Modelling cause‐specific hazards with radial basis function artificial neural networks: application to 2233 breast cancer patients

The clinical course of a disease is often characterized by the possible occurrence of different types of events acting in a competing way. From a statistical point of view this translates into the need of modelling the dependence of cause-specific hazards as a function of covariates. Generalized linear models with Poisson error have previously been adopted for the analysis of competing risks as a function of discrete covariates. In the present paper an artificial neural network extension for the flexible joint estimation of cause-specific hazards depending on both discrete and continuous covariates is proposed. This approach is based on radial basis function networks which have the advantage of allowing parameter estimation by the adoption of standard software for generalized linear models. We have applied this method to data from 2233 breast cancer patients to investigate the effects of age, tumour size, number of metastatic axillary nodes, histology and tumour site on cause-specific hazards for intra-breast tumour recurrences and distant metastases. The adoption of a radial basis function network made it possible to highlight effects that were not considered by previous analyses of the same data.