Model uncertainty estimates for deep learning mammographic density prediction using ordinal and classification approaches

<i>Purpose</i>. Mammographic density is associated with the risk of developing breast cancer and can be predicted using deep learning methods. Model uncertainty estimates are not produced by standard regression approaches but would be valuable for clinical and research purposes. Our objective is to produce deep learning models with in-built uncertainty estimates without degrading predictive performance.<i>Approach</i>. We analysed data from over 150,000 mammogram images with associated continuous density scores from expert readers in the Predicting Risk Of Cancer At Screening (PROCAS) study. We re-designated the continuous density scores to 100 density classes then trained classification and ordinal deep learning models. Distributions and distribution-free methods were applied to extract predictions and uncertainties. A deep learning regression model was trained on the continuous density scores to act as a direct comparison.<i>Results</i>. The root mean squared error (RMSE) between expert assigned density labels and predictions of the standard regression model were 8.42 (8.34-8.51) while the RMSE for the classification and ordinal classification were 8.37 (8.28-8.46) and 8.44 (8.35-8.53) respectively. The average uncertainties produced by the models were higher when the density scores from pairs of expert readers density scores differ more, when different mammogram views of the same views are more variable, and when two separately trained models show higher variation.<i>Conclusions</i>. Using either a classification or ordinal approach we can produce model uncertainty estimates without loss of predictive performance.