Uncertainty Quantification in Automated Detection of Vertebral Metastasis Using Ensemble Monte Carlo Dropout

Abstract

The accurate and early detection of vertebral metastases is crucial for improving patient outcomes. Although deep-learning models have shown potential in this area, their lack of prediction reliability and robustness limits their clinical utility. To address these challenges, we propose a novel technique called Ensemble Monte Carlo Dropout (EMCD) for uncertainty quantification (UQ), which combines the Monte Carlo dropout and deep ensembles. In this retrospective study, we analyzed 11,468 abdominal computed tomography images from 116 patients diagnosed with vertebral metastases and 957 images from 11 healthy controls. Uncertainty was quantified and visualized using single number, predictive probability interval, posterior distribution and uncertainty class activation maps to provide a detailed understanding of prediction confidence. The EMCD model demonstrated superior performance compared with traditional UQ methods, achieving an area under the receiver operating characteristic curve (AUC) of 0.93 and an expected calibration error of 0.09, indicating high predictive accuracy and reliability. In addition, the model exhibited strong performance in handling out-of-distribution data. When data retention was applied based on uncertainty values, the AUC of the model improved to 0.96, highlighting the potential of uncertainty-driven data selection to enhance performance. The EMCD model represents a significant advancement in the automated detection of vertebral metastases, providing superior diagnostic accuracy and introducing a robust UQ framework to aid clinicians in making informed decisions.