key: cord-0304105-dfq3pqc5
authors: Harris, J. E.
title: Estimated Fraction of Incidental COVID Hospitalizations in a Cohort of 250 High-Volume Hospitals Located in 164 Counties
date: 2022-01-24
journal: nan
DOI: 10.1101/2022.01.22.22269700
sha: f083e55927e238ccff276c8d99ec64a1cc78cbdd
doc_id: 304105
cord_uid: dfq3pqc5

Scattered reports have suggested that as many as one-half of all hospital inpatients identified as COVID-positive are incidental cases who were admitted primarily for reasons other than their viral infections. To date, however, there are no systemic studies of a representative panel of hospitals based on pre-established criteria for determining whether an individual patient was in fact admitted as a result of the disease. To fill this gap, we developed a formula to estimate the fraction of incidental COVID hospitalizations that relies upon measurable, population-based parameters. We applied this approach to a longitudinal panel of 164 counties throughout the United States, covering on a 4-week interval ending in the first week of January 2022. Within this panel, we estimated that COVID incidence has been rising exponentially at a rate of 9.34% per day (95% CI, 8.93-9.87). Assuming that only one-quarter of all recent Omicron infections have been reported by public authorities, we further estimated the aggregate prevalence of active SARS-CoV-2 infection during the first week of January to be 4.89%. During the same week, among 250 high-COVID-volume hospitals within our 164-county panel, an estimated 1 in 4 inpatients was COVID-positive. Among such COVID-positive hospitalized patients, 15.2% were estimated to be incidental infections. Across individual counties, the median fraction of incidental COVID hospitalizations was 13.7%, with an interquartile range of 9.5 to 18.4%. Incidental COVID infections appear to be a nontrivial fraction of all COVID-positive hospitalized patients. In the aggregate, however, the burden of patients admitted for complications of their viral infections appears to be far greater.

Scattered, anecdotal reports have suggested that up to one-half of all hospital inpatients identified as COVID-positive are incidental cases who have been admitted primarily for reasons other than their viral infections [1] [2] [3] . To date, however, there have been no broad-based, systemic studies of a representative panel of hospitals to determine what fraction of COVIDpositive hospitalizations are indeed incidental. The ideal design would be to prospectively follow a cohort of individuals, evaluating each hospitalization according to pre-established criteria for determining whether or not each patient was in fact admitted as a result of the disease. Such formal criteria would not leave it to arbitrary, subjective judgment how to assess, say, a young adult with COVID-associated headache, fever, rigors, body aches, dizziness, and severe fatigue, who suffered acute brain injury while driving under the influence of Omicron.

To fill this gap, we developed a formula to estimate the fraction of incidental COVID hospitalizations that relies upon objectively measurable, population-based parameters. We applied this approach to a longitudinal panel of 164 counties throughout the United States, which contained 250 high-COVID-volume hospitals. Our analysis covered the 4-week interval ending in the first week of January 2022, during which time the Omicron variant of SARS-CoV-2 was far and away the dominant strain [4] . While this exercise requires us to make some difficult-toverify assumptions and involves a significant attendant range of uncertainty, it still educates us as to whether there is any reasonable chance that the incidental COVID fraction is as high as a handful of sources have reported.

We develop a model that permits us to formally define the fraction of incidental COVID hospitalizations and to express this fraction as a function of other, observable quantities.

To that end, consider a closed population at a particular point in time. We will refer to any individual within this population who has a detectable SARS-CoV-2 infection at that time as a COVID case. This definition does not require that the individual has in fact tested positive or even has symptoms of COVID.

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The copyright holder for this preprint this version posted January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint Let (where 1 > > 0) denote the proportion of all COVID cases that are hospitalized because of their illness. For shorthand, will refer to these as the severe cases. We refer to all other COVID cases, whether they are hospitalized or not, as non-severe.

While the severe cases are, by definition, hospitalized because of their COVID illness, some of the remaining non-severe cases will also be hospitalized for non-COVID reasons. We refer to the latter group as incidental COVID hospitalizations. Let denote the proportion of non-severe cases that is hospitalized, where 1 > > 0. Then, by Bayes' rule, the proportion of all COVID hospitalizations that are incidental is:

We refer to as the fraction of incidental COVID hospitalizations. We see that is increasing in and decreasing in .

The problem with the formulation of equation (1) is that it doesn't render as a function of readily observable quantities. If we could longitudinally follow a closed cohort of individuals as they contracted COVID and then observe who got hospitalized because of their illness, we would have . To get as well, we would also need to track who got hospitalized for other reasons. In the absence of such a comprehensive longitudinal study, it is hardly obvious how to proceed.

One way to proceed is to explore the consequences of a key simplifying assumption, namely, that those individuals without COVID have the same probability of hospitalization as those with non-severe COVID. We examine the validity of this assumption later in the Discussion.

Let denote the proportion of individuals in the entire population who are COVID cases, where 1 > > 0. We refer to as the prevalence of COVID. The proportion without COVID is thus 1 − . Under our key simplifying assumption, the proportion of individuals in the population who do not have COVID and are hospitalized is thus (1 − ). We can also express the proportion who have non-severe COVID and are incidentally hospitalized as (1 − ) ,

while the proportion who have severe COVID and are hospitalized as .

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The copyright holder for this preprint this version posted January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint Now focus solely on those individuals who are hospitalized. We test every hospitalized patient to determine who is COVID-positive and who is COVID-negative. Let denote the fraction of all hospitalized individuals who are COVID-positive. This quantity differs from the prevalence , which represents the fraction of all individuals in the entire population who are COVID-positive. Utilizing the foregoing expressions, we have =

. We can write the odds that a hospitalized patient is COVID-positive as

, which can be rewritten as .

Utilizing the definition of in equation (1) and rearranging terms gives:

(2).

In equation (2), is now a function of the prevalence of COVID in the population, the fraction of all hospitalized patients who are COVID-positive, and the proportion of COVID-positive individuals requiring hospitalization because of their disease. If we can obtain reasonably accurate estimates of these three parameters, we can in turn estimate . Table 1 below summarizes these points. 

We focus now on the estimation of the prevalence of COVID, deferring for now the estimation of the remaining quantities and . To estimate the prevalence , we would ordinarily rely upon the classic formula in epidemiology, that is, prevalence equals the incidence of SARS-CoV-2 infection per unit time multiplied by the average duration of infection. The . CC-BY-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 January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint difficulty with this formula is that it applies only to a population with a stable incidence rate, and that is certainly not the case here [5] .

Let ℎ( ) denote the incidence rate of SARS-CoV-2 infection at time ≥ 0. We assume that incidence is growing exponentially, that is, ℎ( ) = ℎ + ,-, where ℎ + , > 0. Let the duration . Inserting the assumed functional forms for ℎ and , we get:

For sufficiently large , the second term inside the parentheses gets small, so that we have:

.

Note that when the incidence ℎ is stable (that is, = 0), this formula collapses to the classic result. To estimate the prevalence during an epidemic with exponentially growing incidence, we therefore need data on the incidence ℎ, the growth rate of infection and the mean duration 1⁄ of infection.

Determination of the actual incidence ℎ of COVID is no trivial task, as it is widely acknowledged that cases have been and continue to be significantly underreported [6] [7] [8] [9] . To address this difficulty, we follow the usual approach of incorporating an under-ascertainment factor into our analysis [10] . Let ( ) denote the reported incidence of COVID, and let ( ) > 0 denote the fraction of COVID cases that are reported at time . Then we have:

Accordingly, to estimate , we need data on the parameters , , , ℎ, and , as indicated in Table 2 . For clarity, we have dropped the time argument from the functions ℎ, , and listed in the table.

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Definition Reported COVID incidence Exponential rate of increase of COVID incidence Fraction of COVID cases reported ℎ Actual COVID incidence, ℎ = . CC-BY-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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For each hospital and each week, we calculated the number of COVID-positive patients as the sum of variables (2) and (3), while variable (1) gives the total number of hospital patients.

For each week, summing over all 250 hospitals, we computed cohort-wide numbers of COVIDpositive inpatients and total inpatients, from which we then computed , the fraction of all inpatients who were COVID-positive. While we display the entire timeline of the fraction in Estimating the Exponential Rate of Increase of COVID Incidence, , and Reported COVID Incidence, -We relied upon the county-specific data derived from the Community Profile Reports

[12] to estimate the exponential rate of increase of COVID incidence, . To that end, we ran the following log-linear fixed-effects regression model on our panel of 4 serial weekly observations (indexed = 1,…4) on 164 counties (indexed = 1,…,164):

.

In equation (5), the observations 3-corresponded to the data variable Cases -last 7 days, while the observationsrepresented the ending date of each of the four weeks. The parameter was an overall constant term, the parameters 3 were county-specific fixed effects, and the terms 3- were spherical errors. The parameter was estimated by ordinary least squares.

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The copyright holder for this preprint this version posted January 24, 2022. To test whether the data adequately fit an exponential growth model, we plotted the reported incidencefor all 164 counties combined againstto check for serial correlation of residuals. The reported incidence was computed as -= ∑ 3 3-

Cases per 100k -last 7 days and 3 denotes Population. We show a plot ofversusin Fig. 3 below. While we used a continuous-time model to develop our formula for prevalence in equation (3), here we use the discrete time notation to refer to computations made from the panel of 164 observations in each of 4 successive weeks.

Estimating the Fraction of COVID Cases Reported, -, and Actual COVID Incidence, ℎ -For our estimate of the fraction of COVID cases reported, -, we relied upon recent estimates issued by the Institute for Health Metrics and Evaluation (IHME) [13] . [13] .) By relying on reported COVID incidencerather than actual COVID incidence ℎto estimate above, we effectively assumedto be constant during the 4 weeks covered by our panel, and we do so here as well.

Thus, for each week = 1,…,4, we compute actual incidence as

A recent technical report from the UK Health Security Agency [14] noted that 3,019

Omicron cases were hospitalized among 528,176 Omicron cases total, which gives ≈ 0.006.

While hospitalization practices may differ in the UK's National Health Service, this source has the advantage that the denominator closely approximates all Omicron infections, and not just symptomatic cases.

We estimated the fraction of incidental hospitalizations not only for all 164 counties combined, but also for each county individually. We focused on the first week in January, that is, 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 January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint 9 dropping the subscript ). Assuming the parameters , , , and to be constant across counties, we then computed county-specific values for each 3 . [11] . For the most recent week ending January 7, 2022, the fraction of inpatients who were COVID-positive was 0.2517, which we took as the value of the parameter . The corresponding odds ratio was " #$" = 0.336.

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The copyright holder for this preprint this version posted January 24, 2022. For the four most recent weeks, Fig. 3 plots the population-weighted mean values of confirmed COVID incidence among all 164 counties combined. These values represent our estimates of reported incidence -. The fixed-effect log linear regression described on our panel of 164 counties over 4 weeks, described in equation (5), gave an estimate of = 0.0934 per day . CC-BY-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 January 24, 2022. 

For the most recent week ending January 9, 2022, the mean weekly confirmed COVID incidence for the 164 counties in our panel was 1,663 per 100,000 population (Fig. 3) , which comes to a reported incidence of = 237.6 per 100,000 per day. Given our estimate of the fraction of cases reported at = 0.25, we obtain an estimate of actual incidence of ℎ = ⁄ = 950.4 per 100,000 per day.

In a recent review of the literature, the U.S. Centers for Disease Control and Prevention (CDC) has estimated that the mean duration of infectiousness for Omicron is 5-6 days [15] . That Table 3 . 

Our overall estimate of = 15.2 percent is an average that does not capture its variability across the 164 counties under study. When we applied the formula of equation (2) individually to each county, once again restricting the computations to the first week of January 2022, the median value of was 13.7 percent, with an interquartile range of 9.5 to 18.4 percent.

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The copyright holder for this preprint this version posted January 24, 2022. Dade has the highest estimated prevalence of = 11.9 percent, the estimated fraction of incidental COVID hospitalizations is 20.8 percent. As equation (2) shows, when the overall prevalence of COVID in the county is higher, the fraction of incidental COVID hospitalizations tends to be higher. But as hospitals in the county fill up with COVID patients, thus pushing higher, the fraction of incidental COVID hospitalizations tends to go lower. . CC-BY-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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The principal source of uncertainty in our estimate of incidental COVID hospitalization is the fraction of reported COVID cases. During the Omicron wave, as noted above, this fraction has declined to 25 percent of actual cases [13] , in great part as a result of a surge in asymptomatic and mildly symptomatic infections, as well as an increasing proportion of rapid test results not tabulated by public health authorities. Our formula for the prevalence of 

In the derivation of our population-based formula, we made the key assumption that those individuals without COVID have the same probability of hospitalization as those with nonsevere COVID. Strict adherence to the notion of causality would seem to require this assumption. If a concurrent COVID infection increases the probability of hospitalization, then the infection has a causal role in the hospitalization and is thus not incidental. If a hospitalization is purely incidental, then the probability of hospitalization would be the same with or without COVID.

Consider a patient the hypertensive heart disease who, as a result of high fevers and dehydration from an Omicron infection, develops atrial fibrillation, a cardiac arrhythmia. He needs to be hospitalized to get his heart rate down and convert his heart rhythm back to normal.

His would not be an incidental COVID hospitalization. Consider instead a patient with a history of extreme myopia since childhood who suffers a spontaneous retinal detachment and is hospitalized for eye surgery. During her admission workup, she is found to be COVID-positive.

Since the infection did not apparently affect her probability of hospitalization, hers would be an incidental COVID hospitalization. (This is not to deny that the COVID epidemic has delayed the . CC-BY-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 January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint time when patients have sought treatment and thus affected the severity of vision loss upon initial presentation [16] .)

The problem with the foregoing logic is that individuals in the two groups -those without COVID and those with non-severe COVID -are different people. Thus, one individual with a white-collar occupation may be able to work remotely and does not contract COVID.

Another individual with a blue-collar occupation cannot work remotely and comes down with a non-severe infection at work. The latter individual may also have a higher risk of hospitalization from an onsite workplace accident.

Generalizing our formula for , we suppose that those without a COVID infection have a hospitalization probability ′ that is not necessarily equal to the hospitalization probability of those with non-severe COVID. Then the fraction of incidental COVID hospitalizations becomes , where = !4 ! is the relative risk of hospitalization between the two groups and is as already defined in equation (2). This does not mean that our strong assumption that = 1 necessarily understates . In the foregoing example comparing white-collar and blue-collar workers, < 1 and thus would be overstated. More generally, when those individuals who take precautions to reduce the risk of infection, such as getting vaccinated [17] , also tend to adopt other preventive measures to reduce the risk of hospitalization generally, such as not smoking, our strong assumption that = 1 will tend to overstate .

Relying on data reported by the UK Health Security Agency [14] , we took , the probability that an infected individual would have a severe case requiring hospitalization, as 0.006. It is worth inquiring whether there are any U.S.-based sources that might provide a more reliable estimate. The difficulty is that computation of needs to be based upon a population denominator that includes all cases of COVID, even asymptomatic and unreported cases.

A study of symptomatic patients infected with the Omicron variant in the Houston Methodist hospital system [18] revealed that out of 2,232 symptomatic patients, 313 were admitted to the hospital. This source, it would seem, yields an estimate of = 0.14, which is an order of magnitude greater than the estimate derived from the UK data. The problem with relying upon this alternative data source is that the denominator reflects symptomatic patients primarily presenting to the emergency department, rather than all COVID cases. In fact, the percentage . CC-BY-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 January 24, 2022. Fig. A2 .

While our aggregate measure of the incidental COVID fraction for all 164 counties is on the order of 15 percent, Fig. 4 shows significant variability across individual counties. Some of this variability is no doubt due to sampling errors in the measurement of the parameters 3 , the proportions of inpatients who are COVID-positive, especially in counties with only one highvolume hospital. Our assumption that the fraction of COVID cases reported was uniform across counties may have introduced errors in the county-specific incidence estimates ℎ 3 = 3 ⁄ .

Likewise, our assumption that the exponential rate of increase of COVID incidence was uniform across counties may have introduced errors in the county-specific prevalence estimates

Still, some of the variability of the variability may be due to systemic differences between hospitals in their range of services and patient populations. These hospitals may be genuine outliers. For example, a hospital may have a large, specialized transplant service with many immunosuppressed patients who are persistently COVID-positive.

Assuming that only one-quarter (that is, = 0.25) of all recent Omicron infections have been reported by public authorities, we estimated the aggregate prevalence of active SARS-CoV-2 infection during the first week of January to be 4.89% (that is, = 0.0489). During the same week, among 250 high-COVID-volume hospitals within our 164-county panel, an estimated 1 in 4 inpatients were found to be COVID-positive (more precisely, = 0.2517). Among all COVIDpositive hospitalized patients in all 164 counties combined, an estimated 15.2% were incidental infections (that is, = 0.152). Across individual counties, the median fraction of incidental COVID hospitalizations was 13.7%, with an interquartile range of 9.5 to 18.4%.

Scattered, anecdotal reports have suggested that as many as half of COVID-positive hospital inpatients are merely incidental cases [1] [2] [3] . In the absence of a sufficiently large, longitudinal study of a representative sample of hospitalized patients, and without uniformly . CC-BY-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 January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint established clinical criteria for determining when a COVID infection is incidental, it is hardly obvious how such fragmentary evidence is supposed to be interpreted.

In this study, we have inquired whether such estimates of the fraction of incidental COVID infections are consistent with available data on COVID cases in hospitals and in the population generally. Our population-based estimates suggest that incidental COVID infections are indeed a nontrivial fraction of all COVID-positive hospitalized patients. In the aggregate, however, the burden of patients admitted for complications of their viral infections appears to be far greater.

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The copyright holder for this preprint this version posted January 24, 2022. ; https://doi.org/10.1101/2022.01.22.22269700 doi: medRxiv preprint Technical Notes to Fig. A2 .

The data source was U.S. Department of Health and Human Services [11] , as described under Data: Cohort of 250 High-Volume Hospitals in the section on Methods and Data in the main text.

Emergency department visits to each of the cohort hospitals was derived from the variable previous_day_covid_ED_visits_7_day_sum, defined as "Sum of total number of ED visits who were seen on the previous calendar day who had a visit related to COVID-19 (meets suspected or confirmed definition or presents for COVID diagnostic testing -do not count patients who present for pre-procedure screening) reported in 7-day period."

Hospital admissions were determined as the sum of two variables: a) previous_day_admission_adult_covid_confirmed_7_day_sum, defined as "Sum of number of patients who were admitted to an adult inpatient bed on the previous calendar day who had confirmed COVID-19 at the time of admission reported in the 7-day period." b) previous_day_admission_pediatric_covid_confirmed_7_day_sum, defined as "Sum of number of pediatric patients who were admitted to an inpatient bed, including NICU, PICU, newborn, and nursery, on the previous calendar day who had confirmed COVID-19 at the time of admission."

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