Stay-at-home policy is a case of exception fallacy

By late January, 2021, approximately 2.1 million people worldwide had died from the new coronavirus (COVID-19)¹. Wearing masks, taking personal precautions, testing for COVID-19 and social distancing have been advocated for controlling the pandemic^2,3,4. To achieve source control and stop transmission, social distancing has been interpreted by many as staying at home. Such policies across multiple jurisdictions were suggested by some experts⁵. These measures were supported by the World Health Organization^6,7, local authorities^8,9,10, and encouraged on social media platforms^11,12,13.

Some mathematical models and meta-analyses have shown a marked reduction in COVID-19 cases^{14,15,16,17,18,19} and deaths^20,21 associated with lockdown policies. Brazilian researchers have published mathematical models of spreading patterns²² and suggested implementing social distancing measures and protection policies to control virus transmission²³. By May 5th, 2020, an early report, using the number of curfew days in 49 countries, found evidence that lockdown could be used to suppress the spread of COVID-19²⁴.

Measures to address the COVID-19 pandemic with Non-Pharmacological Interventions (NPIs) were adopted after Brazil enacted Law No. 13979²⁵, and this was followed by many states such as Rio de Janeiro²⁶, the Federal District of Brasília (Decree No. 40520, dated March 14th, 2020)²⁷, the city of São Paulo (Decree No. 59.283, dated March 16th, 2020)²⁸, and the State of Rio Grande do Sul (Decree No. 55240/2020, dated May 10th, 2020)²⁹. It was expected that, with these actions, the number of deaths by COVID-19 would be reduced.

Of note, the country’s most populous state, São Paulo, adopted rigorous quarantine measures and put them into effect on March 24th, 2020²⁸. Internationally, Peru adopted the world’s strictest lockdown³⁰.

Recently, Google LLC published datasets indicating changes in mobility (compared to an average baseline before the COVID-19 pandemic). These reports were created with aggregated, anonymized sets of daily and dynamic data at country and sub-regional levels drawn from users who had enabled the Location History setting on their cell phones.

These data reflect real-world changes in social behavior and provide information on mobility trends for places like grocery stores, pharmacies, parks, public transit stations, retail and recreation locations, residences, and workplaces, when compared to the baseline period prior to the pandemic³¹.

Mobility in places of residence provides information about the “time spent in residences”, which we will hereafter call “staying at home” and use as a surrogate for measuring adherence to stay-at-home policies.

Studies using Google COVID-19 Community Mobility Reports and the daily number of new COVID-19 cases have shown that over 7 weeks a strong correlation between staying at home and the reduction of COVID-19 cases in 20 counties in the United States³²; COVID-19 cases decreased by 49% after 2 weeks of staying at home³³; the incidence of new cases/100,000 people was also reduced³⁴; social distancing policies were associated with reduction in COVID-19 spread in the US³⁵; as well as in 49 countries around the world²⁴.

A recent report using Brazilian and European data has shown a correlation between NPI stringency and the spread of COVID-19^36,37; these analyses are debatable, however, due to their short time span and the type of time series behavior³⁸, or for their use of Pearson’s correlation in the context of non-stationary time series³⁵. The same statistical tools cannot be applied to stationary and non-stationary time series alike³⁹, and the latter is the case with this COVID-19 data. A 2020 Cochrane systematic review of this topic reported that they were not completely certain about this evidence for several reasons.

The COVID-19 studies based their models on limited data and made different assumptions about the virus¹⁷; the stay-at-home variable was analyzed as a binary indicator⁴⁰; and the number of new cases could have been substantially undocumented⁴¹; all which may have biased the results. A sophisticated mathematical model based on a high-dimensional system of partial differential equations to represent disease spread has been proposed⁴².

According to this model, staying at home did not play a dominant role in disease transmission, but the combination of these, together with the use of face masks, hand washing, early-case detection (PCR test), and the use of hand sanitizers for at least 50 days could have reduced the number of new cases.

Finally, after 2 months, the simulations that drove the world to lockdown have been questioned⁴³. These studies applied relatively complex epidemiological models with unrealistic assumptions or parameters that were either user-chosen or not deemed to work properly. Furthermore, the effects in the death rates were directly inferred from the aftermath of a given intervention without a control group. Finally, the temporal delay between the introduction of a certain intervention and the actual measurable variation in death rates was not properly taken into account^44,45.

The rationale we are looking for is the association between two variables: deaths/million and the percentage of people who remained in their residences. Comparison, however, is difficult due to the non-stationary nature of the data. To overcome these problems, we proposed a novel approach to assess the association between staying at home values and the reduction/increase in the number of deaths due to COVID-19 in several regions around the world.

If the variation in the difference between the number of deaths/million in two countries, say A and B, and the variation in the difference of the staying at home values between A and B present similar patterns, this is due to an association between the two variables. In contrast, if these patterns are very different, this is evidence that staying at home values and the number of deaths/million are not related (unless, of course, other unaccounted for factors are at play). In view of this, the proposed approach avoids altogether the problems enumerated above, allowing a new approach to the problem.

After more than 25 epidemiological weeks of this pandemic, verifying if staying at home had an impact on mortality rates is of particular interest. A PUBMED search with the terms “COVID-19” AND (Mobility) (search made on September 8th, 2020) yielded 246 articles; of these, 35 were relevant to mobility measures and COVID-19, but none compared mobility reduction to mortality rates.

Results

A flowchart of the data manipulation is depicted in Fig. 1. Briefly, Google COVID-19 Community Mobility Report data between February 16th and August 21st, 2020, yielded 138 separate countries and their regions. The website Our World in Data provided data on 212 countries (between December 31st, 2019, and August 26th, 2020), and the Brazilian Health Ministry website provided data on all states (n = 27) and cities (n = 5,570) in Brazil (February 25th to August 26th, 2020).

Figure 1

After data compilation, a total of 87 regions and countries were selected: 51 countries, 27 States in Brazil, six major Brazilian State capitals [Manaus, Amazonas (AM), Fortaleza, Ceará (CE), Belo Horizonte, Minas Gerais (MG), Rio de Janeiro, Rio de Janeiro (RJ), São Paulo, São Paulo (SP) and Porto Alegre, Rio Grande do Sul (RS)], and three major cities throughout the world (Tokyo, Berlin and New York) (Fig. 1).

The global comparison yielded 3,741 combinations; from these, 184 (4.9%) had a p-value < 0.05, after correcting for False Discovery Rate (Table S1). After performing the residual analysis, by testing for cointegration between response and covariate, normality of the residuals, presence of residual autocorrelation, homoscedasticity, and functional specification, only 63 (1.6%) of models passed all tests (Table S2).

Closer inspection of several cases where the model did not pass all the tests revealed a common factor: the presence of outliers, mostly due to differences in the epidemiological week in which deaths started to be reported. A heat map showing the comparison between the 87 regions is presented in Fig. 2.

Figure 2

Comparisons

The restrictive analysis between controlled and not controlled areas yielded 33 appropriate comparisons, as shown in Table 2. Only one comparison out of 33 (3%)—State of Roraima (Brazil) versus State of Rondonia (Brazil)—was significant (p-value = 0.04). After correction for residual analysis, it did not pass the autocorrelation test (p-value of the Lagrange Multiplier test = 0.04). (Further details are in Auxiliary Supplementary Material—Restrictive Analysis).

The global comparison yielded 3,741 combinations; from these, 184 (4.9%) had a p-value < 0.05, after correcting for False Discovery Rate (Table S1 suppl). After performing the residual analysis, by testing for cointegration between response and covariate, normality of the residuals, presence of residual autocorrelation, homoscedasticity, and functional specification, only 63 (1.6%) of models passed all tests (Table S2—suppl). Closer inspection of several cases where the model did not pass all the tests revealed a common factor: the presence of outliers, mostly due to differences in the epidemiological week in which deaths started to be reported. A heat map showing the comparison between the 87 regions is presented in Fig. 2.

Discussion

We were not able to explain the variation of deaths/million in different regions in the world by social isolation, herein analyzed as differences in staying at home, compared to baseline. In the restrictive and global comparisons, only 3% and 1.6% of the comparisons were significantly different, respectively. These findings are in accordance with those found by Klein et al.⁴⁶ These authors explain why lockdown was the least probable cause for Sweden’s high death rate from COVID-19⁴⁶.

Likewise, Chaudry et al. made a country-level exploratory analysis, using a variety of socioeconomic and health-related characteristics, similar to what we have done here, and reported that full lockdowns and wide-spread testing were not associated with COVID-19 mortality per million people⁴⁷. Different from Chaudry et al., in our dataset, after 25 epidemiological weeks, (counting from the 9th epidemiological week onwards in 2020) we included regions and countries with a “plateau” and a downslope phase in their epidemiological curves.

Our findings are in accordance with the dataset of daily confirmed COVID-19 deaths/million in the UK. Pubs, restaurants, and barbershops were open in Ireland on June 29th and masks were not mandatory⁴⁸; after more than 2 months, no spike was observed; indeed, death rates kept falling⁴⁹. Peru has been considered to be the most strict lockdown country in the world³⁰, nevertheless, by September 20th, it had the highest number of deaths/million⁵⁰.

Of note, differences were also observed between regions that were considered to be COVID-19 controlled, e.g., Sweden versus Macedonia. Possible explanations for these significant differences may be related to the magnitude of deaths in these countries. After October 2020, when our study was published in a preprint server for Health Sciences, new articles were published with similar results^51,52,53,54.

Our results are different from those published by Flaxman et al. The authors applied a very complex calculation that NPIs would prevent 3.1 million deaths across 11 European countries⁴⁴. The discrepant results can be explained by different approaches to the data. While Flaxman et al. assumed a constant reproduction number (R _t) to calculate the total number of deaths, which eventually did not occur, we calculated the difference between the actual number of deaths between 2 countries/regions.

The projections published by Flaxman et al.⁴⁴ have been disputed by other authors. Kuhbandner and Homburg described the circular logic that this study involved. Flaxman et al. estimated the R _t from daily deaths associated with SARS-CoV-2 using an a priori restriction that R _t may only change on those dates when interventions become effective. However, in the case of a finite population, the effective reproduction number falls automatically and necessarily over time since the number of infections would otherwise diverge⁵⁵

A recent preprint report from Chin et al.⁵⁶ explored the two models proposed by the Imperial College⁴⁴ by expanding the scope to 14 European countries from the 11 countries studied in the original paper. They added a third model that considered banning public events as the only covariate. The authors concluded that the claimed benefits of lockdown appear grossly exaggerated since inferences drawn from effects of NPIs are non-robust and highly sensitive to model specification⁵⁶.

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