key: cord-0985065-jlrddb8z
authors: Harris, J. E.
title: Mobility was a Significant Determinant of Reported COVID-19 Incidence During the Omicron Surge in the Most Populous U.S. Counties
date: 2022-03-18
journal: nan
DOI: 10.1101/2022.03.16.22272523
sha: 9214c6bfbf15b4c7eb6e0569452a32e5ada995e6
doc_id: 985065
cord_uid: jlrddb8z

We studied the relationship between declines in mobility and subsequently reported COVID-19 case incidence in 111 of the most populous U.S. counties during the Omicron surge from December 2021 through February 2022. We employed principal component analysis to construct a one-dimensional summary measure of the six Google mobility categories that are regularly reported for each county. Among counties with a lower mobility decline between December 20 and January 3, reported COVID-19 incidence did not peak until the week ending January 17, whereas among counties with a higher mobility decline, incidence peaked earlier by the week ending January 10 and remained significantly lower. Based upon a fixed-effects, longitudinal cohort model, we estimated that every 1-percent decline in mobility between December 20 and January 3 was associated with a 0.63 percent decline in peak incidence during the week ending January 17 (95% confidence interval, 0.40-0.86 percent). Based upon a cross-sectional analysis including mean household size and vaccination participation as covariates, we estimated that the same 1-percent decline in mobility was associated with a 0.36 percent decline in cumulative reported COVID-19 incidence from January 10 through February 28 (95% CI, 0.18-0.54 percent). Omicron did not simply sweep through the U.S. population until it ran out of susceptible individuals to infect. To the contrary, a significant fraction managed to avoid infection by engaging in risk-mitigating behaviors. More broadly, the behavioral response to perceived risk should be viewed as an intrinsic component of the natural course of epidemics in humans.

During the early and middle phases of the COVID-19 pandemic, numerous studies in various countries documented an association between a decline in population mobility and a subsequent reduction in reported case incidence [1] [2] [3] [4] [5] [6] [7] [8] [9] . The principal objective of the present study is to begin to assess whether this mobility-incidence relationship similarly prevailed during the more recent wave driven by the Omicron variant of SARS-CoV-2.

There are several critical reasons why the mobility-incidence relationship observed for the ancestral strain and prior variants of SARS-CoV-2 may not apply equally to Omicron. More than any other variant, Omicron exhibited significant immune escape against vaccination and prior infection [10, 11] , though vaccines continued to protect against serious disease [12, 13] .

Omicron appears to have been about twice as transmissible as the Delta variant [14] , with the larger proportion of asymptomatic Omicron infections likely enhancing the prevalence of super spreaders [15] . While home testing rose markedly in response to the initial news of the variant [16] , later reports of Omicron's tendency to spare the deep tissues of the lung [17] may have alleviated fears of serious illness that drive voluntary risk-mitigation behavior [18] . There is the further concern that frequently changing news reports and public health guidance induced "worry fatigue" [19] , especially when perceptions of risk and compliance with such guidance are themselves subject to herd transmission [20] .

Mobility is a multidimensional concept that has been variously gauged by such diverse measures as smartphone visits to bars and restaurants [21] , traffic patterns [9] , and television watching as a proxy for time spent at home [22] . Here, following the lead of two key papers [23, 24] , we employ the statistical technique of principal component analysis to collapse the sixdimensional Google Mobility Reports [25] into a single mobility indicator. Further adhering to a recent study of reported case incidence and hospitalization in relation to vaccination rates during the Delta surge [26] , we restrict our analysis to the most populous counties in the United States, together comprising approximately 44 percent of the total U.S. population. Such an approach avoids the potential pitfalls of comparing small rural counties with large urban centers. We focus on the wave of reported cases from December 2021 through Feb 2022, during which Omicron was far and away the dominant variant [27] .

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As noted above, we confined our analysis to the most populous counties in the United States. From an initial sample of all 112 counties with population exceeding 600,000, we 

We relied upon Google Mobility Reports [25] to assess changes in mobility in each of the 111 counties in our analytic sample. Compiled from data on the movements of mobile devices, these reports provided daily measures of mobility for six distinct categories of places: retail & recreation; grocery & pharmacy; parks; transit stations; workplaces; and residential [28] . Based upon the number of visits to and length of stay in the places in each category, the reports showed activity as a percent of baseline, where the baseline represented the median value for the corresponding day of the week during the 5-week period from January 3 -February 6, 2020. For each of the 111 counties in the analytic sample and each of the six categories of mobility, we computed weekly mean values of mobility for the week ending Monday, February 24, 2020, through the week ending Monday, February 28, 2022. We chose a weekly ending date of Monday solely to be conformal with the available data on COVID-19 case reports, to be described below.

We relied upon the COVID-19 Community Profile Reports, issued regularly by the White House COVID-19 Team [29] , for data on the reported number of COVID-19 cases in each county for each week, starting with the week ending December 6, 2021, and continuing through the week ending February 28, 2022. We also relied upon this data source for estimates of each county's population, from which we computed COVID-19 incidence rates, as well as two county-specific demographic characteristics: the U.S. Center for Disease Control's social vulnerability index [30] , and the average household size. We included the latter characteristic to capture the important influence of intra-household transmission on COVID-19 incidence [3] .

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In addition to the foregoing county-specific demographic variables, we relied upon a database of COVID-19 vaccination participation rates, compiled by the U.S. Centers for Disease Control and Prevention [31] . These data showed the percentage of each county's population who completed a one-or two-dose series of vaccinations, as well as the cumulative number of booster doses per 100 population, as of December 15, 2021, the earliest date for which both measures were available.

We relied upon the data on the six weekly Google mobility measures in the 111-county database, covering the 106-week period from the week ending February 24, 2020, through the week ending February 28, 2022, to compute the first principal component as a summary measure of mobility [23, 24] . This summary measure, which we refer to here as our mobility indicator, represents the linear combination of the six individual mobility categories that captures the largest fraction of the overall variance of the data [32] . Denoting by !"# the observed value of [33] .

Having relied upon the entire database of multidimensional Google mobility categories from the week ending February 24, 2020, onward to compute our unidimensional mobility indicator, we then focused on the narrower 13-week period from the week ending December 6, 2021 through the week ending February 28, 2022, which encompassed the Omicron surge in the United States [27] .

As described in detail in the Results below, we determined that our mobility indicator "# (where = 1, ... ,111 and = 1, … ,13) declined primarily during the interval between the week ending December 20, 2021 (that is, = 3) to the week ending January 3, 2022 (that is, = 5). For each county , we thus computed the change in the mobility indicator ∆ " = "( − ") . Since mobility declined overall during the 13-week analysis period, the quantities ∆ " were negative.

We then divided the sample of counties into the lower half and upper half of the distribution of . 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 March 18, 2022. ; https://doi.org/10.1101/2022.03.16.22272523 doi: medRxiv preprint the absolute values |∆ " |, denoting counties in the lower half as low mobility decline and those in the upper half as high mobility decline. We defined the binary variable " to equal 0 if county was in the lower half and 1 if county was in the upper half of the distribution.

The available data, described above, thus allowed us to construct a longitudinal cohort of 111 counties, indexed = 1, …, 111, covering the 13-week period running from the week ending December 6, 2021 ( = 1) through the week ending February 28, 2022 ( = 13). For each county and week , we had data not only on our constructed mobility indicator "# , but also on "# , the incidence of reported cases of COVID-19 per 100,000 population.

To examine the qualitative relationships between changes in mobility and changes in COVID-19 incidence, we first plotted the population-weighted mean values of "# and "# over time for the two groups of counties with low and high declines in mobility. For example, the population-weighted mean mobility indicator among low-decline counties at week would equal

, where " is the population of county and where the summations are only over those counties for which " = 0. The other conditional means were computed analogously.

To further examine the quantitative relationships between changes in mobility and changes in COVID-19 incidence, we estimated a fixed-effects longitudinal cohort model with the following specification:

In equation (1), the parameter was an overall mean, while " and # were county-specific and time-specific fixed effects, respectively. The parameters of interest # gauged the impact of county-specific changes in mobility on a week-by-week basis. Finally, "# were assumed to be spherical error terms. This fixed-effects model was estimated by ordinary least squares.

To further study the quantitative relationships between changes in mobility and changes in COVID-19 incidence, we defined the cumulative incidence for each county during the period from week ending January 10, 2022 ( = 6) through the week ending February 28, 2022 ( = 13)

. We then ran the cross-sectional model:

.

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The copyright holder for this preprint this version posted March 18, 2022. ; https://doi.org/10.1101/2022.03. 16.22272523 doi: medRxiv preprint In equation (2), the parameter was an overall mean, while the parameters , captured the effects of county-specific covariates ", . The parameter of interest gauged the proportional impact the change in mobility during the period between December 20, 2021, and January 3, 2022, on the subsequent cumulative reported incidence of COVID-19 from the week ending January 10, 2022, onward. Finally, " were assumed to be uncorrelated error terms. This crosssectional model was estimated by population-weighted least squares.

Appendix Table A . 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 March 18, 2022 as " = 1, shows the paths of another 14 randomly selected counties with an absolute decline more than 31.85. In both panels, the paths of the calculated mobility indicators during the interval from 12/20/21 -1/3/22 have been highlighted. For the low-decline ( " = 0) counties on the left, nearly all the calculated decline in mobility occurred during the first week, that is, during 12/20 -12/27/21. For the high-decline ( " = 1) counties on the right, the calculated mobility indicators continued to decline during the second week, that is, during 12/27/21 -1/3/22. The observed absolute decline of |∆ " | = 33.18 thus placed Philadelphia County in the highdecline ( " = 1) group. One week later, by the week ending January 10, 2022, reported COVID-19 incidence reached a peak of 1,666 cases per 100,000 population and declined thereafter.

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For the low-and high-decline groups separately, Fig. 4 graphs the temporal paths of the population-weighted mean mobility indicator and population-weighted mean COVID-19 incidence during the 13-week study period. Both mobility and incidence have been computed as the change from the week ending December 6, 2021. Changes in mobility (square datapoints, measured on the left axis) are identified by the labels "∆ Mobility," while changes in incidence (circular datapoints, measured on the right axis) are identified by the labels "∆ Incidence."

Both the low-and high-decline counties followed essentially the same mobility path through the week ending December 27, 2021. During the subsequent week ending January 3, 2022, however, the two groups diverged, with the high-decline ( " = 1) group exhibiting a greater continuing drop in mobility. These differences in mobility are reflected in the divergent paths of incremental COVID-19 incidence. Among low-decline ( " = 0) counties, incidence . 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 March 18, 2022. ; https://doi.org/10.1101/2022.03.16.22272523 doi: medRxiv preprint peaked during the week ending January 17, while among high-decline ( " = 1) counties, incidence reached a lower peak one week earlier. 

Appendix Table C displays our estimates of the parameters of the cross-sectional model of equation (2) . The estimated parameter was significantly different from zero in a bivariate specification on the change in mobility (specification A) as well as in multivariate specifications (B and C) that included demographic covariates and vaccination participation rates. Apart from . 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 March 18, 2022. ; https://doi.org/10.1101/2022.03.16.22272523 doi: medRxiv preprint the change in mobility, average household size was the only other explanatory variable exhibiting a statistically significant association with cumulative reported COVID-19 incidence. Fig. 6 plots the cumulative cases per 100 population between the week ending January 10, 2022, and the week ending February 28, 2022 (that is, the variable " in equation (2)) against the change in our calculated mobility indicator (∆ " ) between December 20, 2021, and January 3, 2022 (that is, the variable ∆ " ). In accordance with the log-linear specification of equation (2), the vertical axis is measured on a logarithmic scale. The size of each datapoint reflects the county population. (2) was 0.0124 with 95% CI (0.0060, 0.0187). That is, every additional 1-point reduction in the mobility indicator was associated with a 1.24 percent decline in cumulative reported cases per 100 persons. The outlier in the plot is identified as Cuyahoga County, Ohio. The vertical axis plots cumulative case incidence from the week ending January 10 onward. Cumulative incidence for the entire Omicron wave, from the week ending December 6, 2021, averaged 9 per 100 population.

The superimposed line represents the population-weighted least squares fit to the data. This corresponds to the bivariate regression of log " versus ∆ " without additional covariates " , shown as specification A in Appendix Table C . The estimate of the slope parameter was . 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. 

For each one-percent decline in our unidimensional measure of motility, which we derived from the six-dimensional Google Mobility categories, we have estimated a 0.63-percent decline in peak reported case incidence (95% confidence interval, 0.40 to 0.86 percent) and a 0.36-percent decline in cumulative reported case incidence (95% confidence interval, 0.18 to 0.54 percent). That the short-term elasticity of peak incidence turns out to be greater than the longer-term elasticity of cumulative incidence is hardly unexpected. As the prevalence of infection falls beyond the peak of epidemic wave, the effectiveness of risk-avoidance measures would be expected to decline. The declining marginal effects derived from the longitudinal cohort model, as seen in Fig. 5 , are consistent with this interpretation.

Nor is it unexpected that the estimated mobility-incidence elasticity should be less than 1 even at the peak of the Omicron wave. For it implies that there were some sources of infection whose risks could not be mitigated through the available mobility-reduction strategies. Consider, for example, an individual whose only source of infection was taking public transport to work. If she cut back her exposure through this modality by percent, her risk of infection would likewise decline by percent, and the mobility-elasticity elasticity would be 1. If, on the other hand, intrahousehold transmission from family members was a second, independent source of infection, then her cutting back on public transport by percent would lower her infection risk by less than percent, and the corresponding elastic would be less than unity. Our finding that average household size was a significant determinant of county-specific Omicron case incidence (Appendix Table C ) suggests that this example is more than hypothetical.

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Our results belie the hypothesis that Omicron simply swept through the population until the variant ran out of susceptible individuals to infect. For the entire Omicron surge, cumulative reported incidence averaged approximately 9 cases per 100 population (Fig. 6 ). If only onefourth of all Omicron infections were reported by public authorities [34] , then approximately 36 percent of the population became infected during the Omicron surge. In view of Omicron's documented capacity for immune escape from vaccination and prior infection [10, 11] , there had to be no small fraction of susceptible individuals who, by engaging in risk-mitigating behaviors, managed to avoid infection.

Our findings reinforce the broader conclusion that the behavioral response to perceived risk needs to be regarded as an intrinsic component of the course of epidemics in humans. Quite apart from the evidence now accumulated in the ongoing COVID-19 pandemic, such behavioral responses have been documented for HIV in developing countries [35] , the SARS outbreak in Hong Kong [36] , the swine flu outbreak [37] , the H1N1 influenza outbreak [38] , and sexually transmitted diseases generally [39] .

The principal objection to our findings is that our study design cannot demonstrate a purely causal relation between initial declines in mobility and subsequent reductions in the incidence of infection. To the contrary, the argument goes, the observed declines in our unidimensional mobility indicator between the week ending December 10, 2021, and the week ending January 3, 2022, could also have been an early response to the emerging Omicron wave.

One might conjecture, in fact, that the somewhat greater COVID-19 incidence in high-mobilitydecline counties seen in Fig. 4 , especially during the week ending January 3, was in fact the stimulus for the inhabitants of those counties to continue to engage in mobility-reducing behaviors. Such an interpretation would seem to square with the significant negative estimate of the parameter ( in Fig. 5 .

In view of such reverse causation, our estimates of the parametersthrough &) in Fig.   5 , covering the period from the week ending January 13 onward, may indeed be biased upward, as is our cross-sectional slope parameter in Fig. 6 . However, the magnitude of the bias is likely to be small. After all, the striking temporal relation between the extent of the mobility reductions . 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 March 18, 2022. ;  https://doi.org/10.1101/2022.03.16.22272523 doi: medRxiv preprint observed through the week ending January 3 and the subsequent divergence in COVID-19 incidence, as seen in Fig. 4 , cannot readily be explained by reverse causation.

It would have been preferable, some might contend, to instead construct predictor variables based upon the extent of policy restrictions on mobility imposed in each county, such as renewed requirements on indoor mask use. In principle, such restrictions would be regarded as exogenous instruments to identify the unbiased effect of the endogenous mobility indicator that we have relied upon here [40] . The problem with this approach is that policies intended to restrict mobility are likewise endogenous. A public authority's decision to impose a mask mandate may just as well be a response to news of rising COVID-19 cases as an individual's uncoerced decision not to take the subway.

There is little basis to suppose, in any event, that declines in mobility such as those incidence curve. Yet no government authority ordered New Yorkers to stop taking the subway en masse [4] .

The data in Figs. 1 through 4 make a strong case in favor of the suitability of our unidimensional summary indicator of the six Google mobility categories. In the illustrative plot in Fig. 1 , we saw how five of the individual categories tended to move together, while the residential category tended to move in the opposite direction. Our principal component analysis (Appendix Table A ) confirmed these observations and further demonstrated that visits to retail establishments captured a larger fraction of the overall variance of the six categories. In the illustrative plot of Fig. 2 , we saw how the resulting unidimensional indicator consistently captured changes in mobility during the two-week interval from the week ending December 20 to the week ending January 3. In Figs. 3 and 4 , we saw how the temporal path of our unidimensional mobility indicator during that interval was followed by a peaking in reported Omicron cases one week later.

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In our longitudinal cohort analysis of equation (1), we relied on the statistical technique of fixed effects to capture other, persistent unobserved characteristics of individual counties. In the cross-sectional analysis of equation (2), by contrast, we relied upon county-specific demographic variables and indicators of vaccination participation. Unfortunately, we did not have county-specific data on booster vaccinations before December 15, 2021. Consequently, our data may include a nontrivial number of recent vaccinations in response to emerging news about the coming Omicron wave.

In contrast to our longitudinal study of a cohort of 111 counties over 13 successive weeks, our cross-sectional analysis encompassed only 111 county-specific observations on cumulative reported COVID-19 incidence. As already noted, reported cases of Omicron may have constituted no more than one-quarter of all incident cases [34] . This observation raises the possibility that the degree of underreporting in a particular county was related to the magnitude of the observed decline in mobility. To the extent that counties with a higher perceived risk and greater self-imposed declines in mobility also reported more cases, our cross-sectional estimates would understate the strength of the mobility-incidence relationship.

Our results confirm a quantitative relationship between declines in mobility and subsequent declines in reported case incidence during the Omicron surge in the most populous counties in the United States. Our findings further imply that a significant fraction of the population managed to avoid infection by engaging in risk-mitigating behaviors. More broadly, the behavioral response to perceived risk should be viewed as an intrinsic component of the natural course of epidemics in humans.

. 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) Table B shows the estimates of the parameters ( " , = 2, …, xx) of the fixed-effects model of equation (1). Parameter # for the reference category was set equal to 1. Table C below shows the results of our cross-section model of equation (2) . Specification A includes only the county specific change in mobility (∆ ) as a covariate. Specification B adds . 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 March 18, 2022. ; https://doi.org/10.1101/2022.03.16.22272523 doi: medRxiv preprint average household size as a covariate, while specification C includes the social vulnerability index and our two indicators of vaccination participation. 2243 *In all specifications, the dependent variable was the logarithm of the cumulative case incidence per 100 population between the week ending January 10, 2022 ( = 6) and the week ending February 28, 2022 ( = 13) per 100 population. There was a total of 111 observations. All models estimated by population-weighted least squares. Highlighted in bold are parameter estimates significantly different from 0 (2-sided t-test, p < 0.05). Standard errors are shown in parentheses below each parameter estimate.

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