Estimation of Causal Effects in the Presence of Unobserved Confounding in the Alzheimer's Continuum

Abstract: 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.