Summary Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster-specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow-up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval. By incorporating cluster-specific random effects, generalised linear mixed models can be used to analyse these data. Third, after partitioning the duration of follow-up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log–log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within-cluster homogeneity in outcomes. We illustrate the application of these methods using data consisting of patients hospitalised with a heart attack. We illustrate the application of these methods using three statistical programming languages (R, SAS and Stata).

中文翻译：

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多级生存分析教程：方法、模型和应用

摘要 具有多层次结构的数据经常出现在一系列学科中，包括流行病学、卫生服务研究、公共卫生、教育和社会学。我们描述了用于分析多级生存数据的三类回归模型。首先，具有混合效应的 Cox 比例风险模型包含修改基线风险函数的特定于集群的随机效应。其次，分段指数生存模型将随访的持续时间划分为互斥的区间，并拟合假设风险函数在每个区间内为常数的模型。这等效于包含每个间隔内暴露持续时间的泊松回归模型。通过结合特定于集群的随机效应，可以使用广义线性混合模型来分析这些数据。第三，在将随访持续时间划分为互斥间隔后，可以使用离散时间生存模型，该模型使用互补的对数-对数广义线性模型来模拟每个间隔内感兴趣的结果的发生。可以结合随机效应来解释结果的集群内同质性。我们使用由心脏病发作住院患者组成的数据来说明这些方法的应用。我们使用三种统计编程语言（R、SAS 和 Stata）来说明这些方法的应用。可以结合随机效应来解释结果的集群内同质性。我们使用由心脏病发作住院患者组成的数据来说明这些方法的应用。我们使用三种统计编程语言（R、SAS 和 Stata）来说明这些方法的应用。可以结合随机效应来解释结果的集群内同质性。我们使用由心脏病发作住院患者组成的数据来说明这些方法的应用。我们使用三种统计编程语言（R、SAS 和 Stata）来说明这些方法的应用。