Deep Evidential Learning for Radiotherapy Dose Prediction

TL;DR

This work introduces Deep Evidential Learning (DEL) to radiotherapy dose prediction within the OpenKBP framework, aiming to quantify both data-driven (aleatoric) and model-driven (epistemic) uncertainties. By reformulating the loss and employing a logit-normal likelihood with a normal–inverse–gamma prior, the model outputs four parameters $(\alpha,\beta,\nu,\gamma)$ that yield voxel-wise $U_a$ and $U_e$ and enable uncertainty-aware DVH confidence intervals. Empirical results show that epistemic uncertainty correlates strongly with prediction errors, with calibration superior to MC Dropout and Deep Ensemble in several metrics, while aleatoric uncertainty remains more sensitive to data noise. The approach furnishes uncertainty heatmaps and per-patient DVH bands, illustrating practical utility for clinical decision-making and highlighting a path toward uncertainty-aware knowledge-based planning in radiotherapy. Overall, the work demonstrates that DEL can provide robust, interpretable uncertainty estimates alongside dose predictions, supporting safer and more reliable treatment planning.

Abstract

In this work, we present a novel application of an uncertainty-quantification framework called Deep Evidential Learning in the domain of radiotherapy dose prediction. Using medical images of the Open Knowledge-Based Planning Challenge dataset, we found that this model can be effectively harnessed to yield uncertainty estimates that inherited correlations with prediction errors upon completion of network training. This was achieved only after reformulating the original loss function for a stable implementation. We found that (i)epistemic uncertainty was highly correlated with prediction errors, with various association indices comparable or stronger than those for Monte-Carlo Dropout and Deep Ensemble methods, (ii)the median error varied with uncertainty threshold much more linearly for epistemic uncertainty in Deep Evidential Learning relative to these other two conventional frameworks, indicative of a more uniformly calibrated sensitivity to model errors, (iii)relative to epistemic uncertainty, aleatoric uncertainty demonstrated a more significant shift in its distribution in response to Gaussian noise added to CT intensity, compatible with its interpretation as reflecting data noise. Collectively, our results suggest that Deep Evidential Learning is a promising approach that can endow deep-learning models in radiotherapy dose prediction with statistical robustness. Towards enhancing its clinical relevance, we demonstrate how we can use such a model to construct the predicted Dose-Volume-Histograms' confidence intervals.

Figures (8)

• Figure 1: A sketch of the Deep Evidential model with 3D U-Net backbone architecture. The 4-channel outputs of the model are the parameters of a normal-inverse-gamma distribution schematically plotted on the right. Details of the convolutional and other layer operations in the backbone segment are described earlier in Sec. \ref{['sec:modelh']} and largely identical to the original 3D U-Net of olaf. We adjoined the U-Net structure to the Deep Evidential framework by passing the output obtained after the final upsampling layer to two consecutive pointwise convolution layers with number of channels = 8, 4 respectively. The final output has dimensions $(128, 128, 128, 4)$.
• Figure 2: Plots of the validation and training mean-absolute-error (MAE) for the model equipped with the original (left) and our refined (right) loss functions.
• Figure 3: The median error plotted is that of the subset of the testing dataset which remains after imposing an upper threshold value for the uncertainty. We note that each model generated different ranges of uncertainty values.
• Figure 4: The left diagram pertained to Deep Evidential Learning where we included both the curves for aleatoric and epistemic uncertainties. On the right, we furnished a comparative plot where both median error and uncertainty threshold were normalized using their maximum values. This allows one to differentiate among the curves based on a common overall scaling.
• Figure 5: Dashed lines are the uncertainty eCDF in the absence of noise, while the corresponding solid curves show distributions in the presence of an added Gaussian noise with zero mean and standard deviation of 0.5 for the CT intensity value in each voxel. Shaded regions accentuate the more significant shift associated with aleatoric uncertainty (of the Deep Evidential Model) and Deep Ensemble's uncertainty distributions.