Epidemiologists and biostatisticians investigating spatial variation in diseases are often interested in estimating spatial effects in survival data, where patients are monitored until their time to failure (for example, death, relapse). Spatial variation in survival patterns often reveals underlying lurking factors that could assist public health professionals in their decision–making process to identify regions requiring attention. The Surveillance Epidemiology and End Results (SEER) database of the National Cancer Institute provides a fairly sophisticated platform for exploring novel approaches in modelling cancer survival, particularly with models accounting for spatial clustering and variation. Modelling survival data for patients with multiple cancers poses unique challenges in itself and in capturing the spatial associations of the different cancers. This paper develops the Bayesian hierarchical survival models for capturing spatial patterns within the framework of proportional hazard. Spatial variation is introduced in the form of county–cancer level frailties. The baseline hazard function is modelled semiparametrically using mixtures of beta distributions. We illustrate with data from the SEER database, perform model checking and comparison among competing models, and discuss implementation issues.

中文翻译：

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为患有多种癌症的个体建模空间相关的生存数据

调查疾病空间变化的流行病学家和生物统计学家通常对估计生存数据中的空间效应感兴趣，在这些数据中，患者会受到监测，直到他们失败（例如，死亡、复发）。生存模式的空间变异通常会揭示潜在的潜在因素，这些因素可以帮助公共卫生专业人员在决策过程中识别需要关注的区域。美国国家癌症研究所的监测流行病学和最终结果 (SEER) 数据库为探索癌症生存建模的新方法提供了一个相当复杂的平台，特别是使用考虑空间聚类和变异的模型。为患有多种癌症的患者建模生存数据本身就带来了独特的挑战，并且在捕捉不同癌症的空间关联方面也面临着独特的挑战。本文开发了贝叶斯分层生存模型，用于在比例风险框架内捕获空间模式。空间变异以县癌症级别的虚弱形式引入。基线风险函数是使用混合 β 分布以半参数方式建模的。我们用来自 SEER 数据库的数据进行说明，在竞争模型之间进行模型检查和比较，并讨论实现问题。基线风险函数是使用混合 β 分布以半参数方式建模的。我们用来自 SEER 数据库的数据进行说明，在竞争模型之间进行模型检查和比较，并讨论实现问题。基线风险函数是使用混合 β 分布以半参数方式建模的。我们用来自 SEER 数据库的数据进行说明，在竞争模型之间进行模型检查和比较，并讨论实现问题。