Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?
Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?
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DOI：
10.1002/sim.8171
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发表时间：
2019-08-15
影响因子：
2
通讯作者：
Putter, Hein
中科院分区：
文献类型：
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作者：
Balan, Theodor Adrian;Putter, Hein
在生物医学应用中，多变量生存数据经常以聚集性故障(或复发事件数据)的形式出现。分析这类数据的一种流行方式是使用共享脆弱性模型，该模型假设比例风险假设成立的条件是未观察到的特定于集群的随机效应。在生存分析中，这样的模型经常被合并到更复杂的关节模型中。如果随机效应分布具有有限的期望，则条件比例风险假设不会延续到边际模型。已经证明，对于单变量数据，这使得不可能区分未观察到的异质性的存在(例如，由于缺少协变量)和边际非比例风险。我们表明，在集群故障或经常性事件数据的情况下，当集群大小或经常性事件的数量较小时，依赖于时间的协变量效应可能错误地表现为有利于脆弱性模型的证据。当存在真正的未观察到的异质性时，非比例风险的存在会导致高估脆弱效应。我们表明，随着簇大小的增加，这种现象会有所缓解。我们进行了一项模拟研究，以评估脆弱模型在这种情况下的检验统计量和估计器的行为。使用一种新的软件实现来估计半参数共享脆弱性模型，比较了伽马模型、逆高斯模型和正稳定共享脆弱性模型。在集群故障和重复事件的情况下，解决了两个主要问题：具有时间依赖效应的协变量是否可以显示为未观察到的异质性的指示，以及在这种情况下是否可以检测到未观察到的异质性的附加存在。最后，通过一个真实世界的数据分析实例说明了该方法的实际意义。
Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time-dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows. We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time-dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real-world data analysis example.