Mathematical Institute, Leiden University, Leiden, The Netherlands.
Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, The Netherlands.
Stat Med. 2019 Jan 30;38(2):269-288. doi: 10.1002/sim.8002. Epub 2018 Oct 18.
Survival analysis is used in the medical field to identify the effect of predictive variables on time to a specific event. Generally, not all variation of survival time can be explained by observed covariates. The effect of unobserved variables on the risk of a patient is called frailty. In multicenter studies, the unobserved center effect can induce frailty on its patients, which can lead to selection bias over time when ignored. For this reason, it is common practice in multicenter studies to include a random frailty term modeling center effect. In a more complex event structure, more than one type of event is possible. Independent frailty variables representing center effect can be incorporated in the model for each competing event. However, in the medical context, events representing disease progression are likely related and correlation is missed when assuming frailties to be independent. In this work, an additive gamma frailty model to account for correlation between frailties in a competing risks model is proposed, to model frailties at center level. Correlation indicates a common center effect on both events and measures how closely the risks are related. Estimation of the model using the expectation-maximization algorithm is illustrated. The model is applied to a data set from a multicenter clinical trial on breast cancer from the European Organisation for Research and Treatment of Cancer (EORTC trial 10854). Hospitals are compared by employing empirical Bayes estimates methodology together with corresponding confidence intervals.
生存分析在医学领域中用于确定预测变量对特定事件发生时间的影响。通常，并非所有生存时间的变化都可以用观察到的协变量来解释。未观察到的变量对患者风险的影响称为脆弱性。在多中心研究中，未观察到的中心效应可能会对其患者产生脆弱性，如果忽略不计，随着时间的推移，这可能会导致选择偏差。出于这个原因，在多中心研究中，通常包括一个随机脆弱性项来模拟中心效应。在更复杂的事件结构中，可能会有不止一种类型的事件。可以为每个竞争事件在模型中包含代表中心效应的独立脆弱性变量。然而，在医学背景下，代表疾病进展的事件很可能相关，并且当假设脆弱性独立时，会忽略相关性。在这项工作中，提出了一种加性伽马脆弱性模型，用于在竞争风险模型中考虑脆弱性之间的相关性，以对中心水平的脆弱性进行建模。相关性表示两个事件之间的共同中心效应，并衡量风险之间的相关性程度。说明了使用期望最大化算法对模型进行估计。该模型应用于欧洲癌症研究与治疗组织（EORTC 试验 10854）的一项多中心乳腺癌临床试验的数据集中。通过采用经验贝叶斯估计方法和相应的置信区间来比较医院。
