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中国全科医学

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病例队列设计下乳腺癌患者雌二醇水平及其生存数据的联合建模

吴梦娟, 张涛, 高春洁, 赵婷, 王蕾   

  • 收稿日期:2023-12-21 修回日期:2024-03-04 接受日期:2024-03-20
  • 通讯作者: 王蕾
  • 基金资助:
    国家自然科学基金项目(12061079); “天山英才”青年科技创新人才培养(2022TSYCCX0108); 新疆自然科学基金项目(2022D01C287)

Joint-modeling of Estradiol Levels and Survival Data of Breast Cancer Patients in the Case-Cohort Design

WU Mengjuan, ZHANG Tao, GAO Chunjie, ZHAO Ting, WANG Lei   

  • Received:2023-12-21 Revised:2024-03-04 Accepted:2024-03-20
  • Contact: WANG Lei
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摘要： 背景　乳腺癌是一种性激素受体依赖的恶性肿瘤，雌二醇（E2）的动态变化在乳腺癌发展过程中起着非常重要的作用；经典病例队列设计完全忽略未选入样本的信息，容易产生估计偏倚。目的　探究乳腺癌患者E2水平动态变化对其生存预后的影响，评估改良病例队列设计的优良性。方法　基于经典病例队列设计，通过纳入病例队列样本外患者的生存数据改良病例队列设计。在经典及改良病例队列设计下采用线性混合效应模型和Cox比例风险模型分别拟合乳腺癌患者的纵向数据（纵向子模型）和生存数据（生存子模型），并建立纵向与时间-事件数据的联合模型；进一步采用马尔可夫链蒙特卡罗算法对联合模型参数进行估计；此外，通过受试者工作特征曲线下面积（AUC）以及预测误差（PE）比较经典及改良病例队列设计下联合模型的区分度与校准度。结果　经典和改良病例队列设计下的联合模型结果均显示E2水平动态变化是乳腺癌患者预后的危险因素，且lg(E2)纵向每增加一个单位，患者的死亡风险将分别增加约23%（HR=1.23，R ̂=1.015）和8%（HR=1.08，R ̂=1.020）。此外，改良病例队列设计下的联合模型展现出更好的区分度与校准度（AUC：[0.706，0.962]，PE：[0.001 2，0.010 8]）。结论　乳腺癌患者E2水平纵向升高可能会导致患者生存概率降低。病例队列设计下联合模型能够对纵向与生存数据同时进行分析，且改良病例队列设计优于经典病例队列设计。

关键词: 乳腺癌, 病例队列设计, 联合模型, 生存数据, 雌二醇

Abstract: Background　 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. Objectives　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. Methods　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. Results　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 risk 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, R ̂=1.015) and 8% (HR=1.08, R ̂=1.020), respectively. Moreover, the joint model under the improved case-cohort design showed better discrimination and calibration (AUC: [0.706, 0.962], PE: [0.0012, 0.0108]). Conclusions　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.

Key words: Breast cancer, Case-cohort design, Joint model, Survival data, Estradiol

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