Applicability of the regression approach for histological multi-class grading in clear cell renal cell carcinoma

The histological grading of carcinoma has been one of the central applications of task-specific deep learning in pathology. The deep learning method has pushed away the regression approach, which has been exploited for two-class classification, to address multi-class classification. However, the applicability of the regression approach on multi-class carcinoma grading has not been extensively investigated. Here, we show that the regression approach is sufficiently compatible with classification regarding the four-class grading of clear cell renal cell carcinoma using 11,826 histological image patches from 16 whole slide images. Using convolutional neural network models (DenseNet-121 and Inception-v3), we found that regression models predict as accurately as classification models, achieving an accuracy of 0.990 at the highest, with fewer prediction errors by two or more grades. Furthermore, we found that the predictions by the regression models qualitatively capture intra-tumor heterogeneity of grades using the composite image patches. Our results demonstrate that the regression approach offers advantages in making a core of the multi-class grade prediction tools for practice.