Bayesian combination of mechanistic modeling and machine learning (BaM3): improving personalized tumor growth predictions

In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient’s pathology producing a variety of clinical data. However, exploiting these data faces the following challenges: (C1) we lack the knowledge of the mechanisms involved in regulating these data variables, and (C2) data collection is sparse in time since it relies on patient’s clinical presentation. (C1) implies that only a small subset of the relevant variables can be modeled by virtue of mathematical modeling. This limitation allows models to be effective in analyzing the qualitative dynamics of the system, but limits their predictive accuracy. On the other hand, statistical learning methods are well-suited for quantitative reproduction of data, but they do not provide mechanistic understanding of the investigated problem. Moreover, due to (C2) any algorithm is challenged in learning the corresponding disease dynamics. Herein, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning (BaM 3 ), aiming at improving individualized predictions by addressing the aforementioned challenges. As a proof of concept, we evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two major clinical outputs, namely tumor burden and infiltration. The BaM 3 method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation. In addition, we test the proposed methodology in two settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, BaM 3 predictions show excellent agreement with reported clinical data.