Breast cancer is a hormone receptor-dependent malignant tumor, and the dynamical changes of estradiol (E2) play a critical role in the development of breast cancer. The classical case-cohort design completely ignores the information of non-selected samples, which could easily lead to biased estimating.

To explore the effect of dynamical changes of E2 levels on the survival prognosis in breast cancer patients, and evaluate the superiority of improved case-cohort design.

In this study, we selected 8 226 patients who were diagnosed as breast cancer by pathological examination at the Affiliated Cancer Hospital of Xinjiang Medical University from 2015 to 2019, by using the time of patient diagnosis as the follow-up start date, and defining the death of patients due to breast cancer as the outcome event. The follow-up end date was December 31, 2021. The demographic characteristics, immunohistochemical indicators, clinicopathological characteristics and survival status of patients were gathered, and their serum E2 levels were longitudinally monitored. Based on the classical case-cohort design, the improved case-cohort design was achieved by incorporating survival data from patients outside of the case-cohort sample. Under the classical and improved case-cohort designs, linear mixed effects model and Cox proportional risk model were used to fit the longitudinal data (longitudinal submodel) and survival data (survival submodel) of breast cancer patients, respectively, and two joint models for longitudinal and time-to-event data were further established. Moreover, Markov Chain Monte Carlo algorithm was used to estimate the parameters of two joint models. The area under the receiver operating characteristic curves (AUC) and prediction errors (PE) were further applied to compare the discrimination and calibration of two joint models under the classical and improved case-cohort designs.

Based on the inclusion and exclusion criteria, a total of 895 breast cancer patients were included in the full cohort, of which 53 patients died of breast cancer. The median follow-up time for patients was approximately 28 months. The samples of classical case-cohort design were concluded two parts: one was one quarter of the patients selected from the full cohort as a random subcohort, the other was patients who died during the follow-up period outside the random subcohort, of which included survival data from 236 patients and 1 062 measurements of E2 levels. Moreover, on the basis of the classical case-cohort design, the survival data of breast cancer patients who were outside of the classical case-cohort samples and survived during the follow-up period (G₄) were included as the samples of the improved case-cohort design that included survival data from 895 patients, 1 062 measurements of E2 levels from 236 patients (in which it was assumed that there were 2 958 longitudinally missing measurements of E2 levels) . The results of two joint models under classical and improved case-cohort designs both revealed that dynamical change of E2 levels was identified as the influencing prognostic factors for breast cancer patients. For one-unit longitudinal increment of lg (E2) , the mortality risks for patients would increase by about 23% (HR=1.23, =1.015) and 8% (HR=1.08, =1.020) , respectively. Moreover, the joint model under the improved case-cohort design showed better discrimination and calibration (AUC=0.706-0.962, PE=0.001 2-0.010 8) .

The longitudinal increment of E2 levels could cause a decrease of the survival probability for breast cancer patients. The joint model under case-cohort design could both analyze longitudinal and survival data, and the improved case-cohort design would be superior to that of the classical case-cohort design.