Social distancing remains an important strategy to combat the COVID-19 pandemic in the United States. However, the impacts of specific state-level policies on mobility and subsequent COVID-19 case trajectories have not been completely quantified. Using anonymized and aggregated mobility data from opted-in Google users, we found that state-level emergency declarations resulted in a 9.9% reduction in time spent away from places of residence. Implementation of one or more social distancing policies resulted in an additional 24.5% reduction in mobility the following week, and subsequent shelter-in-place mandates yielded an additional 29.0% reduction. Decreases in mobility were associated with substantial reductions in case growth two to four weeks later. For example, a 10% reduction in mobility was associated with a 17.5% reduction in case growth two weeks later. Given the continued reliance on social distancing policies to limit the spread of COVID-19, these results may be helpful to public health officials trying to balance infection control with the economic and social consequences of these policies.

We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test statistic conditional on the observed covariate imbalance. We prove that the conditional randomization test has the correct significance level and introduce original notation to describe covariate balance more formally. Through simulation, we verify that conditional randomization tests behave like more traditional forms of covariate adjustmet but have the added benefit of having the correct conditional significance level. Finally, we apply the approach to a randomized product marketing experiment where covariate information was collected after randomization.

Background Social distancing have been widely used to mitigate community spread of SARS-CoV-2. We sought to quantify the impact of COVID-19 social distancing policies across 27 European counties in spring 2020 on population mobility and the subsequent trajectory of disease. Methods We obtained data on national social distancing policies from the Oxford COVID-19 Government Response Tracker and aggregated and anonymized mobility data from Google. We used a pre-post comparison and two linear mixed-effects models to first assess the relationship between implementation of national policies and observed changes in mobility, and then to assess the relationship between changes in mobility and rates of COVID-19 infections in subsequent weeks. Results Compared to a pre-COVID baseline, Spain saw the largest decrease in aggregate population mobility (~70%), as measured by the time spent away from residence, while Sweden saw the smallest decrease (~20%). The largest declines in mobility were associated with mandatory stay-at-home orders, followed by mandatory workplace closures, school closures, and non-mandatory workplace closures. While mandatory shelter-in-place orders were associated with 16.7% less mobility (95% CI: -23.7% to -9.7%), non-mandatory orders were only associated with an 8.4% decrease (95% CI: -14.9% to -1.8%). Large-gathering bans were associated with the smallest change in mobility compared with other policy types. Changes in mobility were in turn associated with changes in COVID-19 case growth. For example, a 10% decrease in time spent away from places of residence was associated with 11.8% (95% CI: 3.8%, 19.1%) fewer new COVID-19 cases. Discussion This comprehensive evaluation across Europe suggests that mandatory stay-at-home orders and workplace closures had the largest impacts on population mobility and subsequent COVID-19 cases at the onset of the pandemic. With a better understanding of policies’ relative performance, countries can more effectively invest in, and target, early nonpharmacological interventions.

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Many games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.