Causal inference for the effect of mobility on COVID-19 deaths

In this paper we develop statistical methods for causal inference in epi-demics. Our focus is in estimating the effect of social mobility on deaths in the first year of the Covid-19 pandemic. We propose a marginal structural model motivated by a basic epidemic model. We estimate the counterfactual time series of deaths under interventions on mobility. We conduct several types of sensitivity analyses. We find that the data support the idea that reduced mo-bility causes reduced deaths, but the conclusion comes with caveats. There is evidence of sensitivity to model misspecification and unmeasured confound-ing which implies that the size of the causal effect needs to be interpreted with caution. While there is little doubt the effect is real, our work highlights the challenges in drawing causal inferences from pandemic data.