R/Shiny Developer, Appsilon, Warsaw, Poland.
Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.
Biostatistics. 2023 Oct 18;24(4):945-961. doi: 10.1093/biostatistics/kxac028.
The confounding between fixed effects and (spatial) random effects in a regression setup is termed spatial confounding. This topic continues to gain attention and has been studied extensively in recent years, given that failure to account for this may lead to a suboptimal inference. To mitigate this, a variety of projection-based approaches under the class of restricted spatial models are available in the context of generalized linear mixed models. However, these projection approaches cannot be directly extended to the spatial survival context via frailty models due to dimension incompatibility between the fixed and spatial random effects. In this work, we introduce a two-step approach to handle this, which involves (i) projecting the design matrix to the dimension of the spatial effect (via dimension reduction) and (ii) assuring that the random effect is orthogonal to this new design matrix (confounding alleviation). Under a fully Bayesian paradigm, we conduct fast estimation and inference using integrated nested Laplace approximation. Both simulation studies and application to a motivating data evaluating respiratory cancer survival in the US state of California reveal the advantages of our proposal in terms of model performance and confounding alleviation, compared to alternatives.
在回归设置中，固定效应和（空间）随机效应之间的混淆称为空间混淆。由于未能考虑到这一点可能会导致次优的推断，近年来这个话题引起了越来越多的关注，并得到了广泛的研究。为了减轻这种情况，可以在广义线性混合模型的背景下，使用受限空间模型类中的各种基于投影的方法。然而，由于固定效应和空间随机效应之间的维度不兼容，这些投影方法不能通过脆弱性模型直接扩展到空间生存环境中。在这项工作中，我们引入了一种两步处理方法，包括（i）将设计矩阵投影到空间效应的维度上（通过降维）和（ii）确保随机效应与这个新的设计矩阵正交（混淆缓解）。在完全贝叶斯范例下，我们使用集成嵌套拉普拉斯逼近进行快速估计和推断。模拟研究和对一个有动机的数据的应用，评估了美国加利福尼亚州的呼吸癌生存情况，与替代方案相比，我们的建议在模型性能和混淆缓解方面都具有优势。
