. While existing methods based on exponential tilting or density ratio models have shown promise, their assumptions may be overly restrictive in practice. In this paper, we adopt a flexible semiparametric model that relates the density ratio of diseased to healthy subjects through an unknown monotone transformation of a linear combination of biomarkers. To enhance estimation efficiency, we propose a smoothed likelihood framework that exploits the smoothness in the underlying densities and transformation function. Building on the maximum smoothed likelihood methodology, we construct estimators for the model parameters and the associated probability density functions. We develop an effective computational algorithm for implementation, derive asymptotic properties of the proposed estimators, and establish procedures for estimating the receiver operating characteristic (ROC) curve and the area under the curve (AUC). Through simulation studies and a real-data application, we demonstrate that the proposed method yields more accurate and efficient estimates than existing approaches.

Problem

• diagnostic tests combination
• ROC estimation
• density ratio model
• multiple biomarkers
• classification accuracy

Innovation

• maximum smoothed likelihood
• semiparametric modeling
• density ratio
• monotone transformation
• ROC estimation