Seminar Series: Patrick Schnell

Confounding by unmeasured spatial variables has received some attention in the spatial statistics and causal inference literatures, but concepts and approaches have remained largely separated. We aim to bridge these distinct strands of statistics by considering unmeasured spatial confounding within a formal causal inference framework, and estimating effects using modifications of outcome regression tools popular within the spatial literature. This approach is motivated by and used to estimate the county-level effect of the proportion of households with limited access to supermarkets on the rate of cardiovascular disease deaths in the 65+ age range in the United States. First, we show that using spatially correlated random effects in the outcome model, an approach common among spatial statisticians, does not mitigate bias due to spatial confounding. Motivated by the bias term of commonly-used estimators, we propose an affine estimator which addresses this deficiency. We discuss how unbiased estimation of causal parameters in the presence of unmeasured spatial confounding can only be achieved under an untestable set of assumptions which will often be application-specific, and provide one set of assumptions that is sufficient for identification of the causal effect based on the observed data. These assumptions describe how the exposure and outcome of interest relate to the unmeasured variables. We examine identifiability issues through the lens of restricted maximum likelihood estimation, and implement our method using a fully Bayesian approach.