Isotonic proportional hazard model for breast cancer patients

Abstract

Aim: There are many survival analysis methods in oncological studies. Each model is used in dif - ferent data structures. The isotonic proportional hazard model is a survival model among these methods. The use of isotonic models is proposed to evaluate the relationship between time to event outcome and monotonically increasing covariate in survival analysis. The aim of this study is to explain the theoretical properties and usage of isotonic models and demonstrate their applica- tion on an appropriate dataset. Methods: Data on breast cancer patients treated at Seoul National University Hospital was used to make the application of isotonic models. In the modeling of recurrence risk, estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and proliferation marker (Ki-67) variables were considered as independent risk factors. The tumor size was included in the model as covariate. The isotonic proportional hazard model was used in modeling. Estimation of model coefficients was made by partial likelihood method. Results: The tumor size had monotone increasing effect on recurrence events. It was determined that the risk of recurrence increased 1.008 times as the value of Ki-67 increased. It has been ob- served that ER and PR negativity increase the risk, while HER2 positivity increases the risk. Conclusion: As a result, in cases where the covariate variable has a monotone increasing effect on the disease process, the isotonic regression model can be used by considering the relationships between the covariate and the event. Thus, the function that takes into account the monotone relationship between the covariate and the event will be included in the survival analysis.