Social distancing and COVID-19: Randomization inference for a structured dose-response relationship

Abstract

Social distancing is widely acknowledged as an effective public health policy combating the novel coronavirus. But extreme forms of social distancing, like isolation and quarantine, have costs, and it is not clear how much social distancing is needed to achieve public health effects. In this article we develop a design-based framework to test the causal null hypothesis and make inference about the dose-response relationship between reduction in social mobility and COVID-19 related public health outcomes. We first discuss how to embed observational data with a time-independent, continuous treatment dose into an approximate randomized experiment and develop a randomization-based procedure that tests if a structured dose-response relationship fits the data. We then generalize the design and testing procedure to a longitudinal setting and apply them to investigate the effect of social distancing during the first phased reopening in the United States on public health outcomes using data compiled from $\mathsf{Unacast}{}^{\text{™}}$, the United States Census Bureau, and the County Health Rankings and Roadmaps Program. We rejected a primary analysis null hypothesis that stated the social distancing from April 27, 2020 to June 28, 2020, had no effect on the COVID-19-related death toll from June 29, 2020 to August 2, 2020 (p-value < 0.001), and found that it took more reduction in mobility to prevent exponential growth in case numbers for nonrural counties compared to rural counties.