The effect of lockdown on the COVID-19 epidemic in Brazil: evidence from an interrupted time series design O efeito do lockdown sobre a epidemia da COVID-19 no Brasil: evidências a partir de uma análise de séries temporais interrompidas El efecto del confinamiento por la epidemia de COVID-19 en Brasil: evidencia de un diseño de serie temporal interrumpida

In response to the COVID-19 pandemic, governments worldwide have implemented social distancing policies with different levels of both enforcement and compliance. We conducted an interrupted time series analysis to estimate the impact of lockdowns on reducing the number of cases and deaths due to COVID-19 in Brazil. Official daily data was collected for four city capitals before and after their respective policies interventions based on a 14 days observation window. We estimated a segmented linear regression to evaluate the effectiveness of lockdown measures on COVID-19 incidence and mortality. The initial number of new cases and new deaths had a positive trend prior to policy change. After lockdown, a statistically significant decrease in new confirmed cases was found in all state capitals. We also found evidence that lockdown measures were likely to reverse the trend of new daily deaths due to COVID-19. In São Luís, we observed a reduction of 37.85% while in Fortaleza the decrease was 33.4% on the average difference in daily deaths if the lockdown had not been implemented. Similarly, the intervention diminished mortality in Recife by 21.76% and Belém by 16.77%. Social distancing policies can be useful tools in flattening the epidemic curve. SARS-CoV-2; COVID-19; Social Distance; Interrupted Time Series ARTIGO ARTICLE This article is published in Open Access under the Creative Commons Attribution license, which allows use, distribution, and reproduction in any medium, without restrictions, as long as the original work is correctly cited.


Introduction
The first confirmed case of SARS-CoV-2 in Brazil was identified on February 26th 2020 (Ministério da Saúde. https://covid.saude.gov.br/, accessed on Jul/2020). Since then, Brazil became the second most affected country worldwide with 1,884,967 diagnosed cases, and has the second-highest number of total deaths due to COVID-19, with 72,833 fatalities as of July 13th (Ministério da Saúde. https:// covid.saude.gov.br/, acessado em Jul/2020). While SARS-CoV-2 spread over space and time, Brazilian President Jair Bolsonaro repeatedly advocated that COVID-19 was not more dangerous than a regular flu 1 and that strict quarantine measures were worse than the disease itself due to its adverse economic net effects 2 .
Contrary to the president's stance, some State Governors adopted lockdown policies trying to prevent the spread of the SARS-CoV-2 pandemic, with specific measures restricting social contact being first introduced in the Northern and Northeast regions. On May 5th, the State of Maranhão, in the Northeast Region, implemented strict regulations imposing social distancing. After this experience, other state governors and city mayors also adopted more stringent social distancing measures. A heated debate accompanied the implementation of hard, statewide lockdowns in several locations on how much they could achieve, how much they would cost, and how long they should last 3 . As some of the states undergoing lockdown measures have announced in June their decision to lift restrictions and resume normalcy progressively, careful analysis is required to assess the effectiveness of such policies.
In this paper, we conducted an interrupted time series (ITS) analysis to estimate the impact of social distance measures on reducing both the number of cases and deaths due to COVID-19 in Brazil. The selected sample included all the Brazilian state capitals that officially adopted more restrictive policies (i.e. "lockdown") in response to the SARS-CoV-2 epidemic: Belém (Pará State), Fortaleza (Ceará State), Recife (Pernambuco State), and São Luís (Maranhão State).

Data collection
On June 25th, we collected data from the Brazilian Ministry of Health website, which provides daily disaggregated information on COVID-19 (https://covid.saude.gov.br/), and later identified the time frame for lockdown measures in each city (Table 1). Following previous literature on the effects of lockdown measures on the COVID-19 pandemic, we adopted a two-week observation window after the end lockdown policies to test the series interruption 4,5,6,7 .
The adoption of 14 days corresponds to the disease incubation period as reported by the World Health Organization (WHO) 8 and medical empirical research 9,10,11 . Thus, we expected to observe a delayed policy effect. For instance, a person who becomes infected on the last day of public intervention may experience symptoms up to 14 days after the end of the policy change.
After data cleaning and coding, we analyzed the trends reported daily in each city before and after their policy change focusing on two primary outcomes: daily new cases and deaths. We specified an ordinary least squares regression model using the logarithmic transformation on the dependent variables.

Statistical analysis
ITS design is the most reliable quasi-experimental approach for evaluating the effects of discrete interventions on longitudinal data 12 . Technically, ITS is flexible, comfortably accommodating both continuous and discrete outcomes measured at regularly spaced intervals 13 . Another vital feature of the ITS is its intuitive graphical display. Visually, we compare the distribution of an outcome variable over time before and after the intervention 14,15 . The higher the difference between the observed series and what should have happened, the more significant the intervention's impact. We assumed that the level (average) and the trend of the series would remain constant in the absence of government policy (intervention) 16,17 . The statistical model was specified as follows: (1) Where Y 1 represents the number of daily new cases/deaths, X 1 is a discrete variable indicating the pre-intervention trend, X 2 is a dummy variable representing the level change immediately after policy intervention (0 = before lockdown, 1 = after lockdown), and X 3 indicates the slope change following the lockdown which is calculated as a multiplicative term between X 1 (time) and X 2 (level). We expected a positive trend before the intervention, e.g., β 1 > 0. Assuming a 14-day incubation period, we considered that β 2 should be positive, regardless of statistical significance. Thus, no immediate trend changes after intervention was expected. Following Bernal et al. 13 , we expected to observe a negative trend of cases and deaths after the policy change (β 3 > 0).
Policy interventions may generate immediate or delayed effects 12 , with direct effects being easier to detect and visualize. When the impact of the intervention is delayed over time, we should justify the difference between the policy change and its expected effects.

Computational tools
The data was analyzed using R Statistical 3.6.3 (http://www.r-project.org), and all significance tests were two-sided. Replication materials, including raw data and computational scripts, are available at: https://osf.io/ns3k6/. Figure 1 shows the epidemic curves for COVID-19 cases and deaths in four Brazilian capitals over time. Figure 2 compares the expected number of daily cases and deaths and the respective actual values of registered COVID-19 occurrences in each city, with the light blue interval indicating the duration of the intervention.
To acquire more robust estimates, we re-run all regression models using a 15 to 21 days window time frame (Figure 3) and observed the following pattern: β 3 , the coefficient indicating the trend of the post-intervention period, remained negative and statistically significant for all cities and all periods.
Finally, we estimated the average difference in daily deaths in the absence of the lockdown. In São Luís, we observed a reduction of 37.85% while in Fortaleza the decrease was 33.4%, on average. Similarly, the lockdown reduced mortality in Recife by 21.76% and Belém had 16.77% fewer deaths than would be expected without stricter social distance measures.

Figure 3
Interrupted time series (ITS) models using a 15 to 21 days window time frame for new daily cases and newdeaths.

Discussion
Social distance is a well-established non-pharmaceutical intervention that aims to reduce the spread of infectious diseases 18 . Studies using ITS design consistently reports significant effects of social distancing policies on the SARS-CoV-2 epidemic.
In an experimental study involving 149 countries, Islan et al. 19 found that enforcing any social distance measure reduced in 13% the incidence of COVID-19 (IRR = 0.87; 95%CI: 0.85-0.89). Regarding lockdown, the authors state that the rapid implementation of these measures promotes an even more significant reduction (pooled IRR = 0.86; 95%CI: 0.84-0.89; n = 105) compared with a delayed implementation. Figueiredo et al. 20 estimated the impact of lockdown policies on COVID-19 incidence and mortality in China, which reported a daily reduction of 6.43% in the number of cases and of 7.88% in registered deaths. Molefi et al. 4 identified a 47% decrease in daily cases comparing the pre and postintervention periods.
Siedner et al. 21 , also employing ITS to evaluate the effect of social distancing policies in the United States, found a statistically significant daily decrease of 0.8% on mean state-level COVID-19 epidemic growth. Ghanbari et al. 22 assessed the impact of lockdown policies on SARS-CoV-2 in Iran, and the results indicate an average decrease of 288.57 on new confirmed cases and 24.67 deaths after the policy intervention.
Evaluating how lockdown policies affected the spread of the SARS-CoV-2 epidemic in Spain and Italy, Tobías 23 reports that the first lockdown reduced incidence in both countries, though the trends remained positive. After the second and stricter lockdown, the slope of the number of case incidence changed and became negative. Still in Europe, Vokó & Pitter 7 found an average reduction of 0.9% in the incidence of COVID-19 in 28 countries.
Using original data, we provide evidence of how lockdown interventions affected the SARS-CoV-2 epidemic in Brazil. We found that the initial number of new cases and new deaths had a positive trend before the policy change, showing a statistically significant decrease in new confirmed cases in all state capitals after lockdown. We also found evidence that lockdown measures were likely to reverse the trend of daily deaths due to COVID-19.
We identified three main limitations. First, Brazilian official data shows some inconsistencies that may affect estimates efficiency; thus, studies working with small samples could fail to reject the null hypothesis due to micronumerosity. Second, testing intensified during the post-intervention period, resulting in a higher number of diagnosed cases that can lead to underestimating policy change impact. Finally, there is significant delay between testing cases and actual report them in official datasets, which are likely to introduce both random and systematic measurement errors in statistical estimates.