Studying the relationship between neuroanatomy and cognitive decline due to Alzheimer's has been a major research focus in the last decade. However, to infer cause-effect relationships rather than simple associations from observational data, we need to (i) express the causal relationships leading to cognitive decline in a graphical model, and (ii) ensure the causal effect of interest is identifiable from the collected data. We derive a causal graph from the current clinical knowledge on cause and effect in the Alzheimer's disease continuum, and show that identifiability of the causal effect requires all confounders to be known and measured. However, in complex neuroimaging studies, we neither know all potential confounders nor do we have data on them. To alleviate this requirement, we leverage the dependencies among multiple causes by deriving a substitute confounder via a probabilistic latent factor model. In our theoretical analysis, we prove that using the substitute confounder enables identifiability of the causal effect of neuroanatomy on cognition. We quantitatively evaluate the effectiveness of our approach on semi-synthetic data, where we know the true causal effects, and illustrate its use on real data on the Alzheimer's disease continuum, where it reveals important causes that otherwise would have been missed.

翻译：研究阿尔茨海默氏病的神经切除和认知下降之间的关系是过去十年中的一个主要研究重点。然而,为了从观测数据中推断因果关系而不是简单的关联,我们需要(一) 表达导致图形模型认知下降的因果关系,以及(二) 确保从所收集的数据中可辨别利息的因果关系。我们从目前关于阿尔茨海默氏病连续体的原因和影响的临床知识中得出一个因果图表,并表明因果关系的可识别性要求了解和测量所有同源数据。然而,在复杂的神经成形研究中,我们既不知道所有潜在的相联者,也不清楚它们的数据。为了减轻这一需求,我们需要利用多种原因之间的依赖性,通过一种概率性潜在因素模型产生替代的相联者。在我们的理论分析中,我们证明使用替代的相联体能够辨别神经衰竭对认知的因果关系。我们量化地评估了我们在半合成数据上的方法的有效性,因为我们知道在哪些方面真实的因果影响,并展示了它是如何揭示的。