Addressing Confounding in Spatial Causal Inference

Unmeasured confounding can severely bias causal effect estimates from spatiotemporal observational data, especially when the confounders do not vary smoothly in time and space. In this work, we develop a method for addressing unmeasured confounding in spatiotemporal contexts by building on models from the panel data literature and methods in multivariate causal inference. Our method is based on a factor confounding assumption, which posits that effects of unmeasured confounders on exposures and outcomes can be captured by a shared latent factor model. Factor confounding is sufficient to partially identify causal effects, even when there is interference between units. Additional assumptions that limit the degree of spatiotemporal interference, reasonable in most applications, are sufficient to point identify the effects. Simulation studies demonstrate that the proposed approach can substantially reduce omitted variable bias relative to other spatial smoothing and panel data baselines. We illustrate our method in a case study of the effect of prenatal PM2.5 exposure on birth weight in California. 

Unmeasured spatial confounding complicates exposure effect estimation in environmental health studies. This problem is exacerbated in studies with multiple health outcomes and environmental exposure variables, as the source and magnitude of confounding bias may differ across exposure/outcome pairs. We propose to mitigate the effects of spatial confounding in multivariate studies by projecting responses and exposures to the spectral domain to decorrelate the data and separate effects at different spatial resolutions. This transformation replaces the strict causal assumption of no unmeasured confounders with a more realistic assumption of local unconfoundedness, allowing for causal interpretation. Our model for the exposure effects is a three-way tensor over exposure, outcome, and spatial scale. We use a canonical polyadic decomposition and shrinkage priors to encourage sparsity and borrow strength across the dimensions of the tensor. This enables us to identify low-rank structures, such as specific themes among disaster resilience impacting incidence of chronic diseases at particular scales. Combining spectral projections with low-rank modeling results in an efficient method is suitable for large datasets, offering interpretable epidemiological insights.  

When studying associations between environmental exposures and health outcomes, modeling spatially-correlated variation in the health outcome improves precision of regression estimates, but can be insufficient when an exposure variable is collinear with a spatially-correlated random effect. This is commonly referred to as spatial confounding, and can result from a spatially-correlated, unobserved confounding variable, leading to bias and inaccurate variance estimates. Many methods have been proposed to address spatial confounding, but most have focused on Gaussian outcome and exposure data. Some have also only considered point-referenced spatial data. With Gaussian data, it is relatively easy to estimate the latent spatial trends and therefore adjust for spatial confounding. We extend several existing methods for Gaussian data under spatial confounding, including semiparametric methods and explicit Bayesian models for spatial confounding, to model binomial and Poisson response variables. We propose several extensions to add flexibility and improve performance. We compare performance of these methods for non-Gaussian data under spatial confounding using simulation. We find that adjusting for spatial confounding is significantly more difficult with non-Gaussian data, due to the relative lack of information on the spatial trends, and the quality of parameter estimates varies greatly between methods across simulated scenarios. We provide concrete guidance on which methods are best based on the data characteristics. We also extend existing semiparametric methods for point-referenced spatial data to allow areal spatial data. We analyze a spatially-correlated areal data set using the results and methods examined.
 

We propose a novel Bayesian approach to estimate causal effects in spatially clustered survival data. Using Soft Bayesian Additive Regression Trees (SBART), we introduce a nonparametric regression for a log-Normal survival model that accommodates spatial associations among unknown cluster effects through a Directed Acyclic Graph Auto-Regressive (DAGAR) model. We employ a two stage approach, which entails estimating the propensity score in the first step, and incorporating it as a confounder of the outcome model in the second step. In our simulation study, we compare our method with existing approaches under various simulation scenarios, including both correctly specified and misspecified outcome models, to demonstrate the superior performance of our method. We then apply our method to analyze the causal effect of Treatment Delay (TD) on post-treatment survival of breast cancer patients from the Florida Cancer Registry (FCR). Our analysis produces the county-specific as well as state-wide assessment of the causal effects while accommodating spatial association among counties. 

Estimating effects of spatially structured exposures is complicated by unmeasured spatial confounders, which undermine identifiability in spatial linear regression models unless structural assumptions are imposed. We develop a general framework for effect estimation in spatial regression models that relaxes the commonly assumed requirement that exposures contain higher-frequency variation than confounders. We propose basis voting, a plurality-rule estimator - novel in the spatial literature - that consistently identifies causal effects only under the assumption that, in a spatial basis expansion of the exposure and confounder, there exist several basis functions in the support of the exposure but not the confounder. This assumption generalizes existing assumptions of differential basis support used for identification of the causal effect under spatial confounding, and does not require prior knowledge of which basis functions satisfy this support condition. We design this estimator as the mode of several candidate estimators, each computed based on a single working basis function. We also show that the standard projection-based candidate estimator typically used in other plurality-rule based methods is inefficient, and provide a more efficient novel candidate. Extensive simulations and a real-world application demonstrate that our approach reliably recovers unbiased causal estimates whenever exposure and confounder signals are separable on a plurality of basis functions. By not relying on higher-frequency variation, our method remains applicable to settings where exposures are smooth spatial functions, such as distance to pollution sources or major roadways, common in environmental studies.