We used a hierarchical Bayesian model to see what worked in the first wave of the pandemic. Until then, people hadn’t picked apart the individual effects of anti-COVID policies, instead using “lockdown” to name all 20 different things governments tried in spring 2020 (where it should really mean stay-at-home orders).
We collected a big new dataset (41 countries) and were among the first to spot the large effect of closing schools and universities, back when people hoped children were magically not infectious. Our validation was unusually large and rigorous for epidemiology. Stay-at-home orders did surprisingly little (0–25% reduction) if schools, restaurants, and big events were already closed.
We initially attempted a cost–benefit analysis of each policy (surveying Americans on how much each interferes with their lives) but it wasn’t good enough for the final paper — and, to our knowledge, still hasn’t been done well outside secret government documents, despite being essential for good decisions.
Extracted from the published Science PDF (Science 371, eabd9338; 19 Feb 2021) and reflowed from the two-column layout into logical reading order. Citation numbers and figure/table call-outs are dropped; figures and the reference list are omitted. The above is the author’s plain-language summary; the journal’s own abstract and text follow.
Editor’s summary — How to hold down transmission. Early in 2020, SARS-CoV-2 transmission was curbed in many countries by imposing combinations of nonpharmaceutical interventions. Sufficient data on transmission have now accumulated to discern the effectiveness of individual interventions. Brauner et al. amassed and curated data from 41 countries as input to a model to identify the individual NPIs that were most effective at curtailing transmission during the early pandemic. Limiting gatherings to fewer than 10 people, closing high-exposure businesses, and closing schools and universities were each more effective than stay-at-home orders, which were of modest effect in slowing transmission.
Abstract. Governments are attempting to control the COVID-19 pandemic with nonpharmaceutical interventions (NPIs). However, the effectiveness of different NPIs at reducing transmission is poorly understood. We gathered chronological data on the implementation of NPIs for several European and non-European countries between January and the end of May 2020. We estimated the effectiveness of these NPIs, which range from limiting gathering sizes and closing businesses or educational institutions to stay-at-home orders. To do so, we used a Bayesian hierarchical model that links NPI implementation dates to national case and death counts and supported the results with extensive empirical validation. Closing all educational institutions, limiting gatherings to 10 people or less, and closing face-to-face businesses each reduced transmission considerably. The additional effect of stay-at-home orders was comparatively small.
Worldwide, governments have mobilized resources to fight the COVID-19 pandemic. A wide range of NPIs has been deployed, including stay-at-home orders and the closure of all nonessential businesses. Recent analyses show these large-scale NPIs were jointly effective at reducing the virus’s effective reproduction number $R_t$, but it is still largely unknown how effective individual NPIs were. A promising way to estimate NPI effectiveness is data-driven, cross-country modeling: inferring effectiveness by relating the NPIs implemented in different countries to the course of the epidemic. To disentangle the effects of individual NPIs, we leverage data from multiple countries with diverse interventions: we evaluated the impact of several NPIs on the epidemic’s growth in 34 European and 7 non-European countries. Because the COVID-19 response was far less coordinated than a single common intervention day, countries implemented different sets of NPIs at different times and orders, making individual effects identifiable.
Estimating NPI effects remains challenging: models rest on uncertain epidemiological parameters (which we incorporate directly); the data are retrospective and observational (so unobserved factors could confound); and effectiveness estimates can be highly sensitive to arbitrary modeling decisions, as shown by two recent replication studies. We collected a large public dataset on NPI implementation dates validated by independent double entry, and extensively validated our effectiveness estimates — a crucial but often absent element of COVID-19 NPI studies. We only analyzed the effect NPIs had between January and the end of May 2020, and NPI effectiveness may change over time; lifting an NPI does not imply transmission returns to its original level, and our window does not include relaxation of NPIs.
We analyzed the effects of seven commonly used NPIs between 22 January and 30 May 2020, all aimed at reducing contacts within the population (Table 1). If a country lifted an NPI before 30 May, its analysis window terminates on the lifting day. To ensure quality, all NPI data were independently entered by two authors (independent double entry) using primary sources, then compared with several public datasets. Case and death data came from the Johns Hopkins CSSE dataset.
We estimated NPI effectiveness with a Bayesian hierarchical model: case and death data are used to infer new infections over time, which infer the instantaneous reproduction number $R_t$; NPI effects are estimated by relating daily reproduction numbers to the active NPIs across all days and countries. This data-driven approach sidesteps assumptions about contact patterns, infectiousness by age group, etc., and directly models many sources of uncertainty (uncertain epidemiological parameters, between-country differences in NPI effectiveness, unknown changes in testing and infection-fatality rates, and unobserved influences on $R_t$).
Table 1 — the seven NPIs: gatherings limited to 1000 / 100 / 10 people or less; some (high-risk) businesses closed (e.g. restaurants, bars, nightclubs, cinemas, gyms); most nonessential businesses closed; schools closed; universities closed; and stay-at-home order (mandatory; whenever introduced, countries essentially always already had all other NPIs in place, so we estimate its additional effect).
We expressed each NPI’s effect as a percentage reduction in $R_t$, with Bayesian prediction intervals (wider than credible intervals; analogous to the standard deviation of effectiveness across countries). Under default model settings, the percentage reduction in $R_t$ (95% prediction interval) was:
We could not robustly disentangle closing only schools from only universities (implemented on the same day or in close succession in most countries), so reported them as one NPI. Some NPIs co-occurred (partly collinear), but the collinearity was imperfect and the dataset large enough to isolate individual effects: for every NPI pair, on average 504 country-days had one without the other (minimum 148). High sensitivity from excessive collinearity prevented Flaxman et al. (with a smaller dataset) from disentangling NPI effects; our estimates are substantially less sensitive, and posterior correlations between estimates are weak.
Although correlations between individual estimates were weak, we accounted for them when evaluating combined effectiveness. In combination, the NPIs in this study reduced $R_t$ by 77% (67 to 85%). Across countries, the mean $R_t$ without any NPIs (the $R_0$) was 3.3. Starting from this, $R_t$ likely could have been brought below 1 by closing schools and universities, closing high-risk businesses, and limiting gatherings to at most 10 people.
We performed a range of validation and sensitivity experiments. The model generated calibrated forecasts for countries that did not contribute fitting data for up to 2 months, with uncertainty increasing over time. We considered NPI effectiveness under 206 alternative experimental conditions across 11 sensitivity analyses (varying priors over epidemiological parameters, excluding countries, using only deaths or only cases, varying preprocessing, alternative model structures, and possible confounding by unobserved factors). Categorizing effects as small (<17.5%), moderate (17.5–35%), or large (>35%): closing schools and universities was large in 96% of conditions; limiting gatherings to 10 or less was large in 99%; closing most nonessential businesses was moderate in 98%; stay-at-home orders fell into “small effect” in 96%. Three NPIs were less clear-cut (gatherings ≤1000: moderate in 81%; ≤100: moderate in 66%; some high-risk businesses: moderate in 58%). Trends were robust even though precise estimates varied.
We found several NPIs associated with a clear reduction in $R_t$, and that some outperformed others — broadly robust across the 206 conditions. Business closures and gathering bans both seem to have been effective; closing most nonessential businesses was only somewhat more effective than targeted high-risk closures, so targeted closures can be a promising option. Limiting gatherings to 10 or less was more effective and more robust than larger limits (estimates derive from Jan–May 2020, when most gatherings were likely indoors). Issuing a stay-at-home order had only a small effect once educational institutions and nonessential businesses were closed and gatherings banned — suggesting some countries could have reduced $R_t$ below 1 without a stay-at-home order. In contrast, Flaxman et al. and Hsiang et al. folded several NPIs into their “lockdown” effect and accordingly found a large effect.
The large, robust effect for closing schools and universities cannot distinguish direct transmission effects from indirect ones (e.g. the general population behaving more cautiously after closures signaled the gravity of the pandemic), nor school from university closures. Evidence on the role of pupils/students in transmission is mixed.
Limitations: (i) NPI effectiveness depends on implementation context (other NPIs, demographics, details), so estimates indicate effectiveness in the contexts observed; expert judgment should adjust to local circumstances. (ii) $R_t$ may have been reduced by unobserved NPIs or voluntary behavior changes such as mask-wearing; additional analyses found results stable to a range of unobserved factors, but this cannot provide certainty. (iii) Results cannot be used without qualification to predict the effect of lifting NPIs (e.g. reopening with safety measures). (iv) We lack data on some promising interventions (testing, tracing, case isolation), and it is difficult to estimate mask-wearing effects given limited public life under other NPIs.
Dataset. Seven NPIs in 41 countries (33 in Europe). We recorded NPIs implemented nationally or in most regions (affecting ≥3/4 of the population), only mandatory restrictions. Each country’s window starts 22 January and ends at the first NPI lifting or 30 May 2020, whichever came first (ending after first major reopening avoids distribution shift).
Data collection. Two authors independently researched each country and entered NPI data into separate spreadsheets (manual internet searches; ~1.5 hours per researcher per country), then compared against the EFGNPI Database and the Oxford COVID-19 Government Response Tracker, resolving conflicts via primary sources. Each country/NPI was again independently entered by 1–3 paid contractors with primary sources; a researcher resolved conflicts; finally the two spreadsheets were combined and all conflicts resolved. The final dataset contains primary sources for each entry.
Data preprocessing. To avoid bias from imported cases and rapidly changing testing when counts are small, we neglected cases before a country reached 100 confirmed cases and deaths before 10 deaths (both included in the sensitivity analysis).
Model. Building on the semimechanistic Bayesian hierarchical model of Flaxman et al., with additions: (1) observing both case and death data; (2) placing priors over uncertain epidemiological parameters; (3) avoiding assuming a specific infection-fatality or ascertainment rate; (4) allowing all NPI effects to vary across countries. Each NPI independently affects $R_{t,c}$ as a multiplicative factor:
\[R_{t,c} = R_{0,c} \prod_{i=1}^{I} \exp(-a_{i,c}\, x_{i,t,c})\]where $x_{i,t,c}=1$ if NPI $i$ is active in country $c$ on day $t$, $I$ is the number of NPIs, and $a_{i,c}$ is the effect parameter (the multiplicative form encodes that NPIs have a smaller absolute effect when $R_{t,c}$ is already low). The effect parameter is $a_{i,c} = a_i + z_{i,c}$ with $z_{i,c} \sim N(0, \sigma_i^2)$; partial pooling minimizes bias from country-specific sources while reflecting cross-country variation. Effectiveness (percentage reduction in $R_t$) is $1 - \exp(-(a_i + z_i))$. An asymmetric Laplace prior on $a_i$ allows positive and negative effects but places 80% of its mass on positive effects.
During early exponential growth there is a one-to-one correspondence between the daily growth rate and $R_{t,c}$, depending on the generation interval (assumed gamma; prior mean 5.06 days from meta-analysis). New infections are modeled separately for cases and deaths (both growing at the same daily rate in expectation), translating into reported counts after delays (prior mean infection-to-confirmation 10.92 days; infection-to-death 21.8 days). Reported cases and deaths follow negative binomial output distributions. Inference uses MCMC (the No-U-Turn Sampler).