Many health outcomes result from accumulated exposures to one or more environmental factors. Accordingly, spatial risk studies have begun to consider multiple residential locations of participants, acknowledging that participants move and thus are exposed to environmental factors in several places. However, novel methods are needed to estimate cumulative spatial risk for disease while accounting for other risk factors. To this end, we propose a Bayesian model (LRK-MMM) that embeds a multiple membership model (MMM) into a low-rank kriging (LRK) model in order to estimate cumulative spatial risk at the point level while allowing for multiple residential locations per subject. The LRK approach offers a more computationally efficient means to analyze spatial risk in case-control study data at the point level compared with a Bayesian generalized additive model, and as increased precision in spatial risk estimates by analyzing point locations instead of administrative areas. Through a simulation study, we demonstrate the efficacy of the model and its improvement upon an existing multiple membership model that uses area-level spatial random effects to estimate risk. The results show that our proposed method provides greater spatial sensitivity (improvements ranging from 0.12 to 0.54) and power (improvements ranging from 0.02 to 0.94) to detect regions of elevated risk for disease across a range of exposure scenarios. Finally, we apply our model to case-control data from the New England bladder cancer study to estimate cumulative spatial risk while adjusting for many covariates.

中文翻译：

---

使用低秩克里格多成员模型估计随时间推移的累积空间风险

许多健康结果是由于累积暴露于一种或多种环境因素所致。因此，空间风险研究已经开始考虑参与者的多个居住地点，承认参与者移动并因此暴露于多个地方的环境因素。然而，需要新的方法来估计疾病的累积空间风险，同时考虑其他风险因素。为此，我们提出了一种贝叶斯模型 (LRK-MMM)，该模型将多成员模型 (MMM) 嵌入到低秩克里格 (LRK) 模型中，以估计点级别的累积空间风险，同时允许多个住宅位置每个主题。与贝叶斯广义加性模型相比，LRK 方法提供了一种计算效率更高的方法来分析点级别的病例对照研究数据中的空间风险，并通过分析点位置而不是行政区域来提高空间风险估计的精度。通过模拟研究，我们证明了该模型的有效性及其对使用区域级空间随机效应估计风险的现有多成员模型的改进。结果表明，我们提出的方法提供了更高的空间灵敏度（改进范围从 0.12 到 0.54）和功效（改进范围从 0.02 到 0.94）来检测一系列暴露场景中疾病风险升高的区域。最后，