Multi-task banded regression model: A novel individual survival analysis model for breast cancer

To reveal the hazard probability of individual breast cancer patients, a multi-task banded regression model is proposed for individual survival analysis of breast cancer.A banded verification matrix is designed to construct the response transform function of the proposed multi-task banded regression model, which can solve the repeated switching of survival rate. A martingale process is introduced to construct different nonlinear regressions for different survival subintervals. The concordance index (C-index) is used to compare the proposed model with Cox proportional hazards (CoxPH) models and previous multi-task regression models.Two commonly-used breast cancer datasets are employed to validate the proposed model. Specifically, the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) includes 1981 breast cancer patients, of which 57.7% died of breast cancer. The Rotterdam & German Breast Cancer Study Group (GBSG) includes 1546 patients with lymph node-positive breast cancer in a randomized clinical trial, of which 44.4% died. Experimental results indicate that the proposed model is superior to some existing models for overall and individual survival analysis of breast cancer, with the C-index of 0.6786 for the GBSG and 0.6701 for the METABRIC.The superiority of the proposed model can be contributed to three novel ideas. One is that a banded verification matrix can band the response of the survival process. Second, the martingale process can construct different nonlinear regressions for different survival subintervals. Third, the novel loss can adapt the model to making the multi-task regression similar to the real survival process.