key: cord-0833047-la1fb87n authors: Catalano, Ralph; Glymour, M Maria; Chen, Yea-Hung; Bibbins-Domingo, Kirsten title: Sheltering In Place and The Likelihood Of Non-Natural Death date: 2021-03-15 journal: Am J Epidemiol DOI: 10.1093/aje/kwab062 sha: 3a0176d93d8ff22ba4953b863759465110572382 doc_id: 833047 cord_uid: la1fb87n Increasing hospitalizations for COVID-19 in the United States (US) and elsewhere have ignited debate over whether to reinstate shelter-in-place policies adopted early in the pandemic to slow the spread of infection. The debate includes claims that sheltering in place influences deaths unrelated to infection or other natural causes. Testing this claim should improve the benefit/cost accounting that informs choice on reimposing sheltering in place. We use time-series methods to compare weekly non-natural deaths in California to those in Florida. California was the first state to begin, and among the last to end, sheltering in place while sheltering began later and ended earlier in Florida. During weeks when California had shelter-in-place orders in effect, but Florida did not, the odds that a non-natural death occurred in California rather than Florida were 14.4% below expected levels. Sheltering-in-place policies likely reduce mortality from mechanisms unrelated to infection or other natural causes of death. As COVID-19 infections and hospitalizations increase in the US and elsewhere, debate over the prudence of shelter-in-place mandates has intensified (1, 2) . The debate includes claims that the intervention has induced unintended adverse health effects (3) . The "Great Barrington Declaration," for example, justifies opposition to sheltering in place by citing "devastating effects on short and long-term public health (2, 4) ." The literature includes claims that the harms of lockdown include increases in deaths not just from impeded access to health care, but also from suicide (5) and intrafamily violence (6) . Assessing the accuracy of these claim would seem important if for no other reason than to improve the explicit or implicit accounting of costs presumed to inform the choice whether or not to impose sheltering in place. Although clinical anecdote (7) supports the intuition of increased non-Covid-19 mortality during sheltering-in-place, the scholarly literature reports mixed findings (8) (9) (10) . These divergent results likely arise, at least in part, because the observed populations varied in the fraction at risk of what the Centers for Disease Control (CDC) term "natural" death or that "due solely or almost entirely to disease or the aging process" (11). Although information characterizing deaths varies among states, all death certificates in the US use a "manner of death" classification that includes "natural death" (11). Based on data from the last decade, natural deaths account for approximately 89% of deaths in the US (12) . The observed populations also likely varied in the fraction at risk of "non-natural" deaths. How sheltering in place affects these deaths remains, however, even less clear than how it affects natural deaths. As noted above, anecdote implies that suicides (5) and death due to intrafamily violence (7) increased with sheltering in place. Other reports, however, suggest decreases in such non-natural deaths as those by accidents (13) , stranger-on-stranger violence (14) , and medical error (15) . Taken together, these reports raise an important, question --what has been the "net effect" of sheltering in place on non-natural deaths? Answering this question requires an estimate of the association between sheltering in place and the incidence of non-natural deaths. The peer-reviewed literature, however, includes no attempts to estimate that association. We attempt such an estimate using data from two US states. We use time-series methods to compare non-natural deaths in California, the first state to begin and among the last to end sheltering in place in early 2020, with those in another large state, Florida, where sheltering in place began late and ended early. California and Florida responded very differently to the emerging epidemic in early 2020. Large employers, primarily in the technology sector, began telling their California workers to stay at home effective March 8 (16) . Counties in the San Francisco Bay Area issued stay-at-home orders effective March 17 (17) and the Governor issued similar orders for the remainder of the state on March 19 (18) . California began reopening on May 15 (19) . Florida mandated sheltering in place effective April 3 and reopened on May 1 (20, 21) . Data that indirectly measure the behavior of households suggest that the citizens of both states reduced mobility and social contacts when shelter-in-place orders were in effect and increased both when orders were removed (22) . homicide contributed about 6.5% in each state (12) . We computed the weekly odds that a non-natural death in either state occurred in California. We transformed those odds to natural logarithms (i.e., logits) to allow us to express results as percent difference between observed and expected odds during weeks when California alone sheltered in place. We, therefore, express our "dependent variable" in the equations that follow as (Y ct /Y ft ) e in which Y ct and Y ft equal, respectively, the number of non-natural deaths in California and Florida during week t. The weekly odds that a death occurred in California instead of Florida exhibit patterns over time (i.e., autocorrelation) that can lead to an expected or predicted value different from the mean of all weeks. As described below, we identify and model autocorrelation in the logits before shelter in place orders and develop predictions for ensuing weeks. We then ask whether the observed values differed from predicted during periods when shelter-in-place orders were in place in California but not Florida. Our test proceeded through 5 steps consistent with time-series conventions used in epidemiology (24, 25) . First, we used Box-Jenkins methods (26) to identify and model autocorrelation in a 323-week "training period" up to March 8, 2020. The Box-Jenkins approach essentially assumes that values independent of each other and normally distributed passed through an unobserved "filter" that imposed patterns upon them. The method identifies which of a very large family of filters most likely imposed the observed pattern. The methods use well-developed rules to narrow the likely filters to a few models and then applies estimates of "fit" to arrive at the most likely candidate. The model residuals approximate the values that passed through the filter. These "unexpected" values meet the assumptions of traditional tests of association because they are independent of each other (i.e., exhibit no autocorrelation), their expected value equals their mean (i.e., 0), and they exhibit constant variability over time. The general form of a Box Jenkins model for data like ours is as follows. (Y ct /Y ft ) e =c+(1-B q )/(1-B p )a t [1] (Y ct /Y ft ) e is, as described above, the natural log of odds that a non-natural death in California or Florida during week t occurred in California. C is the mean of (Y ct /Y ft ) e through week t. is a moving average parameter.  is an autoregressive parameter. a is the model error term at week t. B is the "backshift operator" or value of a t at week t-q or t-p. Not all time series will exhibit both autoregression and moving averages. Some, those exhibiting both seasonality and the tendency for high or low values to persist into subsequent time periods, can show more than one of either or both. We searched for signals of autocorrelation using methods that detect whether values up to 120 earlier weeks (i.e., "lags) predict observations. Second, we used the training model to forecast values for the next 10 weeks. Third, we created a 333 week "counterfactual series" by joining the 10 forecasts from California during our test period, and from 176 to 452 (mean 340) in Florida. Figure 1 shows the deaths plotted by week. The best fitting Box-Jenkins model, identified and estimated in Step 1, for logits in the 323-week training period was as follows: The forecasts of earlier weeks as in our main test, but from applying autocorrelation in the entire series to observed intra-pandemic values. The approach, though more conservative, has the benefit of anticipating the response of the population to higherthan-expected death counts during the pandemic. Applying this approach, we found autocorrelation essentially the same as in the pre-pandemic data. We also detected, as in our main test, a downward shift the log odds during weeks when California, but not Florida, sheltered in place. The estimated coefficients in the model were as follows. S is the binary shelter in place variable used in our main test. All other notation is the same as in equation 1 above. All the coefficients were at least twice their standard errors. Taking the antilog of -0.132 and subtracting the result from 1 found that the log odds dropped by 12.4% when California, but not Florida, sheltered in place. We also performed a falsification test by repeating our analyses but replacing the binary shelter-in place variable with another that scored the same weeks of the year as "1" but for 2019 rather than 2020. The coefficient for this "correct week, wrong year" variable did not detectably differ from 0 (i.e., -0.052; SE = 0.038). As noted at the outset, we marked the start of sheltering in place in California as Time-series modeling using seven years of weekly non-natural deaths shows that when California ordered sheltering in place but Florida did not, Californians yielded unexpectedly few non-natural deaths. We estimate an approximate 14% reduction below values expected from non-natural deaths in Florida and from historical patterns. The estimated benefit appears larger at the outset of mandated sheltering in place than near its suspension. Our findings have implications for epidemiologic as well as policy research. They imply that to accurately estimate how averted medical care might have raised mortality in the pandemic, epidemiologists must account for the fact that stay at-home orders reduced mortality, which may mask the former association. This circumstance similarly implies that policy analysts attempting to estimate the benefits and costs of sheltering in place need to use prior epidemiologic research with care. The scholarly work intended to estimate deaths accruing to impeded access to routine medical care has included non-natural deaths in the accounting. Using results from research that does not exclude those deaths could lead to an underestimate of deaths and their costs. Advantages of our approach include that Box-Jenkins modeling accounts for autocorrelation including trends, cycles (e.g., seasonality), and the tendency for a series to remain elevated or depressed after high of low values. Using Florida as a comparison population, moreover, allows us to control for events, unrelated to shelter-in-place orders, that influenced non-natural deaths in both California and Florida. Limitations of our approach include that currently available data do not allow us to distinguish among types of non-natural deaths. Nor can we identify non-natural deaths to which COVID-19 directly contributed (e.g. accidents resulting from hypoxia secondary to coronavirus infection), as has been suggested in the literature (27) . Further research should, when CDC publishes more detailed data, test the intuitive hypothesis that some types of these deaths, those by auto crash and medical error, for example, decrease during shelter in place while others, those by suicide and intrafamily violence for instance, may increase. We acknowledge that differences between California and Florida other than sheltering-in-place policies could have influenced our finding. We note, however, that other differences could have induced our results only if they met 2 criteria. First, they appeared (or disappeared), by chance, only in the 2, 3-week periods when California, but not Florida, sheltered in place. Second, they caused either fewer non-natural deaths in California or more non-natural deaths in Florida. We know of no differences other than sheltering in place policies that meet these criteria. We do not claim a full accounting of the costs associated with non-natural deaths in California or Florida. We did not include, for example, the morbidity of non-fatal injuries averted by sheltering in place. CDC data indicate that for every 1 motor vehicle crash fatality, for example, there are 9 non-fatal hospitalizations and 88 individuals treated and released from emergency departments (28) . These facts suggest that the reductions in non-natural fatalities that we measured trace much larger reduction in morbidity and disability. We further note that to the extent Floridians sheltered in place without state requirements to do so, our approach underestimates the impact of the shelter-in-place policy in California. We did not attempt to estimate the association between non-natural deaths and social distancing induced by circumstances other than shelter-in-place orders. Mobility measured by household surveys or cellphone movement (22) , for example, declined whether or not shelter-in-place orders were in effect and, in turn, affected non-natural deaths. Future work should include such indicators of mobility to estimate the separate associations of non-natural death with differing interventions. The association we find will likely vary by time and place depending on the mechanisms that connect sheltering in place with non-natural fatalities. The association of sheltering in place with, for example, physical mobility has reportedly fluctuated over time and varies with the sociodemographic and environmental characteristics of communities (29) . Our findings imply that shelter-in-place orders widely adopted in response to the COVID-19 pandemic likely reduced not only contagious illness but also non-natural mortality. Ignoring averted non-natural deaths when assessing the utility of shelter-inplace policies will, therefore, lead to an underestimate of benefits. Coronavirus: WHO head calls herd immunity approach 'immoral'. 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