Statistical analyses and software

The performance of our model was assessed based on the AUC, accuracy, balanced accuracy, sensitivity, specificity, and Matthews Correlation Coefficient (MCC; ref. 36). ROC curves were plotted using the predicted probability scores together with the ground truth labels. For all cohorts, the probability scores were binarized into predicted classes using the best threshold from the ROC curves of the training data. Slide preprocessing and training the DL model were performed using python (v3.7.5), openslide (v3.4.1), and PyTorch (v1.3.1). Regarding the segmentation and classification of nuclei, we employed the PyTorch (v1.6) implementation of the HoVer-Net model, previously trained on the PanNuke dataset (37, 38). Survival analyses were performed using the survival (v3.3–1; refs. 42, 43) and survminer (v0.4.9; ref. 44) packages. The code used to perform this analysis is publicly available on GitHub and can be accessed using the following link: https://github.com/MohamedOmar2020/pca_ERG