Monotonic Functions Method and Its Application to Staging of Patients with Prostate Cancer According to Pretreatment Data

Prostate cancer is the second most frequent malignancy (after lung cancer). Preoperative staging of PCa is the basis for the selection of adequate treatment tactics. In particular, an urgent problem is the classification of indolent and aggressive forms of PCa in patients with the initial stages of the tumor process. To solve this problem, we propose to use a new binary classification machine-learning method. The proposed method of monotonic functions uses a model in which the disease’s form is determined by the severity of the patient’s condition. It is assumed that the patient’s condition is the easier, the less the deviation of the indicators from the normal values inherent in healthy people. This assumption means that the severity (form) of the disease can be represented by monotonic functions from the values of the deviation of the patient’s indicators beyond the normal range. The method is used to solve the problem of classifying patients with indolent and aggressive forms of prostate cancer according to pretreatment data. The learning algorithm is nonparametric. At the same time, it allows an explanation of the classification results in the form of a logical function. To do this, you should indicate to the algorithm either the threshold value of the probability of successful classification of patients with an indolent form of PCa, or the threshold value of the probability of misclassification of patients with an aggressive form of PCa disease. The examples of logical rules given in the article show that they are quite simple and can be easily interpreted in terms of preoperative indicators of the form of the disease.