key: cord-0797780-hu83hcgd
authors: Basellini, Ugofilippo; Alburez-Gutierrez, Diego; Del Fava, Emanuele; Perrotta, Daniela; Bonetti, Marco; Camarda, Carlo G.; Zagheni, Emilio
title: Linking excess mortality to mobility data during the first wave of COVID-19 in England and Wales
date: 2021-04-21
journal: SSM Popul Health
DOI: 10.1016/j.ssmph.2021.100799
sha: 644a6feeed920d173fb52922403a56b092936430
doc_id: 797780
cord_uid: hu83hcgd

Non-pharmaceutical interventions have been implemented worldwide to curb the spread of COVID-19. However, the effectiveness of such governmental measures in reducing the mortality burden remains a key question of scientific interest and public debate. In this study, we leverage digital mobility data to assess the effects of reduced human mobility on excess mortality, focusing on regional data in England and Wales between February and August 2020. We estimate a robust association between mobility reductions and lower excess mortality, after adjusting for time trends and regional differences in a mixed-effects regression framework and considering a five-week lag between the two measures. We predict that, in the absence of mobility reductions, the number of excess deaths could have more than doubled in England and Wales during this period, especially in the London area. The study is one of the first attempts to quantify the effects of mobility reductions on excess mortality during the COVID-19 pandemic.

1 Introduction 1 J o u r n a l P r e -p r o o f exposures as offset, and time-specific covariates: ln(µ w,t ) = ln(e w,t ) + f (x w,t ) + α 0 + α w ,

where e w,t denotes the exposure to the risk of death, the function f (·) is a smooth function over the 122 time-points x w,t = 1, . . . , m, where m denotes the total number of observations, α 0 is an intercept 123 and α w are week-specific coefficients. To ensure identifiability of the α w coefficients, the first week 124 is taken as the reference group (i.e. α 1 = 1). Exposures over weeks and years are obtained by This approach allows us to readily evaluate the excess number of deathsδ w for the weeks 07-33 145 in 2020 as the difference between the observed and the expected ones, i.e.δ w = d w −d w . In order 146 to account for regional differences in population, we then compute the excess mortality rate, or per 147 capita excess mortality, y w =δ w /e w , dividing excess deaths by the (extrapolated) region-specific 148 exposures in week w of 2020.

In addition to fitting the GAM, we perform a sensitivity analysis on the computation of the 150 excess mortality rate. In particular, we derive another estimate of y w by computing, for each week, (Lu et al., 2008) . In both approaches, the goal is to retain as much as possible the variation 160 present in the original data set. However, whereas standard PCA reduces the dimensionality of a 161 two-dimensional data set, MPCA allows to extract features of a multidimensional object such as 162 the GCMR. 163 To do so, we construct a tensor object (a multidimensional array) containing the three types Given the estimated excess mortality rate for each week and region, we intend to assess whether 170 an association with the change in mobility exists, and its magnitude. The spread of COVID-19 171 mainly occurs through contacts between infectious and susceptible individuals (Zhang et al., 2020) .

Hence, a reduction in mobility should lead to a reduction in social contacts, then in the infection 173 spread and, ultimately, in the COVID-related mortality. However, this process requires time, as we 174 would expect the reduction in physical mobility observed today to possibly have an impact on the 175 infection spread and the related mortality in the coming weeks. This calls for the introduction of 176 a time lag of x weeks in the mobility data, which corresponds to the amount of time necessary for 177 the change in mobility to have an impact on mortality. In other words, we analyse the relationship 178 between excess mortality and changes in human mobility that occurred x weeks before. We do not 179 choose the value of x a priori, but rather we determine its most plausible value from the regression 180 analysis of our data (see Section 3.2).

Moreover, we work with rates that vary over weeks and for different regions. While the mortality 182 trend will be assumed to remain constant in space, we need to account for the regional heterogeneity 183 in excess mortality and response to mobility changes, given that data within each region are likely 184 correlated. This setting calls for a mixed-effects modelling approach, since we aim to know whether 185 an association between excess mortality and human mobility over time still exists, after controlling 186 for the variation across regions.

Let y r,w denote the excess mortality rate for a given region r in week w. We model y r,w as 188 follows:

where β 0 is the common intercept and u r are the region-specific random intercepts, added to capture 190 average regional differences; γ 0 is the common mobility coefficient, which can be interpreted as the 191 average change in per capita excess mortality for a unit change in the mobility indicator (with 192 respect to the baseline period), and γ r are the region-specific random slopes that modify the effect 193 of mobility change for region r during the (lagged) week w − x, i.e., g r,w−x . Random intercepts u r 194 and random slopes γ r are normally distributed with mean zero and variance σ 2 u and σ 2 γ , respectively, 195 with their dependence captured by the covariance term σ u,γ , which allows the computation of a 196 model-based correlation coefficient. Evidence for σ 2 u and σ 2 γ being greater than zero implies the 197 existence of regional differences in the baseline levels of mortality and heterogeneity in the responses 198 to mobility changes, respectively. The baseline mortality time trend is modelled in a flexible way 199 using a non-parametric approach based on B-spline bases B s , with β s denoting the associated 200 coefficients. Finally, ε r,w is the vector of the residuals, distributed as ε r,w ∼ N (0, σ 2 ) and assumed 201 to be independent of the random effects u r and γ r .

To account for uncertainty in the estimates, related to both the computation of excess mortality 203 and the mixed-effects regression in our estimates, we employ a bootstrap approach to derive 95% the category is subject to a higher proportion of missing data (see Figure Next, we compute the excess mortality rate at the regional level during the same period of time. We provide a series of additional graphs related to these two variables in Appendix A. Specifi-242 cally, the estimation of the excess mortality rate using the GAM is exemplified for two regions in 

We investigate the relationship between excess mortality and mobility using a mixed-effects regres-247 sion approach. To account for the delay between the two phenomena, we analyse excess mortality 248 with respect to mobility changes that occurred five weeks in the past. We found this lag to be the 249 shortest one displaying a positive relationship between mortality and mobility (see Table A and find that our results do not change for lags of 6 or 7 weeks (see Table A .1 in Appendix A).

We find a strong and significant association between mobility reduction and excess mortality 253 after five weeks, after controlling in the regression model for the pandemic time trend and for 254 regional differences. Table 1 reports the results of the mixed-effects regression models, considering 255 the combined Google index and the six categories of the GCMR independently. The models include 256 a smooth function of time (using 5 B-splines), as well as random intercepts and random slopes 257 for each region. We standardise the mobility data to aid the interpretation and comparison of the 258 estimated coefficients from the various models. 259 We estimate that a reduction of one standard deviation in the combined Google mobility index 260 is associated with a reduction of 3.77 in the excess mortality rate per 100,000 individuals five 261 weeks later. This is a strong effect, given that the Google index changed by almost 4 standard 262 deviations across all regions following the introduction of the NPIs (see Figure 1 ). Moreover, five 263 J o u r n a l P r e -p r o o f Table 1 . Estimated coefficients and 95% confidence intervals from the linear mixed-effects regression between excess mortality rate (per 100,000 individuals) and changes in mobility occurred five weeks before, measured separately for each model with the combined Google index and the six categories of the GCMR: grocery, workplaces, residential, transit, retail and parks. For the parks category, we considered only random intercepts since the the model with both random intercepts and slopes did not converge. Estimation is performed using restricted maximum likelihood. Source: Authors' own elaboration based on data from Office for National Statistics (2020a Statistics ( , 2021 and Google LLC (2021). These results are robust to a series of sensitivity analysis, which are reported in Appendix B.

The estimated coefficients are robust to a change in the computation of the excess mortality rate.

The historical-based approach to estimate excess mortality is shown and compared to the GAM in Table B .2). Finally, the exclusion of the region of London from 275 the analysis does not influence the magnitude and significance of the estimated coefficients (see 276   Table B .3).

It is important to analyse cross-sectional differences across regions in terms of both excess regional slope coefficient (mobility) regional intercept coefficient (excess mortality) Figure 3 . Estimated region-specific intercepts and mobility slopes, as well as their estimated correlation r from the mixed-effects regression in England and Wales by region during weeks 13-33 of 2020. Source: Authors' own elaboration based on data from Office for National Statistics (2020a, 2021) and Google LLC (2021). Finally, the estimated model allows us to estimate the number of deaths averted by mobility 291 reductions. This is achieved by simulating a counterfactual worst-case scenario in which mobility 292 is assumed not to have dropped with the introduction of the NPIs but rather to have remained Table 2 . Population size, estimated number of excess deaths, and estimated number of deaths averted by the mobility reductions (counterfactual analysis) with 95% confidence intervals by region in England and Wales during weeks 13-33 of 2020. Estimates have been rounded to the nearest hundredth to avoid giving a false sense of precision in the presence of uncertainty (as in Kontis et al., 2020) ; as such, figures for the Total row may differ from the sum of the regions. Source: Authors' own elaboration based on data from Office for National Statistics (2020a, 2021) and Google LLC (2021).

Population ( COVID-19 Community Mobility Reports (Google LLC, 2021) to explore the association between 319 mobility and excess mortality at the regional level in England and Wales. 320 We found a strong positive relationship between the mobility of Google Maps users and 321 population-level excess mortality, which is considered to be the best indicator of the impact of 322 the pandemic on mortality (National Academies of Sciences, Engineering, and Medicine, 2020).

Our analysis determined that a time lag of at least five weeks is needed to reveal a positive as-324 sociation between mobility and mortality, while smaller lags display a negative relationship. A 325 J o u r n a l P r e -p r o o f five-week time period is consistent with preliminary estimates of the disease duration from infection to death, with the incubation period (i.e., from infection to symptom onset) that can last up 327 to two weeks (11.5 days with a 95% CI of 8.2 to 15.6 days (Lauer et al., 2020)), and the course 328 of disease (i.e., from symptom onset to death) that can last up to three weeks (17.8 days with 329 a 95% CI of 16.9 to 19.2 days (Verity et al., 2020) ). This is also consistent with an US-based 330 study, where mobility reductions assessed via mobile phone data were found to anticipate the 331 exponential decay of COVID-deaths by a median of 3 to 4 weeks (Kogan et al., 2021) . Finally, 332 the period of time between infection and death is also related to the individual-level Susceptible- In our work, we exploit the potential of digital-trace data to estimate human mobility and ex-370 plain excess mortality, but we are also aware of the shortcomings related to this data source. These 371 are in particular due to the lack of detail concerning the collection and processing of the mobility 372 data. One limitation is that Google does not share absolute numbers in their reports, but only 373 relative changes with respect to the beginning of 2020. Back-engineering the underlying absolute 374 measurements does not seem possible or desirable, given privacy concerns in sparsely populated 375 areas. Moreover, no information is provided on the population composition of Google Maps users, 376 such as age-group or sex breakdowns, thus limiting our ability to assess the representativeness 377 J o u r n a l P r e -p r o o f of the data. This lack of detail makes the data less informative than it could possibly be, if all raw measures were made available together with the description of the algorithms used to produce 379 them.

Nonetheless, we believe that the Google mobility data provide a first and valuable approxima-381 tion to the changes in human mobility occurred during the COVID-19 pandemic. Such data are 382 necessarily affected by biases related to population sampling, which depends on the market share of 383 the operator providing the data and the different usage across socio-demographic groups. However, and not at the sub-national level, see Figure A .8 in Appendix A). Thus, we are confident that this 396 data source approximates well the overall mobility trends at the regional level.

Our study provides evidence on the positive impact of NPIs to mitigate the mortality burden for an open conversation on how these data can be used ethically to help save lives.

J o u r n a l P r e -p r o o f Schlosser, F., Maier, B. F., Jack, O., Hinrichs, D., Zachariae, A., and Brockmann, D. (2020) . In this Appendix, we report additional results of our analysis. We start by presenting the results of 585 computing the excess mortality rate using the GAM. Figure Next, we present the graphs corresponding to Figure 2 for all the regions analysed in our study. week Figure A .5. Linear relationship (with slope equal to β) between excess mortality rate (per 100,000 individuals) and (scaled) change in workplace mobility in ten regions of England and Wales during weeks 8-33 of 2020, considering different time lags for mobility data. Source: Authors' own elaboration based on data from Office for National Statistics (2020a, 2021) and Google LLC (2021).

Next, we analyse the role played by different time lags in the relationship between excess mor-J o u r n a l P r e -p r o o f tality and mobility within our regression approach. Analysing Figure A. 3, London appears as an outlier compared to the other regions since its level 666 of excess mortality and mobility decreased considerably more than in other regions. For this 667 reason, we re-run all our analysis excluding London from the observations employed in our study.

668 Table B .3 shows that the estimated mobility coefficients vary marginally with respect to those 669 estimated in the presence of London, remaining significant at the 95% confidence level. Finally, Table B .1. Estimated coefficients and 95% confidence intervals of linear mixed-effects regression between excess mortality rate (per 100,000 individuals) and changes in mobility occurred five weeks before, measured separately for each model with the combined Google index and the six categories of the GCMR: grocery, workplaces, residential, transit, retail and parks. Note: the excess mortality rate (per 100,000 individuals) is computed from the historical average of weekly deaths instead of the GAM employed in Table 1 . Source: Authors' own elaboration based on data from Office for National Statistics (2020a, 2021) and Google LLC (2021). the mixed-effects model reduces only slightly when excluding London from the analysis.

J o u r n a l P r e -p r o o f Table B .2. Estimated coefficients and 95% confidence intervals of linear mixed-effects regression between excess mortality rate (per 100,000 individuals) and changes in Google mobility index occurred five weeks before, using five different choices of B-spline bases for describing the time series of the epidemic. Source: Authors' own elaboration based on data from Office for National Statistics (2020a Statistics ( , 2021 and Google LLC (2021). Table B .3. Estimated coefficients and 95% confidence intervals of linear mixed-effects regression between excess mortality rate (per 100,000 individuals) and changes in mobility occurred five weeks before, measured separately for each model with the combined Google index and the six categories of the GCMR: grocery, workplaces, residential, transit, retail and parks. Note: the region of London was removed from the analysis. Source: Authors' own elaboration based on data from Office for National Statistics (2020a, 2021) and Google LLC (2021). 4.0 4.5 5.0 regional slope coefficient (mobility) regional intercept coefficient (excess mortality) Figure B .3. Estimated region-specific intercepts and mobility coefficients, as well as their estimated correlation r from the mixed-effects regression in nine regions of England and Wales (excluding London) during weeks 13-33 of 2020. Source: Authors' own elaboration based on data from Office for National Statistics (2020a Statistics ( , 2021 and Google LLC (2021).

to the historical average, resulting in slightly higher excess mortality. Figure B.2 649 shows the excess mortality rate obtained with the two approaches for all ten regions of England 650 and Wales during the period analysed