Estimation of Total Immunity to SARS-CoV-2 in Texas

Given the underestimate of seroprevalence in the US due to insufficient testing, accurate estimates of population immunity to SARS-CoV-2 or vaccinations do not exist. Although model-based estimates have been proposed, they require inputting unknown parameters such as viral reproduction number, longevity of immune response, and other dynamic factors. In contrast to a model-based approach for estimating population immunity, or simplistic summing of natural- and vaccine- induced immunity, the current study presents a data-driven statistical procedure for estimating the total immunity rate in a region using prospectively collected serological data along with state-level vaccination data. We present a detailed procedure so that efforts can be replicated regionally to inform policy-making decisions relevant to SARS-CoV-2. Specifically, we conducted a prospective longitudinal statewide cohort serological survey with 10,482 participants and more than 14,000 blood samples beginning on September 30, 2020. Along with Department of State Health Services vaccination data, as of July 4, 2021, the estimated percentage of those with naturally occurring antibodies to SARS-CoV-2 in Texas is 35.3% (95% CI = (33.7%, 36.9%) and total estimated immunity is 69.1%. We conclude the seroprevalence of SARS-CoV-2 is 4 times higher than the state-confirmed COVID-19 cases (8.8%). This methodology is integral to pandemic preparedness.

COVID-19; Infectious Diseases; Epidemic; Pandemic; Seroprevalence; Vaccine; Vaccination. 1. Introduction It is increasingly important to estimate the percentage of individuals in the US who may be protected from the novel SARS-CoV-2 virus as a result of having circulating anti-SARS-CoV-2 antibodies. Peo- ple obtain immunity through either natural infection with SARS-CoV-2 or vaccination, and total im- munity is the combination of these two avenues of immunity. Usually, an estimate of total immunity is obtained using mathematical modeling and simulation, which require inputs such as duration of im- munity once infected, viral reproduction rate, population mixing, and additional factors [1, 2, 3, 4, 5]. However, the contributions of these inputs are still not fully known. For example, researchers are unsure 1 . CC-BY-NC-ND 4.0 International licenseIt 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 (which was not certified by peer review) The copyright holder for this preprint this version posted August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 2 deSantis et.al. of the duration of natural and vaccine-induced immunity, and possible T-cell cross-reactivity. Further, continual emergence of SARS-CoV-2 variants threaten progress toward immunity. [e.g.,6, 7, 8] Recent research suggests neutralizing antibodies to SARS-CoV-2 persist for at least 5 months [9,10] or possibly longer [11], and that re-infection risk is low in the several months after initial infection [12]. Additionally, at the time of this publication, there has been great success of mass vaccination’s in lowering viral transmission,e.g., [13] indicate that in Israel where approximately 61% of the population are vaccinated (>80% of adults). This resultant reduction in viral spread has inspired the idea of a path to normality [NYT, 14]. Given the above most current prevailing assumptions that: 1. Reinfection with COVID-19 within a few months is rare [15]; 2. Neutralizing antibodies from natural infections typically last at least 5 months and cross-reactivity of serological tests is rare [16, 17]; and, 3. Vaccination produces a robust and reasonably long-term antibody response, make it possible to estimate regional total immunity as a combination of natural and vaccine-induced immunity [18]. The goal of this report is to demonstrate this estimation process in Texas as of July 4, 2021 us- ing a prospectively designed serological survey. To this end, we first estimate period seroprevalence over 1-week intervals from 14,899 blood specimens collected prospectively from participants through- out Texas. We then compute a census age-adjusted seroprevalence estimate of natural infection and combine it with the Texas Department of State Health Services (DSHS) de-identified population-level vaccination data to obtain an accurate state-level estimate of total immunity. Notably, the approach is not limited to the current pandemic; it is applicable to any infectious disease. 2. Methods 2.1. Participants and Study Design The Texas Coronavirus Antibody REsponse Survey (Texas CARES) initiative has been previously de- scribed [19, 20]. Briefly, Texas CARES is a prospective convenience sample of adult retail/business employees, K-12 and university educators and university students, those attending Health Resources and Services Administration (HRSA)- designated federally qualified health centers (FQHCs), and chil- dren 5-17 years, all of whom agreed to longitudinal monitoring of SARS-CoV-2 antibody status every three months (three time points total) from 10/1/2020-9/30/2021. A consent form and survey ques- tionnaire were administered online at each of the three time points. More details about the study are publicly available on the Texas CARES dashboard [21]. 2.2. Serological Assay and Vaccination Records Antibody status was determined using the Roche Elecsys ® Anti-SARS-CoV-2 (qualitative) assay de- tection of neutralizing antibodies against SARS-CoV-2 nucleocapsid (N) protein, hereafter referred to as “Roche N-test”. The test has a sensitivity (95% confidence interval, CI) of 99.5%(97.0,100.0) and specificity of 99.82%(99.69,99.91) >=14 days after infection. De-identified population level daily vac- cination data (2 doses for mRNA vaccines or 1 dose for Johnson and Johnson vaccine) by age group were obtained from Texas Department of State Health Services (DSHS). All protocols were approved by the UTHealth Committee for the Protection of Human Subjects and were also deemed “public health practice” by the Texas DSHS IRB. . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 3 2.3. Statistical Methods The following components are estimated from the data, (1) immunity from natural infection, (2) im- munity from complete vaccination, and (3) total immunity defined as immunity from either natural infection or vaccination (e.g., “estimated total immunity”). Natural immunity period seroprevalence is calculated at a given time interval of Texas CARES, while vaccine-induced immunity is known (recorded by DSHS). For the current survey, a 1-week interval was deemed appropriate given the par- ticipant accrual rate into Texas CARES, and disease wave fluctuations. Within this interval, we assume serological status from prior infection and vaccine status are not independent events. This assump- tion is very well-supported by the data, which as of July 4th show 18.6% of those with reported prior documented COVID-19 disease are vaccinated, versus 30.7% without prior documented COVID-19. Our data and other research[22, 23] support that natural and vaccine-induced immunity are likely not independent events. 2.3.1. Calculating Total Immunity to SARS-CoV-2 in Texas We describe the methods used to compute the total immunity in Texas over time. Let H denote the total number of census age groups,h = 1,...,H . Assume we have serological and vaccination data for T weeks. Lett index the time window (week), wheret = 1,...,T . Now define: • νht: Vaccination proportion in age group h at week t (provided by state records). Since the vaccination status is cumulative, νh1≤νh2···≤ νhT forh = 1,...,H , and νht is known with certainty. • ηht: Natural immunity proportion in age group h at week t. This is unknown but is estimated cross-sectionally using the Roche N-test from Texas CARES. • wh: Proportion of the Texas population in age grouph. Thus,wh is also known, and∑ hwh = 1. The immunity rate in time window, t. (defined as having received the vaccine or testing positive for antibodies in the time window) in age grouph is ιht =P [natural immunity or vaccine immunity] =P [natural immunity] +P [vaccine immunity & no natural immunity] =P [natural immunity] +P [no natural immunity| vaccine immunity]P [vaccine immunity] =ηht +κhνht (2.1) In (2.1) above, for brevity, we omit the text “in group ageh at weekt”. The definition of κh :=P [no natural immunity in grouph at weekt| vaccine immunity]. This implicitly assumes the probability is equal across all weeks, t = 1,...,T . Also notice that the proportion of the population with both natural and vaccine induced immunity is easily estimated as (1−κh)νht, so a mathematically equivalent expression to (2.1) is ιht =P [natural immunity or vaccine immunity ] =P [natural immunity] +P [vaccine immunity]−P [natural & vaccine immunity] =ηht +νht− (1−κh)νht (2.2) . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint 4 deSantis et.al. which may appear more intuitive: the total immunity rate is equal to the sum of the natural and vaccine induced immunity rates, minus their overlap. The population seroprevalence at weekt is, SPRt = ∑ h whηht (2.3) and the immunity rate (natural or vaccine induced) at weekt in the population is, IRt = ∑ h whιht = ∑ h wh (ηht +κhνht) (2.4) whereιht is given in (2.1). The population proportion with both natural and vaccine-induced immunity is, ∑ h wh(1−κh)νht. In order to estimate SPRt and IRt we must estimate ηht and κh. We show these steps in the following subsubsection. We also note that had we assumed independence between natural and vaccine induced immunity,κh = 1−ηht, as expected. 2.3.2. Estimation of Parameters for calculation of Total Immunity We estimateκh andηht using the Roche N-test results. First, κh is estimated using the information from allT = 26 study weeks since January 1, 2021, as the following sample proportion, ˜κh = # of participants without natural immunity & vaccinated in age grouph at any week # of vaccinated participants in age grouph (2.5) andηht is initially estimated as, ˙ηht = # participants in grouph tested at weekt with natural immunity # participants in grouph tested at weekt . (2.6) Once we have ˙ηi1,..., ˙ηiT (and the denominators in the 2 equations above) we compute the isotonic version (across index t) of ˙ηht, ˜ηht such that that ˜ηh1≤ ˜ηh2≤···≤ ˜ηhT forh = 1,...,H . See Sup- plementary Materials Subsection S.1 for details of this calculation. The isotonic estimate of ηht is appropriate here because it reflects the fact that seroprevalence should not decrease over a short time interval (even though its raw estimate ˙ηht can decrease due to expected sampling error in a small win- dow,t). Once these estimates are obtained, we compute the estimates ofSPRt andIRt, called ˜SPRt and˜IRt, by substituting the values of ˜ηht and ˜κh into equations (2.3) and (2.4). Construction of a 95% confidence interval for ˜SPRt is based on that for a proportion from a stratified design in which the outcome variable is binary [e.g., 24, 25] (details provided in Supplementary Materials S.2). 2.3.3. Algorithm to Estimate the Total Immunity Curve from Jan 1, 2021 to July 4, 2021 Recalling,H is the total number of age groups andT the total number of weeks. The algorithm is: 1. For, h = 1,...,H a) Using the Roche N-test, compute ˜κh in (2.5). b) Obtain the (cumulative) state vaccination rate for week t by age group, denoted νht, from the Texas Dept of State Health Services database. Since they are cumulative,νh1≤νh2≤ ···≤ νhT forh = 1,...,H . . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 5 c) For t = 1,...,T , compute the preliminary estimated N-test positive rate in the study at weekt, ˙ηht in (2.6). Next, compute the isotonic version of ˙ηht, ˜ηht, such that ˜ηh1≤ ˜ηh2≤ ···≤ ˜ηhT 2. Estimate the age-adjusted seroprevalence rate at week t, ˜SPRt = ∑ h wh× ˜ηht and then the total immunity rate at weekt, ˜IRt = ∑ h wh× [˜ηht + ˜κhνht]. 3. Plot t v.s. ˜SPRt andt v.s.˜IRt 3. Results Demographics of the full sample, and adults 18 years and over, respectively are shown in Tables1 and 2. The mean (standard deviation) age of all participants was 45.9 years (16.1) and most participants were in the 50-54 year age group (30.9%). Most were female (69.4%), White (88.9%), and from urban locations (92.0%). Most adults reported having some college education or an advanced or professional degree, and were employed full time. We applied the method with H = 10 age groups, 0-15, 16-17, 18-29, 30-39, 40-49, 50-64, 65- 74, 75-79, 80-84 and 85+ years. The census age-adjusted Texas COVID-19 seroprevalence using the Roche N-protein test over time (i.e., t v.s ˜SPRt) along with the 95% confidence band is shown in Figure 1 . The vertical line on the graph delineates the time of first vaccine availability. The surges in seroprevalence correspond well to the known waves of SARS-CoV-2 in Texas [26]. We note that ˜κh≈ 0.83 in all age groups; thus, the proportion of study participants who reported having had both COVID-19, and being fully vaccinated were roughly 1−κh≈ 17%. This indicates a violation of independence of natural infection and vaccination, which was expected. As these people must not be counted twice in the total immunity estimate, they are subtracted appropriately in each time period (week) per Equation (2.2). The estimated age-adjusted total period immunity in Texas, defined as immunity from either natural infection or full vaccination (solid line) over time (i.e., t v.s˜IRt) is shown in Figure 2. As of July 4, 2021, total immunity is estimated at 69% of the Texas population, with approximately 35.3% (95% CI = (33.7, 36.9) resulting from natural infection. To our knowledge, this is the most robust and accurate non-model based estimate of total immunity to date in the state of Texas. We do not include a confidence interval for total immunity since the proportion vaccinated is a known (fixed) population quantity rather than an estimate, and thus does not lend itself to an estimate of variability. While the seroprevalence is not known or fixed, the large sample of 14,899 blood specimens would result in a very small range for the 95% confidence interval, if one were to be produced for the total immunity line. 4. Discussion Using the methods proposed, the estimated proportion of the Texas population with antibodies against the SARS-CoV-2 virus, either from natural infection or induced by the vaccine, is nearly 70% as of . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint 6 deSantis et.al. July 4, 2021. This means 70% of the population benefit from some degree of protection from rein- fection from SARS-CoV-2 and acquiring COVID-19. There are several challenges to further practical or applied interpretation of these data. First, we do not know the relative degree of protection from antibodies from a natural infection compared to antibodies from the vaccine. The titer of antibodies from a full vaccine regimen is higher than a typical natural infection [27], but the diverse epitopes of a natural infection may offer advantages over antibodies targeting only spike protein. In addition, the SARS-CoV-2 mutates producing new strains that will likely influence the degree of protection of circulating antibodies [28]. Second, there is limited data on how long antibodies to the vaccine and to natural infection last [e.g., 29, 30, 31, 32, 33] Though early findings about the duration of natural and vaccine-generated immunity are promising, it is reasonable to expect the proportion of people with de- tectable antibodies will decline over time. And finally, protection from an infectious agent is complex, and the concept of seroprevalence and protection does not take into account cell-mediated immunity and physical barriers, such as masks. In contrast to model-based approaches, the current research will allow researchers and health depart- ments to calculate regional estimates of total immunity in the least biased manner.

may occur in observational serological surveys; e.g., sample demographics may not be fully representative of the state, which is true for some variables in the current survey. Sampling vari- ability or selection biases may operate within small time windows of a serological survey, and can

in inaccuracies in seroprevalence estimates. It will therefore generally be necessary to smooth estimates using a chosen time window dependent on factors such as the magnitude of the wave of infec- tion and participant accrual rate. Fortunately, we observe that the application of an isotonic restriction to reflect the assumption that seroprevalence should not decrease in a reasonably small time window mostly overcomes the issue of daily or weekly sampling variability. Further, it is necessary to estimate the percentage of people who have both had natural COVID-19 infection and are fully vaccinated in a given time window in order to subtract that proportion from the overall sum. Finally, it is important to age-adjust estimated serological and vaccination rates to the state census so they are commensurate with population demographics. This is especially important since vaccination was rolled out by age group, with older adults first priority in January-March 2021. To our knowledge, this is the first fully data-driven estimation of total immunity to SARS-CoV-2 in the state of Texas, which is the second largest state in the US with a population of 29.2 million. The

proposed and applied here can be applied to any state or geographic area using vaccine counts, and an estimate of seroprevalence. As the pandemic unfolds and new variants are introduced, immunity will require further investigation and re-estimation. Table 1: Texas CARES participants’ demographics. N=10,482 Age (years) Mean (SD) 45.9 (16.1) Missing 0 Age (categorical) 0-15 402 (3.8%) 16-17 124 (1.2%) 18-29 1257 (12.0%) 30-39 1802 (17.2%) 40-49 2331 (22.2%) 50-64 3244 (30.9%) . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 7 65-74 1100 (10.5%) 75-79 170 (1.6%) 80-84 39 (0.4%) 85+ 13 (0.1%) Missing 0 Gender Female 7262 (69.4%) Male 3208 (30.6%) None of these describe me 1 (0.0%) Missing 11 Race American Indian or Alaskan Native 63 (0.6%) Asian 470 (4.7%) Black 382 (3.8%) Hawaiian or Other Pacific Islander 18 (0.2%) Multi-racial 192 (1.9%) White 8974 (88.9%) Missing 383 Ethnicity Hispanic 2711 (26.8%) Non-Hispanic 7409 (73.2%) Missing 362 BMI (categorical) Underweight 126 (1.3%) Normal 3250 (32.6%) Overweight 3131 (31.4%) Obese 3458 (34.7%) Missing 517 Geographic Location Rural 824 (8.0%) Urban 9488 (92.0%) Missing 170 Table 2: Texas CARES participants’ demographics for participants 18 and older. Adults≥ 18 years N=9,956 Education Some high school or less 121 (1.3%) High school graduate/GED 802 (8.4%) Some college, no degree 1505 (15.8%) Two or four year college level degree 3808 (39.9%) Advanced professional or academic degree 3301 (34.6%) Missing 419 . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint 8 deSantis et.al. Employment Status Employed-full time 6326 (67.1%) Employed-part time 902 (9.6%) Not currently employed/Unemployed 1277 (13.5%) Other 920 (9.8%) Missing 531 Employment Industry Accommodation and Food Services 170 (2.4%) Administrative and Support and Waste Management 83 (1.2%) Agriculture, Forestry, Fishing & Hunting 45 (0.6%) Arts, Entertainment and Recreation 106 (1.5%) Central Administrative Office Activity 222 (3.1%) Construction 146 (2.1%) Educational Services 2109 (29.7%) Finance and Insurance 210 (3.0%) Health Care and Social Assistance 2381 (33.6%) Information 157 (2.2%) Management of Companies and Enterprises 98 (1.4%) Manufacturing 139 (2.0%) Mining 11 (0.2%) Other 59 (0.8%) Professional, Scientific and Technical Services 621 (8.8%) Real Estate and Rental and Leasing 126 (1.8%) Retail Trade 197 (2.8%) Transportation and Warehousing 133 (1.9%) Utilities 54 (0.8%) Wholesale Trade 25 (0.4%) Missing 2864 . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 9 Figure 1. Weekly Natural Immunity Texas Cares Roche N-Test. Horizontal axis labels denote the first day of the month. . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint 10 deSantis et.al. Figure 2. Estimated total immunity in Texas (i.e., weekly percentage of fully vaccinated or naturally occurring antibodies). Horizontal axis labels denote the first day of the month. The estimate as of July 4, 2021 is 69.08%. . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 11

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(which was not certified by peer review) The copyright holder for this preprint this version posted August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint Total Immunity to SARS-CoV-2 in Texas 1 Supplementary Material to, “Estimation of Total Immunity to SARS-CoV-2 in Texas” S.1. Order Restricted (Isotonic) Estimation of Probabilities The algorithm below is retrieved from Algorithm 3 in https://core.ac.uk/download/pdf/ 33107977.pdf. The maximum likelihood estimate ofπ = (π1,π 2,...,π H ) under the restriction of π1≤π2≤···≤ πH, is calculated in the following way: Let nh the number of observations in group h, Step 1: Do ˜πh equal to the sample proportion in grouph. Step 2: While notπh≤πh+1, forh = 1,...,H − 1, do Forh = 1,...,H If ˜πh̸≤ ˜πh+1 do ˜πh = nh nh +nh+1 ˜πh + nh+1 nh +nh+1 ˜πh+1, and ˜πh+1 = ˜πh S.2. Confidence Interval for the Seroprevalence The construction of the confidence interval for ˜SPRt is based on the confidence interval for a propor- tion under a stratified sampling design [e.g., 24, 25]. Recall, the weight wh =Nh/N andNh denote the proportion of and the number of individuals in the population in the age grouph, respectively, and N the population total. An estimate of the sampling variance of the sample proportion ˙ηht is ˜Var( ˙ηht) = [Nh−nht Nh− 1 ]˙ηht(1− ˙ηht) nht ≈ ˙ηht(1− ˙ηht) nht wherenht is the number of participants in age group h (at week t). The approximation in the above equation is valid since Nh>>nht. We base the confidence interval on this equation plugging in ˜ηht instead of ˙ηht ˜Var(˜ηht)≈ ˜ηht(1− ˜ηht) nht Then the sampling variance of ˜SPRt is estimated with ˜Var(˜SPRt) = ∑ h w2 h˜Var(˜ηht)≈ ∑ h w2 h ˜ηht(1− ˜ηht) nht The asymptotic 1−α confidence interval forSPRt is then ˜SPRt±z1−α/2 √ ˜Var(˜SPRt) wherezα is the percentileα of the standard normal distribution, so when1−α = 0.95,z1−α/2 = 1.96. . CC-BY-NC-ND 4.0 International licenseIt 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 August 7, 2021. ; https://doi.org/10.1101/2021.08.05.21261610doi: medRxiv preprint