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 social distancing has 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 make inference about the dose-response relationship between social distancing and COVID-19 related death toll and case numbers. We first discuss how to embed observational data with a time-independent, continuous treatment dose into an approximate randomized experiment, and develop a randomizationbased procedure that tests if a structured dose-response relationship fits the data. We then generalize the design and testing procedure to accommodate a time-dependent treatment dose in a longitudinal setting. Finally, we apply the proposed design and testing procedures to investigate the effect of social distancing during the phased reopening in the United States on public health outcomes using data compiled from sources including Unacast ™ , 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 27th to June 28th had no effect on the COVID-19-related death toll from June 29th to August 2nd (p-value < 0.001) and conducted extensive secondary analyses investigating the dose-response relationship between the social distancing level and COVID-19 case numbers.