Algorithm for Constructing the Hazard Function of the Extended Cox Model and its Application to the Prostate Cancer Patient Database

Introduction . In medicine and related industries, bioinspired approaches are used for the survival analysis, among which the Cox regression model holds a specific place. The practice of its application is described in the theoretical and applied literature. However, a significant drawback of this method requires careful study. The fact is that the features correlate with the hazard function linearly, and the model does not use more complex dependences. This causes some difficulties in studying survival analysis. The presented work is aimed at solving this problem. The object of study is the extended Cox model, in which the hazard function includes a nonlinear combination of features. Materials and Methods . A database of prostate cancer patients was used, since this is a common diagnosis in global oncology. A class of extended Cox models with an additive/multiplicative hazard function was defined. To solve the problem using the optimization method, a fitness function was constructed that evaluated the results of prognosis, the number of features, and the degree of overtraining of the model — the complexity and load of the compiled hazard function. An algorithm of pollinating ants has been developed to optimize the fitness function. It simulates the reproduction of flowering plants using pollinating insects and consists of three parts: an ant colony algorithm, a genetic algorithm, and an ant pollinator algorithm. The quality of training of the Cox model was assessed by C-index. Results . A metaheuristic algorithm for ant pollinator optimizing was proposed, providing for the construction of hazard functions of the extended Cox model. The set of parameters for training the standard Cox model was the entire set of features used: TNM, prostate-specific antigen doubling time (PSADT), Gleason score, serum PSA concentration at diagnosis, patient age and education, Rh factor. C-index value of the trained model was 0.853691. The extended Cox model with the found additive/multiplicative hazard function had a higher C-index value — 0.856241 with a smaller number of features used (TNM, PSADT, and Gleason score). In terms of quality, this approach is not inferior to or superior to the classical Cox model. Reducing the number of features involved should improve the efficiency of medical decisions and speed up the start of treatment. Discussion and Conclusion . The presented algorithm for constructing survival analysis models increased the accuracy of predicting the occurrence of a terminal event, and reduced the number of features used for this purpose. The difference in accuracy for the studied data set seemed insignificant — C-index increased from 0.853691 to 0.856241 (by 0.3%). At this, the number of features taken into account was reduced from 7 to 3 (by 57.1%). Consequently, the proposed method effectively solves the problem of feature selection, and can be applied to improve the quality of prognostication.