A data-driven statistical model that estimates measurement uncertainty improves interpretation of ADC reproducibility: a multi-site study of liver metastases

Abstract

Apparent Diffusion Coefficient (ADC) is a potential quantitative imaging biomarker for tumour cell density and is widely used to detect early treatment changes in cancer therapy. We propose a strategy to improve confidence in the interpretation of measured changes in ADC using a data-driven model that describes sources of measurement error. Observed ADC is then standardised against this estimation of uncertainty for any given measurement. 20 patients were recruited prospectively and equitably across 4 sites, and scanned twice (test-retest) within 7 days. Repeatability measurements of defined regions (ROIs) of tumour and normal tissue were quantified as percentage change in mean ADC (test vs. re-test) and then standardised against an estimation of uncertainty. Multi-site reproducibility, (quantified as width of the 95% confidence bound between the lower confidence interval and higher confidence interval for all repeatability measurements), was compared before and after standardisation to the model. The 95% confidence interval width used to determine a statistically significant change reduced from 21.1 to 2.7% after standardisation. Small tumour volumes and respiratory motion were found to be important contributors to poor reproducibility. A look up chart has been provided for investigators who would like to estimate uncertainty from statistical error on individual ADC measurements.

Variability in quantitative diffusion-weighted MR imaging (DWI) across different scanners and imaging sites: is there a potential consensus that can help reducing the limits of expected bias?

“…Recently, a rather mathematically oriented study pursued a statistical approach to minimize ADC variability across four imaging sites with scanners from different vendors by implementing a post hoc correction model to already calculated parametric DW images [10]. The primary endpoint of this study was to define a statistical model of predictable sources of variability that contribute to measurement error (also including data sets with visible motion artifacts) and fit this to observed data in order to quantify the level of uncertainty in mean ADC repeatability.…”

“…According to the authors, implementation of the proposed model will allow significant improvements in sensitivity for detection of change in ADC. They provided a lookup chart to allow investigators to estimate uncertainty due to statistical measurement error, for any given tumor volume and ADC histogram width [10]. This model may help to assess reproducibility with greater confidence, and could also be easily implemented into clinical routine.…”

Considering tumour volume for motion corrected DWI of colorectal liver metastases increases sensitivity of ADC to detect treatment-induced changes

“…As shown in our previous work, uncertainty in the accurate estimation of ADC due to statistical measurement errors also adversely affects the ability to reliably detect change 25 . The smaller the sample and wider the distribution of ADC voxel values, the greater the statistical uncertainty around the mean ADC estimate.…”

“…A statistical measurement error model estimating ADC uncertainty has been described fully in a previous publication within this journal and is available open access 25 . Briefly, the estimate of a mean or percentile to accurately describe a histogram is dependent on the sample size of the distribution (equivalent to tumour volume in this case).…”

Errors-in-Variables Modeling of Personalized Treatment-Response Trajectories

“…In [26], the effect of measurement error on a binary treatment response is analyzed, underlining the devastating impact of ignoring such errors. A model for measurement errors has been used to quantify uncertainty in order to increase the confidence in detecting genuine treatment changes for liver metastases [31].…”