Bivariate Bayesian joint modeling of CEA and E2 values for female breast cancer patients in Xinjiang

We investigate the comprehensive impact of dynamic changes in CEA (carcinoembryonic antigen) and E2 (estradiol) values on the survival prognosis of breast cancer patients in Xinjiang, as well as predict their long-term mortality probabilities. This work is based on the longitudinal and survival data of female breast cancer patients followed up by the Affiliated Tumor Hospital of Xinjiang Medical University. Firstly, the Boruta algorithm was used to screen the independent prognostic factors that related with the breast cancer patients in Xinjiang. Moreover, a bivariate Bayesian joint model for longitudinal and time-to-event data was constructed to investigate how the dynamical changes of CEA and E2 values collectively affect the survival prognosis of breast cancer patients in Xinjiang. The predictive performance of the model was assessed by using ROC curves and calibration curves. As a result, the variable screen results of the Boruta algorithm indicated that CEA, E2, clinical stage, received neoadjuvant treatment, etc., were identified as independent prognostic factors of breast cancer patients in Xinjiang. In addition, it was shown that the association coefficients of the joint model $\alpha _{1}$ and $\alpha _{2}$ were statistically significant. When all other baseline variables were unchanged, patients’ death risk separately increases by approximately 1.577 times ( $HR=2.577$ , 95%CI: $(1.803, 3.563)$ ) and 0.887 times ( $HR=1.887$ , 95%CI: $(1.472, 2.454)$ ) with the one-unit collective increase in the log (CEA) and log (E2). Moreover, the joint model had good discrimination and calibration with an AUC value of 0.778. So the collective increase of CEA and E2 would be associated with the breast cancer patients’ poor survival prognosis. It would be essential to monitor the dynamical changes of CEA and E2 values of breast cancer patients in clinical practice in order to provide more accurate individualized treatment for breast cancer patients.