Modeling and Analyzing of Breast Tumor Deterioration Process with Petri Nets and Logistic Regression

It is important to understand the process of cancer cell metastasis and some cancer characteristics that increase disease risk. Because the occurrence of the disease is caused by many factors, and the pathogenesis process is also complicated. It is necessary to use interpretable and visual modeling methods to characterize this complex process. Machine learning techniques have demonstrated extraordinary capabilities in identifying models and extracting patterns from data to improve medical prognostic decisions. However, in most cases, it is unexplainable. Using formal methods to model can ensure the correctness and understandability of prediction decisions in a certain extent, and can well visualize the analysis process. Coloured Petri Nets (CPN) is a powerful formal model. This paper presents a modeling approach with CPN and machine learning in breast cancer, which can visualize the process of cancer cell metastasis and the impact of cell characteristics on the risk of disease. By evaluating the performance of several common machine learning algorithms, we finally choose the logistic regression algorithm to analyze the data, and integrate the obtained prediction model into the CPN model. Our method allows us to understand the relations among the cancer cell metastasis and clearly see the quantitative prediction results.