Representation of Ordinal Features: Supervised Embeddings in the Survival Prediction of Prostate Cancer Patients

Prostate cancer (PCa) is the most common cancer in men. Treatment decisions for PCa consider factors like age, tumor stage, and grade, along with specific prostate-related factors such as prostate-specific antigen (PSA) level and Gleason score. Most of these features are ordinal, meaning they have an inherent order of their categorical levels. Machine learning (ML) approaches are increasingly used to PCa prognosis. However, most ML models are not able to handle categorical features directly, so they need to be transformed into numerical representations. Common methods are ordinal or one-hot encoding. A more recent and promising approach is embedding encoding, that is able to represent ordinal feature levels more accurately in their clinical relevance. This study investigates the prediction performance in the 5-year event-free survival in PCa patients using an artificial neural network (ANN). We compare the representation of ordinal features through embedding vs. ordinal encoding. By visualizing these embeddings, we aim to illustrate how embeddings capture clinically relevant patterns more effectively. The data used is provided by the Cancer Registry Rhineland-Palatinate, containing information about 10,168 PCa patients. Our results show that one-dimensional embeddings represent ordinal features significantly better than standard techniques. The representation aligns qualitatively with clinical practice for survival prognosis of PCa patients. This highlights the importance of embedding encoding that captures more clinically meaningful patterns and provides deeper insights into how individual feature levels impact PCa patient survival outcomes.