Hierarchical Gaussian Process Modeling and Estimation of State-action Transition Dynamics in Breast Cancer

Breast cancer is the most prevalent type of cancer in the US. Available treatments, including mastectomy, radiation, and chemotherapy, vary in curability, cost, and mortality probability of patients. This research aims at tracking the result of post-treatment for evidence-based decision making in breast cancer. Based on available big data, we implemented conditional probability to estimate multi-age transition probability matrices to predict the progression of disease conditions. The patient state is defined based on patients' age, cancer stage, and treatment history. To tackle the incomplete data in the matrix, we design a novel Hierarchical Gaussian Distribution (HGP) to estimate the missing part of the table. The HGP model leads to the lowest Root Mean Square Error (RMSE), which is 35% lower than the Gaussian Process and 40% lower than Linear Regression. Results of transition probability estimation show that the chance of survival within a year for 40 to 50 years old patient with the distant stage of cancer is 96.5%, which is higher than even younger age groups.