Uncertainty estimation using a 3D probabilistic U-Net for segmentation with small radiotherapy clinical trial datasets

Background and objectives: Bio-medical image segmentation models typically attempt to predict one segmentation that resembles a ground-truth structure as closely as possible. However, as medical images are not perfect representations of anatomy, obtaining this ground truth is not possible. A surrogate commonly used is to have multiple expert observers define the same structure for a dataset. When multiple observers define the same structure on the same image there can be significant differences depending on the structure, image quality/modality and the region being defined. It is often desirable to estimate this type of aleatoric uncertainty in a segmentation model to help understand the region in which the true structure is likely to be positioned. Furthermore, obtaining these datasets is resource intensive so training such models using limited data may be required. With a small dataset size, differing patient anatomy is likely not well represented causing epistemic uncertainty which should also be estimated so it can be determined for which cases the model is effective or not.

Methods: We use a 3D probabilistic U-Net to train a model from which several segmentations can be sampled to estimate the range of uncertainty seen between multiple observers. To ensure that regions where observers disagree most are emphasised in model training, we expand the Generalised Evidence Lower Bound (ELBO) with a Constrained Optimisation (GECO) loss function with an additional contour loss term to give attention to this region. Ensemble and Monte-Carlo dropout (MCDO) uncertainty quantification methods are used during inference to estimate model confidence on an unseen case. We apply our methodology to two radiotherapy clinical trial datasets, a gastric cancer trial (TOPGEAR, TROG 08.08) and a post-prostatectomy prostate cancer trial (RAVES, TROG 08.03). Each dataset contains only 10 cases each for model development to segment the clinical target volume (CTV) which was defined by multiple observers on each case. An additional 50 cases are available as a hold-out dataset for each trial which had only one observer define the CTV structure on each case. Up to 50 samples were generated using the probabilistic model for each case in the hold-out dataset. To assess performance, each manually defined structure was matched to the closest matching sampled segmentation based on commonly used metrics.

Results: The TOPGEAR CTV model achieved a Dice Similarity Coefficient (DSC) and Surface DSC (sDSC) of 0.7 and 0.43 respectively with the RAVES model achieving 0.75 and 0.71 respectively. Segmentation quality across cases in the hold-out datasets was variable however both the ensemble and MCDO uncertainty estimation approaches were able to accurately estimate model confidence with a p-value < 0.001 for both TOPGEAR and RAVES when comparing the DSC using the Pearson correlation coefficient.

Conclusions: We demonstrated that training auto-segmentation models which can estimate aleatoric and epistemic uncertainty using limited datasets is possible. Having the model estimate prediction confidence is important to understand for which unseen cases a model is likely to be useful.