Bayesian Survival Analysis For Breast Cancer

Cancer is a serious threat to human life and health.In China,breast cancer is the most common type of malignant tumor in women.Meanwhile,compared with developed countries in Europe and America,the overall survival rate of breast cancer patients in China is lower.Breast cancer has become a major public health problem,which needs urgent attention.Survival analysis on breast cancer is an important research direction.The aim of survival analysis is to find out the most significant prognostic factors which effect breast cancer patients' prognosis,and to predict the survival time of breast cancer patients.Survival analysis can help physicians to select appropriate therpies for each patients;help patients to predict the likely outcome of their disease;help researchers to estimate the effect of a treatment or drug.In the prognostic survival analysis for breast cancer data,more and more researchers are paying their attention to the effect of Lymph Node Ratio(LNR)on patients'prognosis.The LNR is obtained by calculating the ratio of the number of positive lymph nodes to the total number of lymph nodes on the slice.However,in practical,LNR is affected by reasons such as the different methods of test observations.Because of that,the clinical tested LNR cannot accurately reflected the overall true situation of the patient's LNR.In this paper,we propose using logistic regression and Bayesian methods based on patients' other clinical characters to estimate the overall LNR of patients.The prognostic survival analysis model using the estimated LNR has obtained better outcome than the model using tested LNR.In addition,in order to deal with the features that do not satisfy the proportional hazard assumption,we demonstrated Bayesian stratified and dynamic Cox regression models respectively.At last,in this paper,the tested LNR,the LNR estimated by logistic regression and LNR estimated by Bayesian method are combined separatly with other prognostic factors to construct the classic Cox regression model,Bayesian stratified Cox regression model and Bayesian Cox regression model.The performance of three models with different input data are compared,and the survival rate are predicted.After comparison,the extended Cox regression model using estimated LNR has better performance on the concordance index and ROC/AUC(Receiver Operation Characteristic,ROC;Area Under ROC Curve,AUC),which also predict the prognosis of patients more accurately.