An Empirical Bayes Approach to Robust Variance Estimation: A Statistical Proposal for Quantitative Medical Image Testing

The current standard for measuring tumor response using X-ray, CT and MRI is based on the response evaluation criterion in solid tumors (RECIST) which, while providing simplifications over previous (WHO) 2-D methods, stipulate four response categories: CR (complete response), PR (partial response), PD (progressive disease), SD (stable disease) based purely on percentage changes without consideration of any measurement uncertainty. In this paper, we propose a statistical procedure for tumor response assessment based on uncertainty measures of radiologist's measurement data. We present several variance estimation methods using time series methods and empirical Bayes methods when a small number of serial observations are available on each member of a group of subjects. We use a publically available database which contains a set of over 100 CT scan images on 23 patients with annotated RECIST measurements by two radiologist readers. We show that despite of bias in each individual reader's measurements, statistical decisions on tumor change can be made on each individual subject. The consistency of the two readers can be established based on the intra-reader change assessments. Our proposal compares favorably with the RECIST standard protocol, raising the hope that, statistically sound decision on change analysis can be made in future based on careful variability and measurement uncertainty analysis.