key: cord-0812756-bjgwbhxf
authors: Savaris, R. F.; Pumi, G.; Dalzochio, J.; Kunst, R.
title: Stay-at-home policy: is it a case of exception fallacy? An internet-based ecological study
date: 2020-10-15
journal: nan
DOI: 10.1101/2020.10.13.20211284
sha: a08560435680632cdc8fecd7ec7240ccaf9bc2b8
doc_id: 812756
cord_uid: bjgwbhxf

Background: Countries with strict lockdown had a spike on the number of deaths. A recent mathematical model has suggested that staying at home did not play a dominant role in reducing COVID-19 transmission. Comparison between number of deaths and social mobility is difficult due to the non-stationary nature of the COVID-19 data. Objective: To propose 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. Methods: In this ecological study, data from www.google.com/covid19/mobility/, ourworldindata.org and covid.saude.gov.br were combined. Countries with >100 deaths and with a Healthcare Access and Quality Index of [≥]67 were included. Data were preprocessed and analyzed using the difference between number of deaths/million between 2 regions and the difference between the percentage of staying at home. Analysis was performed using linear regression and residual analysis Results: After preprocessing the data, 87 regions around the world were included, yielding 3,741 pairwise comparisons for linear regression analysis. Only 63 (1.6%) comparisons were significant. Discussion: With our results, we were not able to explain if COVID-19 mortality is reduced by staying as home in ~98% of the comparisons after epidemiological weeks 9 to 34.

2020). By May 5th, 2020, an early report, using number of curfew days in 49 countries, found 58 evidence that lockdown could be used to suppress the spread of COVID-19 (Atalan 2020). 59

Measures to address the COVID-19 pandemic with Non-Pharmacological Interventions (NPIs) 60 were adopted after Brazil enacted Law No. 13979 (Imprensa Nacional), and this was followed by 61 many states such as Rio de Janeiro (Decreto 46970 27/03/2020), the Federal District of Brasília 62 (Decree No. 40520, dated March 14 th , 2020) (Decreto 40520 de 14/03/2020), the city of São 63

Paulo (Decree No. 59 .283, dated March 16 th , 2020) (Decreto 59283 2020 de São Paulo SP), and 64

the State of Rio Grande do Sul (Decree No. 55240/2020, dated May 10 th , 2020) (Decreto 55240 65 de 10/05/2020). It was expected that, with these actions, the number of deaths by COVID-19 66 would be reduced. Of note, the country's most populous state, São Paulo, adopted rigorous 67 quarantine measures and put them into effect on March 24 th , 2020 (Decreto 59283 2020 de São 68

Paulo SP). Internationally, Peru adopted the world's strictest lockdown (Tegel 2020). 69

Recently, Google LLC published datasets indicating changes in mobility (compared to an 70 average baseline before the COVID-19 pandemic). These reports were created with aggregated, 71

anonymized sets of daily and dynamic data at country and sub-regional levels drawn from users 72 who had enabled the Location History setting on their cell phones. These data reflect real-world 73 changes in social behavior and provide information on mobility trends for places like grocery 74 stores, pharmacies, parks, public transit stations, retail and recreation locations, residences, and 75

workplaces, when compared to the baseline period prior to the pandemic (Google LLC). 76

Mobility in places of residence provides information about the "time spent in residences", which 77

we will hereafter call "staying at home" and use as a surrogate for measuring adherence to stay-78 at-home policies. 79

Studies using Google COVID-19 Community Mobility Reports and the daily number of new 80 COVID-19 cases have shown that over 7 weeks a strong correlation between staying at home 81 and the reduction of COVID-19 cases in 20 counties in the United States (Badr et al. 2020); 82 COVID-19 cases decreased by 49% after 2 weeks of staying at home (Banerjee and Nayak 83 2020); the incidence of new cases/100,000 people was also reduced (Wang et al. 2020); social 84 distancing policies were associated with reduction in COVID-19 spread in the US (Gao et al. 85 2020); as well as in 49 countries around the world (Atalan 2020). A recent report using Brazilian 86

and European data has shown a correlation between NPI stringency and the spread of COVID-19 87 (Candido et al. 2020; Islam et al. 2020) ; these analyses are debatable, however, due to their short 88 time span and the type of time series behavior (Bernal et al. 2017) , or for their use of Pearson's 89 correlation in the context of non-stationary time series (Gao et al. 2020) . For instance, applying 90 the same statistical analysis to stationary and non-stationary time series is not sufficient for 91 statistical analysis (Nason 2006) , and the latter is the case with this COVID-19 data. A 2020 92

Cochrane systematic review of this topic reported that they were not completely certain about 93 this evidence for several reasons. taking the sum of deaths/million per epi-week, and the average of the variable "staying at home" 172 per epi-week, non-stationary patterns were mitigated by subtracting week t by week t-1 . 173

Details regarding the pre-processing and methodological details were presented on the approach 175 for analyzing the time series data. Our variables were the difference in the variation of deaths 176 between locations A and B (dependent variable -outcome), and the difference in the variation of 177 staying at home values between the same location (independent variable). 178

Direct comparison, between regions with and without controlled COVID-19 cases, was 180 considered in two scenarios: 1) Restrictive if, at least three out of four of the following 181 conditions were similar: a) population density, b) percentage of the urban population, c) HDI and 182 d) total area of the region. Similarity was considered adequate when a variation in conditions a), 183 b), and c) was within 30%, while, for condition d), a variation of 50% was considered adequate. 184

2) Global: all regions and countries were compared to each other. 185

Rationale 187

Time series on COVID-19 mortality (deaths/millions) display a non-stationary pattern. The daily 188 data present a very distinct seasonal behavior on the weekends, with valleys on Saturdays and 189

Sundays followed by peaks on Mondays ( Figure S1 ) 190

To make it stationary, one may introduce dummy variables for Saturdays, Sundays, and 191 Mondays, regress the number of deaths in these dummy variables, and then analyze the residuals. 192

However, in most cases, the residuals are still non-stationary time series, and special treatment 193 would be required in each case. Although this approach may be feasible for a few series, we are 194 interested in analyzing hundreds of time series from different countries and regions. Hence, we 195 need a more efficient way to deal with this amount of data. The covariates present another issue 196 in regressing the daily time series of deaths/staying at home. The covariates are typically 197 correlated with error terms due to public policies adopted by regions/countries. Mechanisms 198 controlling social isolation are intrinsically related to the number of deaths/cases in each 199

location. An increase in the death rate may cause more stringent policies to be adopted, which 200

increases the percentage of people staying at home. This change causes an imbalance between 201 the observed number of deaths and staying at home levels. In a regression model, this 202 discrepancy is accounted for in the error term. Hence, the error term will change in accordance 203 with staying at home levels. 204

Approach for analyzing the time series data 205 Data aggregation by epidemiological week is a plausible alternative ( Figure S2 ). In this way, 206 artificial seasonality, imposed by work scheduled during weekends and the effect of 207 governmental control over social interaction, in a regression framework, are mitigated. The 208

drawback is that the sample size is significantly reduced from 187 days ( Figure S1 ) to 26 209 epidemiological weeks (Figure S2 CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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denotes the variation of deaths between weeks ‫ݐ‬ and t-1 , also known as the flux 215 of deaths. The same is valid for the staying at home time series. This simple operation yielded, in 216 most cases, stationary time series, and verified with the so-called Phillips-Perron stationarity test 217 (Perron 1988) . In the few cases where the resulting time series did not reject the null hypothesis 218 of non-stationarity (technically, the existence of a unitary root, in the time series characteristic), 219

this was due to the presence of one or two outliers combined with the small sample size. These 220 outliers were usually related to the very low incidence of COVID-19 deaths by the 9 th 221 epidemiological week when paired with countries with a significant number of deaths in that 222 same week, thus resulting in an outlier which cannot be accounted for by linear 223

regression.(Perron 1988) 224

To investigate pairwise behavior, we propose a method to assess the relationship between deaths 225 and staying at home data between various countries and regions. ; consequently, we conclude that the behavior, 237 between A and B, is similar and the number of deaths and the percentage of staying at home are 238 associated in these regions. The other non-spurious situation implying ߚ ଵ ് 0 occurs when the 239 variation in the number of deaths in locations A and B increases/decreases over time following a 240 certain pattern, while the variation in the percentage of "staying at home" values also 241 increases/decreases following the same pattern (apart from the direction). In this situation, we 242

found different epidemiological patterns as in the variation in the number of deaths, and in the 243 staying at home values, in locations A and B were on opposite trends. However, if these patterns 244

were similar (proportional), this would be captured in the difference and, as a consequence, in 245 the regression. This means that the different trends were near proportional and, hence, the 246 variation in staying at home is associated with the variation in deaths. 247

The proposed approach presents a way to evaluate staying at home and the number of deaths 248 between two countries/regions. In the section below "Definition of areas with and without 249 controlled cases of COVID-19", each country/region was classified into a binary class: either 250 controlled or not controlled areas for COVID-19. The proposed method allows for insights 251 regarding the association of the number of deaths and staying at home levels between 252 countries/regions with similar/different degrees of COVID-19 control. 253

Estimation of ߚ and ߚ ଵ is carried out through ordinary least squares. Assumptions related to 254 consistency, efficiency, and asymptotic normality of the ordinary least squares, in the context of 255 time series regression, can be found in Greene, 2012 (Greene 2012). Since we are comparing 256 many time series, to avoid any problem with spurious regression, we performed a cointegration 257 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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A flowchart of the data manipulation is depicted in Figure 1 The global comparison yielded 3,741 combinations; from these, 184 (4.9%) had a p-value < 297 0.05, after correcting for False Discovery Rate (Table S3) . After performing the residual 298 analysis, by testing for cointegration between response and covariate, normality of the residuals, 299

presence of residual autocorrelation, homoscedasticity, and functional specification, only 63 300

(1.6%) of models passed all tests (Table S4 ). Closer inspection of several cases where the model 301 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20211284 doi: medRxiv preprint did not pass all the tests revealed a common factor: the presence of outliers, mostly due to 302 differences in the epidemiological week in which deaths started to be reported. A heat map 303

showing the comparison between the 87 regions is presented in Figure 2 . 304

We were not able to explain the variation of deaths/million in different regions in the world by 306 social isolation, herein analyzed as differences in staying at home, compared to baseline. In the 307 restrictive and global comparisons, only 3% and 1.6% of the comparisons were significantly 308 different, respectively. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. also affect the consistency of the ordinary least square estimates. Nevertheless, given the 370 importance of social isolation promoted by world authorities (COVID-19 advice -Physical 371 distancing), we expected a higher incidence of significant comparisons, even though it could be 372 an ecological fallacy. The low number of significant associations between regions for mortality 373 rate and the percentage of staying at home may be a case of exception fallacy, which is a 374 generalization of individual characteristics applied at the group-level characteristics (Miller and 375

Brewer 2003). 376

There are strengths to highlight. Inclusion criteria and the Healthcare Access and Quality Index 377 were incorporated. We obtained representative regions throughout the world, including major 378 cities from 4 different continents. Special attention was given to compiling and analyzing the 379 dataset. We also devised a tailored approach to deal with challenges presented by the data. To 380 our knowledge, our modeling approach is unique in pooling information from multiple countries 381 all at once using up-to-date data. Some criteria, such as population density, percentage of urban 382 population, HDI, and HAQI, were established to compare similar regions. Finally, we gave 383 special attention to the residual analysis in the linear regression, an absolutely essential aspect of 384 studies using small samples. 385

In conclusion, using this methodology and current data, in ~98% of the comparisons using 87 386 different regions of the world we found no evidence that the number of deaths/million is reduced 387 by staying at home. Regional differences in treatment methods and the natural course of the virus 388 may also be major factors in this pandemic, and further studies are necessary to better understand 389 it. 390

The Python and R scripts are available at 392 https://gist.github.com/rsavaris66/eccfc6caf4c9578d676c134fac74d3fe 393 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Approach for analyzing the time series data 606

Time series on COVID-19 mortality (deaths/millions) display a non-stationary pattern. The da 607 data present a very distinct seasonal behavior on the weekends, with valleys on Saturdays a 608

Sundays followed by peaks on Mondays ( Figure S1 ). 609 610 611 Figure S1 . Characteristics of the time series data on new daily deaths/million in the city of S 612

Paulo over 187 days. Note the non-stationary time series pattern. 613 daily s and f São . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 15, 2020 . . https://doi.org/10.1101 /2020 e. ntrol f the ward total ealth n in . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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Data aggregation of the number of deaths/million in the city of São Paulo

Argentina over several epidemiological weeks, compared to the percentage of staying at home

In this way, artificial 647 seasonality, imposed by work scheduled during weekends and the effect of governmental contr 648 over social interaction, in a regression framework, are mitigated. The drawback is that the 649 sample size is significantly reduced from 187 days (Figure S1) to 26 epidemiological weeks

Regions were classified as controlled for cases of COVID-19 if they present at least 2 out of t 653 3 following conditions: a) type of transmission classified as "clusters of cases", b) a downwa 654 curve of newly reported deaths in the last 7 days, and c) a flat curve in the cumulative to 655 number of deaths in the last 7 days

Organization (WHO Coronavirus Disease (COVID-19) Dashboard). An example is shown 657 Figure S3