Predicting survival outcomes using topological features of tumor pathology images

Tumor shape and size have been used as important markers for cancer diagnosis and treatment. Recent developments in medical imaging technology enable more detailed segmentation of tumor regions in high resolution. This paper proposes a topological feature to characterize tumor progression from digital pathology images and examine its effect on the time-to-event data. We develop distance transform for pathology images and show that a topological summary statistic computed by persistent homology quantifies tumor shape, size, distribution, and connectivity. The topological features are represented in functional space and used as functional predictors in a functional Cox regression model. A case study is conducted using non-small cell lung cancer pathology images. The results show that the topological features predict survival prognosis after adjusting for age, sex, smoking status, stage, and size of tumors. Also, the topological features with non-zero effects correspond to the shapes that are known to be related to tumor progression. Our study provides a new perspective for understanding tumor shape and patient prognosis.