{"paper_id":"475d1b18-ee75-41d8-81ea-0f21dd234ffd","body_text":"Bias and negative values of COVID-19 vaccine effectiveness estimates from a test-negative design without controlling for prior SARS-CoV-2 infection | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Bias and negative values of COVID-19 vaccine effectiveness estimates from a test-negative design without controlling for prior SARS-CoV-2 infection Ryan Wiegand, Bruce Fireman, Morgan Najdowski, Mark Tenforde, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4802667/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Test-negative designs (TNDs) are used to assess vaccine effectiveness (VE). Protection from infection-induced immunity may confound the association between case and vaccination status, but collecting reliable infection history can be challenging. If vaccinated individuals have less infection-induced protection than unvaccinated individuals, failure to account for infection history could underestimate VE, though the bias is not well understood. We simulated individual-level SARS-CoV-2 infection and COVID-19 vaccination histories. VE against symptomatic infection and VE against severe disease estimates unadjusted for infection history underestimated VE compared to estimates adjusted for infection history, and unadjusted estimates were more likely to be below 0%. TNDs assessing VE immediately following vaccine rollout introduced the largest bias and potential for negative VE against symptomatic infection. Despite the potential for bias, VE estimates from TNDs without prior infection information are useful because underestimation is rarely more than 8 percentage points. Health sciences/Medical research/Epidemiology Health sciences/Diseases/Infectious diseases/Viral infection vaccine effectiveness test-negative design prior infection Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Test-negative designs (TNDs) are an indispensable tool for assessing vaccine effectiveness (VE). TNDs were designed to assess VE against symptomatic infection of seasonal influenza, 1,2 but have been used to estimate VE against SARS-CoV-2 symptomatic infection, 3 emergency department or urgent care encounters, 4 hospitalizations, 5 invasive mechanical ventilation, 6 and death 7 and to support policy decisions. 8 A TND can be performed rapidly, at lower cost than other studies, and with reduced confounding from health care seeking behavior compared to other observational study designs. 1,2 The efficiency and feasibility of a TND comes with many challenges, 9,10 especially regarding the assumptions of how cases and controls are ascertained; controls should be representative of the source population that yielded the cases. 11 Protection from infection-induced immunity can present challenges when estimating VE from a TND. Participants' history of prior SARS-CoV-2 infection has often not been incorporated into VE studies. 11 For COVID-19 studies, infection history data is not collected due to self-testing, asymptomatic infection, and mild infections not requiring medical attention. 12 Bias can arise if prior infection status is misclassified 13 or not accounted for in models 14 and could result in a VE estimate below zero. 15 Serologic testing has been recommended to correct this bias 14 but possesses many challenges, including decreasing sensitivity due to antibody decay, 16 potential inability to detect past infection in people with a current infection, increased cost, and decreased power 17 since over 87% of the US population had detectable SARS-CoV-2 antibodies from infection in October-December of 2023. 18 Additionally, many people have had multiple prior SARS-CoV-2 infections, and serologic testing does not provide information on number of total infections nor time since or variant of last infection, which are important for understanding the potential impact of past infection on VE. Considering these challenges, we endeavored to assess the bias in VE against symptomatic SARS-CoV-2 infection and severe disease from a TND when prior infection is unaccounted for in analyses. Microsimulations were created based on the COVID-19 pandemic, where each person’s vaccination and infection history was generated up to May 2023, followed by a hypothetical vaccination campaign and TND to estimate VE against symptomatic infection or severe disease. Multiple parameters relating to vaccine and infection protection waning and the TND study design were varied. Methods Simulation methods A thorough summary of the simulation methods and a full list of microsimulation parameter sets and results are included in the supplementary materials. We created populations of 100,000 people aged 18–49 years without protection against SARS-CoV-2 infection at the beginning of the COVID-19 pandemic (the Morbidity and Mortality Weekly Report [MMWR] week of January 19, 2020). 19 Each week until the MMWR week of May 7, 2023, we updated each person’s vaccine- and infection-induced protection against SARS-CoV-2 infection based on their most recent infection and vaccine dose since people could accumulate multiple infections and doses over time (Fig. 1 ). Weekly infection probabilities were derived from aggregated case count data from 60 U.S. jurisdictions 19 divided by 2020 population estimates 20 (Figure S1 ). These proportions were increased by a multiplier (Figure S2 ) to account for underreporting of infections 21 and to reach approximately 95%-98% of the population acquiring a prior infection by the end of the study period (Figure S3). Individual, weekly probabilities of vaccination receipt utilized U.S. vaccination data, the number of prior doses and prior infection status. Data on vaccination distributions by vaccination dosage and week for U.S. people aged 18–49 years 22 (Figure S4) were fit to probability distributions (Figure S5). For naïve people, we set the probability of obtaining two vaccination doses at 0.70, the probability of a third dose conditional on having two doses at 0.30, and the probability of a fourth dose conditional on having a third dose at 0.10. 22 People with a prior SARS-CoV-2 infection have been less likely to initiate or subsequently receive an additional vaccination dose. 23–28 We assumed people with a prior infection were less likely to receive an additional dose with an odds ratio of 0.525. 23–28 A person’s protection was based on the most recent week of vaccination and infection. Waning curves were based on trajectories in published literature. 29–34 A week after vaccination we assumed 90% vaccine-induced protection against infection (VP) prior to Omicron predominance and 70% protection thereafter. VP waned linearly to zero ( 1 ) at 48 weeks post-vaccination prior to Omicron predominance and 24 weeks thereafter or ( 2 ) at 24 weeks post-vaccination prior to Omicron predominance and 12 weeks thereafter (Figure S6) with variability by person (Figure S7). A week after infection, infection-induced protection (IP) had 90% protection against infection that waned to zero at 96 or 72 weeks (Figure S8) again with variability by person (Figure S9). Hybrid immunity or protection (HP) definitions were taken from meta-analyses of protective effectiveness: 33,35 ( 1 ) the greater of VP or IP was boosted by 30% of the other (Figure S10); or ( 2 ) VP was boosted by 30% of IP or IP was boosted by 10% of VP, whichever was greater (Figure S11). Both HP definitions were truncated at 99%. In these simulations, we considered 8 different protection calculations since we simulated each combination of the two VP, two IP, and two HP definitions. Infections were generated from a person’s weekly protection with the function $$\\:\\text{P}\\text{r}\\left({I}_{j,k}\\right)=\\text{P}\\text{r}\\left({c}_{k}\\right)\\text{*}\\left(1-{\\psi\\:}_{j,k-1}\\right),$$ where the probability of infection for each person ( \\(\\:j\\) ) and week ( \\(\\:k\\) ), \\(\\:\\text{P}\\text{r}\\left({I}_{j,k}\\right)\\) , depended on \\(\\:\\text{P}\\text{r}\\left({c}_{k}\\right)\\) , the case probability in week \\(\\:k\\) and person \\(\\:j\\) ’s protection calculated from the previous week ( \\(\\:{\\psi\\:}_{j,k-1}\\) ). An infection for person \\(\\:j\\) in week \\(\\:k\\) was generated from a Bernoulli distribution with probability \\(\\:\\text{P}\\text{r}\\left({I}_{j,k}\\right)\\) . A total of 200 populations were generated for each of the 8 protection definition combinations. An example of protection trajectories is included in the supplementary materials (Figure S12). The analytic period consisted of a hypothetical 32-week period beginning immediately after the historical period. Infections, vaccination doses, and protection were generated similarly to the historical period. Parameters were the 8 protection definition combinations, case distribution, vaccination rollout timing, total vaccination coverage, TND timing, and type of outcome (infection or severe disease). Four infection distributions were utilized during the analytic period (Figure S13): weekly 2%; weekly 4%; weekly 2% increasing to a peak of 4% at weeks 16 and 17 before returning to 2%; and weekly 2% increasing to a peak of 6% at weeks 16 and 17 before returning to 2%. The vaccination rollout happened in weeks 1–12 (before the case peak), weeks 11–22 (during the case peak), or weeks 21–32 (after the case peak) and followed a lognormal distribution with a mean of 1.5 and a standard deviation of 0.5 (Figure S14). Other weeks had a vaccination probability of 0.005. Total vaccination coverage in the analytic period was 10% based on fourth dose vaccination coverage 22 or 25% (Figure S15). The TND for symptomatic infections was implemented in weeks 1–12, weeks 11–22, or weeks 21–32. Since we implemented all possible combinations of vaccination rollout and TND timing, some scenarios involve assessing VE via the TND before the vaccination rollout. This is the equivalent of assessing VE long after vaccination has been given. All 32 weeks were used for the TND for severe disease. COVID-19 symptoms were expected in 80% of infected people (Figure S16) and were present only in the week of infection. An uninfected person in week \\(\\:k\\) was expected to have COVID-like symptoms with a probability of 0.20 divided by the number of weeks in the TND (Figure S17). For estimating VE against symptomatic infection, all symptomatic people were included in the TND. Diagnostic testing was assumed to have perfect specificity, but sensitivity was 90% during the week of infection and declined thereafter 36 (Table S1 ). For estimating VE against severe disease, VP was 90% the week after vaccination and waned to zero after 48 months. 31,32,34,37 IP against severe disease started at 95% protection the week after infection and waned to zero after 96 months 33 (Figure S18). For people with a SARS-CoV-2 infection, the probability of severe disease was $$\\:\\text{P}\\text{r}\\left({S}_{j,k}|{I}_{j,k}=1\\right)=\\frac{\\left(1-{{\\psi\\:}^{s}}_{j,k-1}\\right)}{\\left(1-{\\psi\\:}_{j,k-1}\\right)},$$ where \\(\\:{S}_{j,k}\\) is a severe disease event for person \\(\\:j\\) in week \\(\\:k\\) , and \\(\\:{{\\psi\\:}^{s}}_{j,k-1}\\) is the protection against severe disease for person \\(\\:j\\) in week \\(\\:k\\) . All people with severe disease were included in the TND with perfect detection. A total of 1000 simulations were run for each parameter set. Each of the 200 populations was utilized five times in each parameter set. Statistical methods Exposures analyzed were vaccination at any time during the analytic period, vaccination in the previous 2 months, vaccination in the previous 3 months, vaccination in the previous 4 months, vaccination in the previous 5 months, vaccination in the previous 6 months, the number of doses (unvaccinated as the reference group, 2-dose, 3-dose, 4-dose, or 5-dose), and the time since vaccination (unvaccinated as the reference group, 0–2 months, 3–4 months, 5–11 months, and 12 or more months). Two logistic regression models were fit to each exposure definition. The first model included only the exposure variable (henceforth, the unadjusted model), whereas the second model added categorical time since the last infection (categories were monthly from 1 to 11 months and 12 or more months) and the number of prior infections as a continuous variable (the adjusted model). Odds ratios (OR) from logistic regressions were converted to VE in percentage points by the formula \\(\\:\\text{VE}=\\left(1-\\text{OR}\\right)*100\\) . Our primary measurement is the difference between the VE estimate from the unadjusted model and the VE estimate from the adjusted model, which we refer to as bias. Bias is defined not in the traditional sense as the deviation from truth, but as the percentage point difference in VE from the unadjusted model and VE from the adjusted model. Bias less than zero indicated VE was underestimated without accounting for prior infection. A small percentage of simulations resulted in small sample sizes and unstable estimates. Details on bias definition and handling of unstable estimates are in the supplementary methods. Results were aggregated by parameter set and exposure and plotted by exposure with ridgeline plots (Figure S20). Simple, random effects meta regression was used to estimate the expected VE and bias and, for infection outcomes, the percentage of simulations with a negative VE estimate. Separate meta regressions were run for the unadjusted and adjusted VE estimates. Multivariable meta regression models were run with simulation parameters to determine the mean VE, bias, and negative VE associated with each parameter level and the 95% confidence intervals. The overall mean and 95% confidence interval from simple meta regressions are used in Figs. 2 and 3 and values from multivariable meta regressions in Figs. 4 and 5 including the overall mean as a dashed line and the 95% CI as a shaded background. All simulations were performed in R version 4.0.4 and analyses in R version 4.2.4. Results Results from all simulated parameter sets and aggregated estimates are included as a supplemental file (Supplemental Excel File). VE against symptomatic infection Per simulated population, the median protection against symptomatic infection at the end of the historical period ranged from 0.26 to 0.51 and, on aggregate, the distribution of median protection against symptomatic infection was lower when infection protection completely waned by 72 weeks compared to 96 weeks (Table S2 ). The distribution of median protection against symptomatic infection by similar across the number of vaccinations (Table S3) but increased with increasing number of infections (Table S4). VE against symptomatic infection (Fig. 2 , left column) in unadjusted models was highest for people 1–2 months since vaccination (VE = 46.3%; CI: 45.6, 47.0) and decreased with more months since vaccination, reaching the lowest at 5–11 or more months (VE =-1.6%; CI: -1.9, -1.3). VE against symptomatic infection was also lower the more months included in the recent vaccination exposure, the longer time since vaccination, and the fewer number of total vaccination doses. Distributions of estimated VE against symptomatic infection tended to be wide and cover a wide range of VE values, except for exposures with VE against symptomatic infection estimates close to zero which had narrow, unimodal distributions (Figure S19). Bias of VE against symptomatic infection in unadjusted analyses was at most 5.5 percentage points (pp) for each exposure definition (Fig. 3 , left column). For recent vaccination definitions, bias was smallest for recent vaccination in the last 2 months (Bias=-0.9 pp; CI: -0.9, -0.8) and largest for vaccination during the last 6 months (Bias=-2.9 pp; CI: -3.0, -2.8). For vaccination 1–2 months prior, bias was − 1.5 pp (CI: -1.6, -1.4). This increased to -4.8 pp (CI: -5.0, -4.7) at 3–4 months prior, decreased to -4.4 pp (CI: -4.5, -4.2) for those people 5–11 months since vaccination and decreased further for 12 or more months since vaccination (-0.9 pp; CI: -1.0, -0.9). Bias increased for each additional vaccination dose (2-dose=-0.8 pp; CI: -0.9, -0.8; 3-dose=-1.5; CI: -1.6, -1.5; 4-dose=-3.3 pp; CI: -3.4, -3.1; 5-dose=-5.2 pp, CI: -5.4, -5.0). For the exposure of vaccination in the previous 3 months (Fig. 4 ), the overall mean bias was − 1.4 pp (CI: -1.5, -1.3). Bias was higher when hybrid protection was defined as the greater source of protection boosted by 30% (Bias=-1.7 pp; CI: -1.8, -1.6) and lower when the greater of VP or boosted by 30% of IP or IP boosted by 10% of VP (Bias=-1.1 pp; CI: -1.2, -1.0). The timing of the vaccination rollout and TND also impacted bias. For people vaccinated in the previous 3 months, the largest bias occurred when the vaccination rollout happened immediately before the TND (vaccination rollout in weeks 1–12 and TND in weeks 11–12: Bias=-1.9 pp; CI: -2.1, -1.7; vaccination rollout in weeks 11–22 and TND in weeks 21–32: Bias=-2.2 pp; CI: -2.4, -2.0) and the smallest bias was when the vaccination rollout and TND took place in weeks 1–12 and 21–32, respectively (Bias=-0.9 pp; CI: -1.4, -0.5), though the confidence interval overlapped with multiple other timing combinations. In addition, the timing of the vaccination rollout in relation to the TND influenced VE against symptomatic infection estimates. For people vaccinated in the previous 3 months, VE against symptomatic infection from unadjusted models was nearly 20 pp lower when the vaccination rollout immediately preceded the TND (vaccination rollout in weeks 1–12 and TND in weeks 11–12: VE = 25.4%; CI: 24.6, 26.3; vaccination rollout in weeks 11–22 and TND in weeks 21–32: VE = 26.4%; CI: 25.6, 27.3) compared to when vaccination rollout and TND overlapped (weeks 1–12: VE = 46.0%; CI: 45.5, 47.0; weeks 11–22: VE = 45.1%; CI: 44.4, 45.7; weeks 21–32: VE = 46.2%; CI: 45.5, 47.0) (Fig. 4 ). Other exposure definitions also attributed the largest differences in bias to the hybrid protection definition and the timing of the vaccination rollout and TND (Figures S20-S32), though the waning of vaccine-induced protection also impacted bias for multiple exposures (Figures S20, S21, S24-S27, S31). The timing of the vaccination rollout and TND was the only factor which contributed to unadjusted VE against symptomatic infection being negative for people vaccinated in the previous 3 months (Fig. 4 ). Negative VE against symptomatic infection was most likely when the vaccination rollout happened after the TND, which is similar to performing a TND long after a vaccination campaign was completed (0.2% when vaccination rollout in weeks 11–22 and TND in weeks 1–12 and vaccination rollout in weeks 21–32 and TND in weeks 1–12) which was similar to exposures with a long time since vaccination, e.g., in people 12 or more months since vaccination which had at least 40% of VE estimates below zero (Figure S28). VE against severe disease The median protection against severe disease at the end of the historical period ranged from 0.87 to 0.97 and the distribution of median protection was higher when hybrid protection boosted by 30% compared to VP boosted by 30% of IP or IP was boosted by 10% of VP (Table S2 ). The distribution of median protection against severe disease increased with increasing number of vaccinations (Table S3) and was lower for those without a prior infection compared to any number of prior infections (Table S4). VE against severe disease (Fig. 2 , right column) in unadjusted models was highest for people 1–2 months since vaccination (VE = 91.1%; CI: 90.8, 91.3) and lowest for people 12 or more months since vaccination (VE = 42.2%; CI: 40.3, 44.1). For recent vaccination definitions, VE against severe disease had a small range from 87.4% (CI: 87.0, 87.7) for vaccination in the last 2 months to 85.9% (CI: 85.6, 86.2) for vaccination in the last 6 months. Unadjusted models underestimated VE against severe disease compared to adjusted models for recent vaccination exposures, with bias ranging from − 1.3 pp (CI: -1.4, -1.1) for vaccination in the last 2 months to -2.0 pp (CI: -2.2, -1.9) for vaccination in the last 6 months (Fig. 3 , right column). Bias of VE against severe disease for people 1–2 months since vaccination was − 1.4 pp (CI: -1.5, -1.2), increased for people 3–4 months since vaccination (Bias=-2.1 pp; CI: -2.2, -1.9) and 5–11 months since vaccination (Bias=-4.7 pp; CI: -4.9, -4.4), before decreasing for people 12 + months (Bias=-2.5 pp; CI: -2.8, -2.3). Bias was similar for people with two (Bias=-2.2 pp; CI: -2.4, -2.0) or three doses (Bias=-2.1 pp; CI: -2.3, -1.8) and higher for people with four (Bias=-4.8 pp; CI: -5.1, -4.5) or five doses (Bias=-4.3 pp; CI: -4.6, -4.0). Overall bias for VE against severe disease for those vaccinated in the previous 3 months (Fig. 4 ) was − 1.8 pp (CI: -2.0, -1.6). Bias for all parameter levels overlapped with those limits, except bias was less when a constant 4% case distribution was assumed (Bias=-2.0 pp; CI: -2.3, -1.7). Other vaccination exposure definitions (Figures S33-S45) also demonstrated differences in bias by variable levels, including by case definition (Figures S33, S35, S38, S41, S44, S45), hybrid protection (Figures S40-S44), and vaccine-induced protection definition (Figures S33, S36, S37, S39-S45). Discussion These microsimulations suggest that, when many people have experienced at least one prior infection, failure to adjust for infection-induced protection does not dramatically change VE estimates from a TND. On the aggregate, across an array of exposure definitions, VE against symptomatic infection and VE against severe disease were underestimated by a maximum of 5.4 percentage points. Biases of between 6 to 8 percentage points in TNDs has been considered minimal enough to use for vaccine policy making, 38–41 and, as has been argued previously, biases toward 0% should not restrict the utility of a VE estimate as a downward biased VE estimate may provide a lower bound. 13 Though, the aggregated results mask some variability. First, for simulation parameters, the bias of VE against symptomatic infection was impacted by the timing of the vaccination rollout and TND. The association between bias and timing varied by exposure, but tended to be lowest when the vaccination rollout and TND were contemporaneous and largest when the vaccination rollout started three months prior to the TND. The increase in bias may be due to increased time since vaccination since vaccination was most likely early in the 12-week vaccination period, indicating vaccine-induced protection waned before the TND. Differential depletion of susceptibles 14,42 may also be a factor since vaccination is assumed to offer limited protection against infection and higher protection against severe disease. Second, bias for exposure and parameter combinations was as low as -13.2 pp (CI: -18.1, -8.8). In total, 150 exposure and parameter combinations possessed a bias of less − 8 pp out of 10,752 total combinations (1.4%). One hundred of those were from VE against symptomatic disease simulations where the vaccination rollout occurred before the TND period. The most common exposures with a bias of less than − 8 pp were 4- or 5-dose VE in 40 parameter combinations. These results suggest recognizing the entire context and all parameters are important to understanding the potential bias. The timing of the vaccination rollout and TND also affected VE against symptomatic infection. VE against symptomatic infection for vaccination in the previous 3 months was approximately 46% with concurrent vaccination rollout and TND, 27% when rollout immediately preceded the TND, and 38% otherwise. These results suggest an impact for VE against COVID-19 symptomatic infection, potentially of 20 percentage points. Since VE against symptomatic infection wanes quickly, understanding the relative timing of the TND and vaccination rollout is critical for estimating VE for all exposures. VE against symptomatic infection less than zero (negative VE) was more likely for exposure groups with more months since the last vaccination dose or fewer vaccination doses. Waning of vaccination-induced protection is a potential contributor to negative VE estimates. 31,45 Vaccinated individuals further from their last vaccination dose or with fewer doses have vaccination-induced protection that has completely or near-completely waned, which is likely driving the negative VE estimates in these exposures. This is especially true for symptomatic infection since waning may mean vaccinated individuals can be at a similar or greater risk of a mild outcome with SARS-CoV-2 infection compared to unvaccinated individuals during the TND since unvaccinated individuals are more likely to have a prior SARS-CoV-2 infection compared to vaccinated individuals, 12 indicating that unvaccinated people are at greater likelihood of protection unaccounted for in unadjusted analyses compared to vaccinated people. As a comparison, VE against severe disease had no lower confidence limits below zero since VE against severe disease is greater than VE against symptomatic infection and VE against severe disease wanes at a much slower rate than VE against symptomatic infection. Vaccine protection waning and existing infection-induced protection in unvaccinated participants suggest a higher outcome rate may be observed in vaccinated TND participants compared to unvaccinated TND participants, leading to a negative VE estimate. In addition, scenarios where a TND was performed three months after the vaccination rollout had the greatest likelihood of negative VE, further supporting vaccine-induced protection waning as a contributor to negative VE estimates. Bias also can contribute to negative VE, 15 and we found a positive VE in adjusted analyses of < 6% could be underestimated in unadjusted analyses enough to bias an estimate below zero. Finally, random variation may also play a role and some exposures from individual parameter sets with a VE against symptomatic infection point estimate above 40% has lower confidence intervals below zero. Therefore, exposure categories further out from the last vaccination possessed a high enough VE estimate to avoid the underestimation from unadjusted models resulting in a negative VE. Our finding that VE estimates unadjusted for prior infection remain reliable and thus can be used to inform policy is especially important as prior infection is challenging to accurately measure. For example, adult vaccine effectiveness studies from the US during SARS-CoV-2 Omicron variant circulation found approximately 15% of included patients with prior documented or self-reported laboratory-confirmed SARS-CoV-2 infection during a period when the vast majority of adults in the US had serological evidence of past infection. 46,47 A number of factors are likely to contribute to this, including asymptomatic or paucisymptomatic infection 48 that does not prompt testing, a lack of clinical testing despite symptomatic illness, receiving a prior positive test for SARS-CoV-2 in settings not captured in the surveillance network such as a different healthcare system and at-home testing, 49,50 and imperfect accuracy of SARS-CoV-2 diagnostic assays. In addition, while a binary indication of prior infection may be available via serology in some study platforms, infection-induced protection is likely related to the number of prior infections, variant of prior infection(s), and time since prior infection, none of which are indicated via serology or fully captured by electronic health records or self-reporting. The results also suggest that, when measuring VE for recent vaccination exposures, VE against severe disease is more stable than VE against symptomatic infection due to the slower waning of protection against severe disease. For all evaluated durations of the recent vaccination exposure, unadjusted VE against severe disease ranged from 83.9–85.9% whereas VE against symptomatic infection ranged from 21.2–46.2% indicating that bias of VE against severe disease was less likely to be influenced by the exposure duration. The lack of a clear function of how infection-induced and vaccine-induced protection combine to become hybrid protection was one of multiple limitations of these simulations. We utilized published meta-analyses that attempted to characterize the waning effectiveness of vaccines 32 and hybrid protection, 33,35 but we required additional assumptions for our simulations. There is rich information on antibody titer trajectories 53,54 but challenges remain for determining the relationship between neutralization titers and protection. 55 We tried to create realistic simulations that were also succinct and understandable. As a result, we did not incorporate other known sources of bias such as errors in vaccine registry linkage 56 or correlation between COVID-19 and influenza vaccination. 39 Another major consequence of creating realistic simulations was the true VE was dependent on the population in each simulation. Therefore, bias in these simulations was not based on a true, underlying parameter. In addition, although we found differences in the bias associated with vaccination doses, this likely was attributable to the timing of the last vaccination dose. Fewer vaccination doses was typically associated with a longer duration since the last vaccination dose. Therefore, in this simulation people with fewer doses possessed less vaccine-induced protection and were more likely to have overall protection levels similar to unvaccinated people. Conclusion TNDs have been recommended as the most efficient and feasible method for assessing VE. 57 Effectiveness of vaccinations delivered are based not only on the vaccine formulations and the circulating pathogens, but also on characteristics of the population, including people’s underlying immunity from past infections. Prior SARS-CoV-2 infections, including the number, variant, and timing of past infections, cannot be ascertained with certainty and are more common in unvaccinated compared to vaccinated individuals. 12 Although VE estimates unadjusted for prior infection are lower than adjusted estimates, the difference was in line with accepted underestimates of VE. Extra care should be taken when performing analyses by number of total vaccine doses as more recent doses have the potential for greater bias when not controlled for past infection and doses further in the past have greater potential to result in negative VE estimates. Ideally, researchers could adjust VE estimates from a TND for prior infection history if data are available, but unadjusted VE estimates from a TND remain useful. Declarations Disclaimer: The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the CDC. Conflicts of interest: The authors declare that they do not have any commercial or other association that might pose a conflict of interest. Financial support: This study was supported by the Centers for Disease Control and Prevention. Dr. Fireman’s time was supported by the Centers for Disease Control and Prevention contract number 75D30120C07765 to Kaiser Foundation Hospitals. Declaration of interests The authors declare no conflicts of interest. Acknowledgments The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the CDC. References Jackson ML, Nelson JC (2013) The test-negative design for estimating influenza vaccine effectiveness. Vaccine 31:2165–2168. https://doi.org/10.1016/j.vaccine.2013.02.053 Foppa IM, Haber M, Ferdinands JM, Shay DK (2013) The case test-negative design for studies of the effectiveness of influenza vaccine. 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PLoS ONE 17:e0278624. https://doi.org/10.1371/journal.pone.0278624 Westreich D, Hudgens MG (2016) Invited Commentary: Beware the Test-Negative Design. Am J Epidemiol 184:354–356. https://doi.org/10.1093/aje/kww063 Shi X, Li KQ, Mukherjee B (2023) Current Challenges With the Use of Test-Negative Designs for Modeling COVID-19 Vaccination and Outcomes. Am J Epidemiol 192:328–333. https://doi.org/10.1093/aje/kwac203 Sullivan SG, Tchetgen T, E. J., Cowling BJ (2016) Theoretical Basis of the Test-Negative Study Design for Assessment of Influenza Vaccine Effectiveness. Am J Epidemiol 184:345–353. https://doi.org/10.1093/aje/kww064 Tenforde MW, Link-Gelles R, Patel MM (2022) Long-term Protection Associated With COVID-19 Vaccination and Prior Infection. JAMA 328:1402–1404. https://doi.org/10.1001/jama.2022.14660 Ayoub HH et al (2023) Estimating protection afforded by prior infection in preventing reinfection: applying the test-negative study design. Am J Epidemiol , kwad239 https://doi.org/10.1093/aje/kwad239 Kahn R, Schrag SJ, Verani JR, Lipsitch M (2022) Identifying and Alleviating Bias Due to Differential Depletion of Susceptible People in Postmarketing Evaluations of COVID-19 Vaccines. Am J Epidemiol 191:800–811. https://doi.org/10.1093/aje/kwac015 Bodner K, Irvine MA, Kwong JC, Mishra S (2023) Observed negative vaccine effectiveness could be the canary in the coal mine for biases in observational Covid-19 studies. Int J Infect Dis. https://doi.org/10.1016/j.ijid.2023.03.022 Bailie CR et al (2022) Trend in Sensitivity of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Serology One Year After Mild and Asymptomatic Coronavirus Disease 2019 (COVID-19): Unpacking Potential Bias in Seroprevalence Studies. Clin Infect Dis 75:e357–e360. https://doi.org/10.1093/cid/ciac020 Cohen J (1977) Statistical Power Analysis for the Behavioral Sciences. 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Lancet Infect Dis. https://doi.org/10.1016/S1473-3099(22)00801-5 Ciesla AA et al (2023) Effectiveness of Booster Doses of Monovalent mRNA COVID-19 Vaccine Against Symptomatic SARS-CoV-2 Infection in Children, Adolescents, and Adults During Omicron Subvariant BA.2/BA.2.12.1 and BA.4/BA.5 Predominant Periods. Open Forum Infect Dis 10:ofad187. https://doi.org/10.1093/ofid/ofad187 Stein C et al (2023) Past SARS-CoV-2 infection protection against re-infection: a systematic review and meta-analysis. Lancet. https://doi.org/10.1016/S0140-6736(22)02465-5 Miller TE et al (2020) Clinical sensitivity and interpretation of PCR and serological COVID-19 diagnostics for patients presenting to the hospital. FASEB J 34:13877–13884. https://doi.org/10.1096/fj.202001700RR Tartof SY et al (2022) Effectiveness of a third dose of BNT162b2 mRNA COVID-19 vaccine in a large US health system: A retrospective cohort study. Lancet Reg Health Am 9:100198. https://doi.org/https://doi.org/10.1016/j.lana.2022.100198 Graham S et al (2023) Bias assessment of a test-negative design study of COVID-19 vaccine effectiveness used in national policymaking. Nat Comm 14:3984. https://doi.org/10.1038/s41467-023-39674-0 Doll MK, Pettigrew SM, Ma J, Verma A (2022) Effects of Confounding Bias in Coronavirus Disease 2019 (COVID-19) and Influenza Vaccine Effectiveness Test-Negative Designs Due to Correlated Influenza and COVID-19 Vaccination Behaviors. Clin Infect Dis 75:e564–e571. https://doi.org/10.1093/cid/ciac234 Segaloff HE et al (2020) Influenza Vaccine Effectiveness in the Inpatient Setting: Evaluation of Potential Bias in the Test-Negative Design by Use of Alternate Control Groups. Am J Epidemiol 189:250–260. https://doi.org/10.1093/aje/kwz248 Jackson ML, Rothman KJ (2015) Effects of imperfect test sensitivity and specificity on observational studies of influenza vaccine effectiveness. Vaccine 33:1313–1316. https://doi.org/10.1016/j.vaccine.2015.01.069 Kahn R, Feikin DR, Wiegand RE, Lipsitch M (2023) Examining bias from differential depletion of susceptibles in vaccine effectiveness estimates in settings of waning. Am J Epidemiol Kahn R, Hitchings M, Wang R, Bellan SE, Lipsitch M (2019) Analyzing Vaccine Trials in Epidemics With Mild and Asymptomatic Infection. Am J Epidemiol 188:467–474. https://doi.org/10.1093/aje/kwy239 Young B, Sadarangani S, Jiang L, Wilder-Smith A, Chen MIC (2018) Duration of Influenza Vaccine Effectiveness: A Systematic Review, Meta-analysis, and Meta-regression of Test-Negative Design Case-Control Studies. J Infect Dis 217:731–741. https://doi.org/10.1093/infdis/jix632 Chemaitelly H et al (2022) Duration of mRNA vaccine protection against SARS-CoV-2 Omicron BA.1 and BA.2 subvariants in Qatar. Nat Comm 13:3082. https://doi.org/10.1038/s41467-022-30895-3 Adams K et al (2022) Vaccine effectiveness of primary series and booster doses against covid-19 associated hospital admissions in the United States: living test negative design study. BMJ 379. https://doi.org/10.1136/bmj-2022-072065 . e072065 Link-Gelles R et al (2023) Estimation of COVID-19 mRNA Vaccine Effectiveness and COVID-19 Illness and Severity by Vaccination Status During Omicron BA.4 and BA.5 Sublineage Periods. JAMA Netw Open 6:e232598–e232598. https://doi.org/10.1001/jamanetworkopen.2023.2598 Oran DP, Topol EJ (2021) The Proportion of SARS-CoV-2 Infections That Are Asymptomatic. Ann Intern Med 174:655–662. https://doi.org/10.7326/M20-6976 Rader B et al (2022) Use of At-Home COVID-19 Tests - United States, August 23, 2021-March 12, 2022. MMWR Morb Mortal Wkly Rep 71:489–494. https://doi.org/10.15585/mmwr.mm7113e1 Lazer D et al (2022) in The COVID States Project: A 50-state COVID-19 survey Vol. 79 Silk BJ et al (2023) COVID-19 Surveillance After Expiration of the Public Health Emergency Declaration - United States, May 11, 2023. MMWR Morb Mortal Wkly Rep 72:523–528. https://doi.org/10.15585/mmwr.mm7219e1 Scobie HM et al (2023) Correlations and Timeliness of COVID-19 Surveillance Data Sources and Indicators - United States, October 1, 2020-March 22, 2023. MMWR Morb Mortal Wkly Rep 72:529–535. https://doi.org/10.15585/mmwr.mm7219e2 Epsi NJ et al (2023) Understanding Hybrid Immunity: Comparison and Predictors of Humoral Immune Responses to Severe Acute Respiratory Syndrome Coronavirus 2 Infection (SARS-CoV-2) and Coronavirus Disease 2019 (COVID-19) Vaccines. Clin Infect Dis 76:e439–e449. https://doi.org/10.1093/cid/ciac392 Wei J et al (2022) SARS-CoV-2 antibody trajectories after a single COVID-19 vaccination with and without prior infection. Nat Comm 13:3748. https://doi.org/10.1038/s41467-022-31495-x Khoury DS et al (2021) Neutralizing antibody levels are highly predictive of immune protection from symptomatic SARS-CoV-2 infection. Nat Med 27:1205–1211. https://doi.org/10.1038/s41591-021-01377-8 Brookmeyer R, Morrison DE (2022) Estimating Vaccine Effectiveness by Linking Population-Based Health Registries: Some Sources of Bias. Am J Epidemiol 191:1975–1980. https://doi.org/10.1093/aje/kwac145 World Health Organization (2021) Evaluation of COVID-19 vaccine effectiveness: interim guidance, 17 March 2021. Geneva, Switzerland. Report No. WHO/2019 -nCoV/vaccine_effectiveness/measurement/2021.1 Additional Declarations There is NO Competing Interest. Supplementary Files supplementaryoutput20240318.xlsx tndpriorinfectionsupplement20240716.docx Cite Share Download PDF Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4802667\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":334342325,\"identity\":\"cb6d8d8c-738c-450a-9ebf-3c731c4f786d\",\"order_by\":0,\"name\":\"Ryan Wiegand\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmklEQVRIiWNgGAWjYBAC9gY2xgcfGJhJ0MJzgI3ZcAapWtikeUjTIpGWIG1TYy3PwL/4mASxWg4Y5xxLN2yQeJZGnBZ76fSG5NyGwwkMEmeMDYizBajlsCWJWtIONjOCtPD3GD4gTov8s2TGHqBf2iTYEonUwnPM/McPYIjx8x8+cIAoLXDAJpFAmgYg4CfRjlEwCkbBKBg5AABMPinM7mOBiQAAAABJRU5ErkJggg==\",\"orcid\":\"https://orcid.org/0000-0002-9486-1850\",\"institution\":\"CDC\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Ryan\",\"middleName\":\"\",\"lastName\":\"Wiegand\",\"suffix\":\"\"},{\"id\":334342326,\"identity\":\"43b0b52b-a423-4514-8027-f645915f30fc\",\"order_by\":1,\"name\":\"Bruce Fireman\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Kaiser Permanente Northern California, Vaccine Study Center\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Bruce\",\"middleName\":\"\",\"lastName\":\"Fireman\",\"suffix\":\"\"},{\"id\":334342327,\"identity\":\"a0791120-3aa3-4b27-bbe7-93cd596d1aba\",\"order_by\":2,\"name\":\"Morgan Najdowski\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Centers for Disease Control and Prevention\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Morgan\",\"middleName\":\"\",\"lastName\":\"Najdowski\",\"suffix\":\"\"},{\"id\":334342328,\"identity\":\"b90b06d3-e80a-48be-8ff7-932a3e08aa13\",\"order_by\":3,\"name\":\"Mark Tenforde\",\"email\":\"\",\"orcid\":\"https://orcid.org/0000-0002-8702-8393\",\"institution\":\"Centers for Disease Control and Prevention\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Mark\",\"middleName\":\"\",\"lastName\":\"Tenforde\",\"suffix\":\"\"},{\"id\":334342329,\"identity\":\"d09dc15f-c27b-4778-857b-99c1a5f63583\",\"order_by\":4,\"name\":\"Ruth Link-Gelles\",\"email\":\"\",\"orcid\":\"https://orcid.org/0000-0002-9617-806X\",\"institution\":\"US Centers for Disease Control and Prevention\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Ruth\",\"middleName\":\"\",\"lastName\":\"Link-Gelles\",\"suffix\":\"\"},{\"id\":334342330,\"identity\":\"e40c3a1b-cd3c-455e-840f-14764f5ddda1\",\"order_by\":5,\"name\":\"Jill Ferdinands\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"US Centers for Disease Control and Prevention\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jill\",\"middleName\":\"\",\"lastName\":\"Ferdinands\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-07-25 14:50:07\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-4802667/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-4802667/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1038/s41467-024-54404-w\",\"type\":\"published\",\"date\":\"2024-11-20T05:00:00+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":61809948,\"identity\":\"d4afa088-ff8f-4a1d-a132-3a231a5f7117\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:17:42\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":242168,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eBasic diagram of the simulation process.\\u003c/p\\u003e\\n\\u003cp\\u003eNotes: IP=infection-induced protection, VP=vaccination-induced protection, TND=test-negative design.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/dece0e48d2988a6da4955183.png\"},{\"id\":61809947,\"identity\":\"b5bd2d12-49ff-4981-a2ac-b453d190a60b\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:17:42\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":95989,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003ePlot of estimated marginal means of VE against symptomatic infection and VE against severe disease for each exposure.\\u003c/p\\u003e\\n\\u003cp\\u003eNotes: VE estimates are generated from a simple meta-regression of aggregated results from all simulation conditions without controlling for simulation parameters. Estimates are denoted by dots and the 95% confidence intervals are represented by bars.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/cb96632a9322c7e0e18b56e1.png\"},{\"id\":61809952,\"identity\":\"71e45aea-87da-4203-8167-4561a4b50882\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:17:43\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":85063,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003ePlot of estimated marginal means of bias of VE against symptomatic infection and VE against severe disease for each exposure.\\u003c/p\\u003e\\n\\u003cp\\u003eNotes: Bias is computed as the difference between VE calculated from the model that does not adjust for prior infection (“unadjusted”) and the model adjusted for prior infection (“adjusted”). Bias estimates are generated from a meta-regression of aggregated results from all simulation conditions. Estimates are denoted by dots and the 95% confidence intervals are represented by bars.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/6d8ee37673c03e656b1651ac.png\"},{\"id\":61811301,\"identity\":\"6e631534-180d-4d72-8750-cbb9144159a1\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:25:42\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":216966,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003ePlot of estimated marginal means of unadjusted VE (not controlling for prior infection) against symptomatic infection, bias compared to adjusted VE (controlling for prior infection) against symptomatic infection, and the percentage of simulations with an unadjusted VE estimate less than zero (negative VE) for people vaccinated in the previous 3 months.\\u003c/p\\u003e\\n\\u003cp\\u003eNotes: Estimates are generated from a meta-regression of aggregated results from all simulation conditions after controlling for all other simulation parameters. Bias is computed as the difference between the unadjusted VE estimate compared to the VE estimate adjusted for prior infection. Estimates are denoted by dots and the 95% confidence intervals for VE and bias are represented by bars. The bars may be narrower than the dot and not visible.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/418fd463ce0673131cee1968.png\"},{\"id\":61811302,\"identity\":\"89af5dbf-9b9b-4a03-ba3f-b4a8a1cd0acc\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:25:42\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":122275,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003ePlot of estimated marginal means of unadjusted VE (not controlling for prior infection) against severe disease and bias compared to adjusted VE (controlling for prior infection) for people vaccinated in the previous 3 months.\\u003c/p\\u003e\\n\\u003cp\\u003eNotes: Estimates are generated from a meta-regression of aggregated results from all simulation conditions and controlling for all other simulation parameters. Bias is computed as the difference between the unadjusted VE estimate compared to the VE estimate adjusted for prior infection. Estimates are denoted by dots and the 95% confidence intervals are represented by bars.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/cdf10a8cd592a910f7c8f6f5.png\"},{\"id\":69514962,\"identity\":\"8cfab753-c634-4d93-97fc-f36665c18cca\",\"added_by\":\"auto\",\"created_at\":\"2024-11-21 08:06:25\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":911337,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/2a50eab3-fcda-4d85-a5c9-55d29fbc479a.pdf\"},{\"id\":61809949,\"identity\":\"dfc996cc-c514-41f3-83cf-d44b92f305a8\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:17:42\",\"extension\":\"xlsx\",\"order_by\":2,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":2103896,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"supplementaryoutput20240318.xlsx\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/355b371ce16721f44ed821e7.xlsx\"},{\"id\":61809953,\"identity\":\"ac2a4068-fdbd-4b15-987d-be82666daacf\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 20:17:43\",\"extension\":\"docx\",\"order_by\":3,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":529845,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"tndpriorinfectionsupplement20240716.docx\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4802667/v1/74e7ab33acf3233618de52c1.docx\"}],\"financialInterests\":\"There is \\u003cb\\u003eNO\\u003c/b\\u003e Competing Interest.\",\"formattedTitle\":\"Bias and negative values of COVID-19 vaccine effectiveness estimates from a test-negative design without controlling for prior SARS-CoV-2 infection\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003eTest-negative designs (TNDs) are an indispensable tool for assessing vaccine effectiveness (VE). TNDs were designed to assess VE against symptomatic infection of seasonal influenza,\\u003csup\\u003e1,2\\u003c/sup\\u003e but have been used to estimate VE against SARS-CoV-2 symptomatic infection,\\u003csup\\u003e3\\u003c/sup\\u003e emergency department or urgent care encounters,\\u003csup\\u003e4\\u003c/sup\\u003e hospitalizations,\\u003csup\\u003e5\\u003c/sup\\u003e invasive mechanical ventilation,\\u003csup\\u003e6\\u003c/sup\\u003e and death\\u003csup\\u003e7\\u003c/sup\\u003e and to support policy decisions.\\u003csup\\u003e8\\u003c/sup\\u003e A TND can be performed rapidly, at lower cost than other studies, and with reduced confounding from health care seeking behavior compared to other observational study designs.\\u003csup\\u003e1,2\\u003c/sup\\u003e The efficiency and feasibility of a TND comes with many challenges,\\u003csup\\u003e9,10\\u003c/sup\\u003e especially regarding the assumptions of how cases and controls are ascertained; controls should be representative of the source population that yielded the cases.\\u003csup\\u003e11\\u003c/sup\\u003e\\u003c/p\\u003e \\u003cp\\u003eProtection from infection-induced immunity can present challenges when estimating VE from a TND. Participants' history of prior SARS-CoV-2 infection has often not been incorporated into VE studies.\\u003csup\\u003e11\\u003c/sup\\u003e For COVID-19 studies, infection history data is not collected due to self-testing, asymptomatic infection, and mild infections not requiring medical attention.\\u003csup\\u003e12\\u003c/sup\\u003e Bias can arise if prior infection status is misclassified\\u003csup\\u003e13\\u003c/sup\\u003e or not accounted for in models\\u003csup\\u003e14\\u003c/sup\\u003e and could result in a VE estimate below zero.\\u003csup\\u003e15\\u003c/sup\\u003e Serologic testing has been recommended to correct this bias\\u003csup\\u003e14\\u003c/sup\\u003e but possesses many challenges, including decreasing sensitivity due to antibody decay,\\u003csup\\u003e16\\u003c/sup\\u003e potential inability to detect past infection in people with a current infection, increased cost, and decreased power\\u003csup\\u003e17\\u003c/sup\\u003e since over 87% of the US population had detectable SARS-CoV-2 antibodies from infection in October-December of 2023.\\u003csup\\u003e18\\u003c/sup\\u003e Additionally, many people have had multiple prior SARS-CoV-2 infections, and serologic testing does not provide information on number of total infections nor time since or variant of last infection, which are important for understanding the potential impact of past infection on VE.\\u003c/p\\u003e \\u003cp\\u003eConsidering these challenges, we endeavored to assess the bias in VE against symptomatic SARS-CoV-2 infection and severe disease from a TND when prior infection is unaccounted for in analyses. Microsimulations were created based on the COVID-19 pandemic, where each person\\u0026rsquo;s vaccination and infection history was generated up to May 2023, followed by a hypothetical vaccination campaign and TND to estimate VE against symptomatic infection or severe disease. Multiple parameters relating to vaccine and infection protection waning and the TND study design were varied.\\u003c/p\\u003e\"},{\"header\":\"Methods\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eSimulation methods\\u003c/h2\\u003e \\u003cp\\u003eA thorough summary of the simulation methods and a full list of microsimulation parameter sets and results are included in the supplementary materials. We created populations of 100,000 people aged 18\\u0026ndash;49 years without protection against SARS-CoV-2 infection at the beginning of the COVID-19 pandemic (the Morbidity and Mortality Weekly Report [MMWR] week of January 19, 2020).\\u003csup\\u003e19\\u003c/sup\\u003e Each week until the MMWR week of May 7, 2023, we updated each person\\u0026rsquo;s vaccine- and infection-induced protection against SARS-CoV-2 infection based on their most recent infection and vaccine dose since people could accumulate multiple infections and doses over time (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eWeekly infection probabilities were derived from aggregated case count data from 60 U.S. jurisdictions\\u003csup\\u003e19\\u003c/sup\\u003e divided by 2020 population estimates\\u003csup\\u003e20\\u003c/sup\\u003e (Figure \\u003cspan refid=\\\"MOESM1\\\" class=\\\"InternalRef\\\"\\u003eS1\\u003c/span\\u003e). These proportions were increased by a multiplier (Figure \\u003cspan refid=\\\"MOESM2\\\" class=\\\"InternalRef\\\"\\u003eS2\\u003c/span\\u003e) to account for underreporting of infections\\u003csup\\u003e21\\u003c/sup\\u003e and to reach approximately 95%-98% of the population acquiring a prior infection by the end of the study period (Figure S3).\\u003c/p\\u003e \\u003cp\\u003eIndividual, weekly probabilities of vaccination receipt utilized U.S. vaccination data, the number of prior doses and prior infection status. Data on vaccination distributions by vaccination dosage and week for U.S. people aged 18\\u0026ndash;49 years\\u003csup\\u003e22\\u003c/sup\\u003e (Figure S4) were fit to probability distributions (Figure S5). For na\\u0026iuml;ve people, we set the probability of obtaining two vaccination doses at 0.70, the probability of a third dose conditional on having two doses at 0.30, and the probability of a fourth dose conditional on having a third dose at 0.10.\\u003csup\\u003e22\\u003c/sup\\u003e People with a prior SARS-CoV-2 infection have been less likely to initiate or subsequently receive an additional vaccination dose.\\u003csup\\u003e23\\u0026ndash;28\\u003c/sup\\u003e We assumed people with a prior infection were less likely to receive an additional dose with an odds ratio of 0.525.\\u003csup\\u003e23\\u0026ndash;28\\u003c/sup\\u003e\\u003c/p\\u003e \\u003cp\\u003eA person\\u0026rsquo;s protection was based on the most recent week of vaccination and infection. Waning curves were based on trajectories in published literature.\\u003csup\\u003e29\\u0026ndash;34\\u003c/sup\\u003e A week after vaccination we assumed 90% vaccine-induced protection against infection (VP) prior to Omicron predominance and 70% protection thereafter. VP waned linearly to zero (\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e) at 48 weeks post-vaccination prior to Omicron predominance and 24 weeks thereafter or (\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e) at 24 weeks post-vaccination prior to Omicron predominance and 12 weeks thereafter (Figure S6) with variability by person (Figure S7). A week after infection, infection-induced protection (IP) had 90% protection against infection that waned to zero at 96 or 72 weeks (Figure S8) again with variability by person (Figure S9).\\u003c/p\\u003e \\u003cp\\u003eHybrid immunity or protection (HP) definitions were taken from meta-analyses of protective effectiveness:\\u003csup\\u003e33,35\\u003c/sup\\u003e (\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e) the greater of VP or IP was boosted by 30% of the other (Figure S10); or (\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e) VP was boosted by 30% of IP or IP was boosted by 10% of VP, whichever was greater (Figure S11). Both HP definitions were truncated at 99%. In these simulations, we considered 8 different protection calculations since we simulated each combination of the two VP, two IP, and two HP definitions.\\u003c/p\\u003e \\u003cp\\u003eInfections were generated from a person\\u0026rsquo;s weekly protection with the function\\u003cdiv id=\\\"Equa\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equa\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\:\\\\text{P}\\\\text{r}\\\\left({I}_{j,k}\\\\right)=\\\\text{P}\\\\text{r}\\\\left({c}_{k}\\\\right)\\\\text{*}\\\\left(1-{\\\\psi\\\\:}_{j,k-1}\\\\right),$$\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere the probability of infection for each person (\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:j\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) and week (\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e), \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\text{P}\\\\text{r}\\\\left({I}_{j,k}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, depended on \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\text{P}\\\\text{r}\\\\left({c}_{k}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, the case probability in week \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and person \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:j\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u0026rsquo;s protection calculated from the previous week (\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:{\\\\psi\\\\:}_{j,k-1}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e). An infection for person \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:j\\\\)\\u003c/span\\u003e\\u003c/span\\u003e in week \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e was generated from a Bernoulli distribution with probability \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\text{P}\\\\text{r}\\\\left({I}_{j,k}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003eA total of 200 populations were generated for each of the 8 protection definition combinations. An example of protection trajectories is included in the supplementary materials (Figure S12).\\u003c/p\\u003e \\u003cp\\u003eThe analytic period consisted of a hypothetical 32-week period beginning immediately after the historical period. Infections, vaccination doses, and protection were generated similarly to the historical period. Parameters were the 8 protection definition combinations, case distribution, vaccination rollout timing, total vaccination coverage, TND timing, and type of outcome (infection or severe disease).\\u003c/p\\u003e \\u003cp\\u003eFour infection distributions were utilized during the analytic period (Figure S13): weekly 2%; weekly 4%; weekly 2% increasing to a peak of 4% at weeks 16 and 17 before returning to 2%; and weekly 2% increasing to a peak of 6% at weeks 16 and 17 before returning to 2%. The vaccination rollout happened in weeks 1\\u0026ndash;12 (before the case peak), weeks 11\\u0026ndash;22 (during the case peak), or weeks 21\\u0026ndash;32 (after the case peak) and followed a lognormal distribution with a mean of 1.5 and a standard deviation of 0.5 (Figure S14). Other weeks had a vaccination probability of 0.005. Total vaccination coverage in the analytic period was 10% based on fourth dose vaccination coverage\\u003csup\\u003e22\\u003c/sup\\u003e or 25% (Figure S15). The TND for symptomatic infections was implemented in weeks 1\\u0026ndash;12, weeks 11\\u0026ndash;22, or weeks 21\\u0026ndash;32. Since we implemented all possible combinations of vaccination rollout and TND timing, some scenarios involve assessing VE via the TND before the vaccination rollout. This is the equivalent of assessing VE long after vaccination has been given. All 32 weeks were used for the TND for severe disease.\\u003c/p\\u003e \\u003cp\\u003eCOVID-19 symptoms were expected in 80% of infected people (Figure S16) and were present only in the week of infection. An uninfected person in week \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e was expected to have COVID-like symptoms with a probability of 0.20 divided by the number of weeks in the TND (Figure S17). For estimating VE against symptomatic infection, all symptomatic people were included in the TND. Diagnostic testing was assumed to have perfect specificity, but sensitivity was 90% during the week of infection and declined thereafter\\u003csup\\u003e36\\u003c/sup\\u003e (Table \\u003cspan refid=\\\"MOESM1\\\" class=\\\"InternalRef\\\"\\u003eS1\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eFor estimating VE against severe disease, VP was 90% the week after vaccination and waned to zero after 48 months.\\u003csup\\u003e31,32,34,37\\u003c/sup\\u003e IP against severe disease started at 95% protection the week after infection and waned to zero after 96 months\\u003csup\\u003e33\\u003c/sup\\u003e (Figure S18). For people with a SARS-CoV-2 infection, the probability of severe disease was\\u003cdiv id=\\\"Equb\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equb\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\:\\\\text{P}\\\\text{r}\\\\left({S}_{j,k}|{I}_{j,k}=1\\\\right)=\\\\frac{\\\\left(1-{{\\\\psi\\\\:}^{s}}_{j,k-1}\\\\right)}{\\\\left(1-{\\\\psi\\\\:}_{j,k-1}\\\\right)},$$\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:{S}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is a severe disease event for person \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:j\\\\)\\u003c/span\\u003e\\u003c/span\\u003e in week \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:{{\\\\psi\\\\:}^{s}}_{j,k-1}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the protection against severe disease for person \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:j\\\\)\\u003c/span\\u003e\\u003c/span\\u003e in week \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:k\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. All people with severe disease were included in the TND with perfect detection.\\u003c/p\\u003e \\u003cp\\u003eA total of 1000 simulations were run for each parameter set. Each of the 200 populations was utilized five times in each parameter set.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eStatistical methods\\u003c/h2\\u003e \\u003cp\\u003eExposures analyzed were vaccination at any time during the analytic period, vaccination in the previous 2 months, vaccination in the previous 3 months, vaccination in the previous 4 months, vaccination in the previous 5 months, vaccination in the previous 6 months, the number of doses (unvaccinated as the reference group, 2-dose, 3-dose, 4-dose, or 5-dose), and the time since vaccination (unvaccinated as the reference group, 0\\u0026ndash;2 months, 3\\u0026ndash;4 months, 5\\u0026ndash;11 months, and 12 or more months).\\u003c/p\\u003e \\u003cp\\u003eTwo logistic regression models were fit to each exposure definition. The first model included only the exposure variable (henceforth, the unadjusted model), whereas the second model added categorical time since the last infection (categories were monthly from 1 to 11 months and 12 or more months) and the number of prior infections as a continuous variable (the adjusted model). Odds ratios (OR) from logistic regressions were converted to VE in percentage points by the formula \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\:\\\\text{VE}=\\\\left(1-\\\\text{OR}\\\\right)*100\\\\)\\u003c/span\\u003e\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003eOur primary measurement is the difference between the VE estimate from the unadjusted model and the VE estimate from the adjusted model, which we refer to as bias. Bias is defined not in the traditional sense as the deviation from truth, but as the percentage point difference in VE from the unadjusted model and VE from the adjusted model. Bias less than zero indicated VE was underestimated without accounting for prior infection. A small percentage of simulations resulted in small sample sizes and unstable estimates. Details on bias definition and handling of unstable estimates are in the supplementary methods.\\u003c/p\\u003e \\u003cp\\u003eResults were aggregated by parameter set and exposure and plotted by exposure with ridgeline plots (Figure S20). Simple, random effects meta regression was used to estimate the expected VE and bias and, for infection outcomes, the percentage of simulations with a negative VE estimate. Separate meta regressions were run for the unadjusted and adjusted VE estimates. Multivariable meta regression models were run with simulation parameters to determine the mean VE, bias, and negative VE associated with each parameter level and the 95% confidence intervals. The overall mean and 95% confidence interval from simple meta regressions are used in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e and \\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e and values from multivariable meta regressions in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e and \\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e including the overall mean as a dashed line and the 95% CI as a shaded background.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eAll simulations were performed in R version 4.0.4 and analyses in R version 4.2.4.\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cp\\u003eResults from all simulated parameter sets and aggregated estimates are included as a supplemental file (Supplemental Excel File).\\u003c/p\\u003e \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eVE against symptomatic infection\\u003c/h2\\u003e \\u003cp\\u003ePer simulated population, the median protection against symptomatic infection at the end of the historical period ranged from 0.26 to 0.51 and, on aggregate, the distribution of median protection against symptomatic infection was lower when infection protection completely waned by 72 weeks compared to 96 weeks (Table \\u003cspan refid=\\\"MOESM2\\\" class=\\\"InternalRef\\\"\\u003eS2\\u003c/span\\u003e). The distribution of median protection against symptomatic infection by similar across the number of vaccinations (Table S3) but increased with increasing number of infections (Table S4).\\u003c/p\\u003e \\u003cp\\u003eVE against symptomatic infection (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e, left column) in unadjusted models was highest for people 1\\u0026ndash;2 months since vaccination (VE\\u0026thinsp;=\\u0026thinsp;46.3%; CI: 45.6, 47.0) and decreased with more months since vaccination, reaching the lowest at 5\\u0026ndash;11 or more months (VE =-1.6%; CI: -1.9, -1.3). VE against symptomatic infection was also lower the more months included in the recent vaccination exposure, the longer time since vaccination, and the fewer number of total vaccination doses. Distributions of estimated VE against symptomatic infection tended to be wide and cover a wide range of VE values, except for exposures with VE against symptomatic infection estimates close to zero which had narrow, unimodal distributions (Figure S19).\\u003c/p\\u003e \\u003cp\\u003eBias of VE against symptomatic infection in unadjusted analyses was at most 5.5 percentage points (pp) for each exposure definition (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, left column). For recent vaccination definitions, bias was smallest for recent vaccination in the last 2 months (Bias=-0.9 pp; CI: -0.9, -0.8) and largest for vaccination during the last 6 months (Bias=-2.9 pp; CI: -3.0, -2.8). For vaccination 1\\u0026ndash;2 months prior, bias was \\u0026minus;\\u0026thinsp;1.5 pp (CI: -1.6, -1.4). This increased to -4.8 pp (CI: -5.0, -4.7) at 3\\u0026ndash;4 months prior, decreased to -4.4 pp (CI: -4.5, -4.2) for those people 5\\u0026ndash;11 months since vaccination and decreased further for 12 or more months since vaccination (-0.9 pp; CI: -1.0, -0.9). Bias increased for each additional vaccination dose (2-dose=-0.8 pp; CI: -0.9, -0.8; 3-dose=-1.5; CI: -1.6, -1.5; 4-dose=-3.3 pp; CI: -3.4, -3.1; 5-dose=-5.2 pp, CI: -5.4, -5.0).\\u003c/p\\u003e \\u003cp\\u003eFor the exposure of vaccination in the previous 3 months (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e), the overall mean bias was \\u0026minus;\\u0026thinsp;1.4 pp (CI: -1.5, -1.3). Bias was higher when hybrid protection was defined as the greater source of protection boosted by 30% (Bias=-1.7 pp; CI: -1.8, -1.6) and lower when the greater of VP or boosted by 30% of IP or IP boosted by 10% of VP (Bias=-1.1 pp; CI: -1.2, -1.0).\\u003c/p\\u003e \\u003cp\\u003eThe timing of the vaccination rollout and TND also impacted bias. For people vaccinated in the previous 3 months, the largest bias occurred when the vaccination rollout happened immediately before the TND (vaccination rollout in weeks 1\\u0026ndash;12 and TND in weeks 11\\u0026ndash;12: Bias=-1.9 pp; CI: -2.1, -1.7; vaccination rollout in weeks 11\\u0026ndash;22 and TND in weeks 21\\u0026ndash;32: Bias=-2.2 pp; CI: -2.4, -2.0) and the smallest bias was when the vaccination rollout and TND took place in weeks 1\\u0026ndash;12 and 21\\u0026ndash;32, respectively (Bias=-0.9 pp; CI: -1.4, -0.5), though the confidence interval overlapped with multiple other timing combinations.\\u003c/p\\u003e \\u003cp\\u003eIn addition, the timing of the vaccination rollout in relation to the TND influenced VE against symptomatic infection estimates. For people vaccinated in the previous 3 months, VE against symptomatic infection from unadjusted models was nearly 20 pp lower when the vaccination rollout immediately preceded the TND (vaccination rollout in weeks 1\\u0026ndash;12 and TND in weeks 11\\u0026ndash;12: VE\\u0026thinsp;=\\u0026thinsp;25.4%; CI: 24.6, 26.3; vaccination rollout in weeks 11\\u0026ndash;22 and TND in weeks 21\\u0026ndash;32: VE\\u0026thinsp;=\\u0026thinsp;26.4%; CI: 25.6, 27.3) compared to when vaccination rollout and TND overlapped (weeks 1\\u0026ndash;12: VE\\u0026thinsp;=\\u0026thinsp;46.0%; CI: 45.5, 47.0; weeks 11\\u0026ndash;22: VE\\u0026thinsp;=\\u0026thinsp;45.1%; CI: 44.4, 45.7; weeks 21\\u0026ndash;32: VE\\u0026thinsp;=\\u0026thinsp;46.2%; CI: 45.5, 47.0) (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eOther exposure definitions also attributed the largest differences in bias to the hybrid protection definition and the timing of the vaccination rollout and TND (Figures S20-S32), though the waning of vaccine-induced protection also impacted bias for multiple exposures (Figures S20, S21, S24-S27, S31).\\u003c/p\\u003e \\u003cp\\u003eThe timing of the vaccination rollout and TND was the only factor which contributed to unadjusted VE against symptomatic infection being negative for people vaccinated in the previous 3 months (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e). Negative VE against symptomatic infection was most likely when the vaccination rollout happened after the TND, which is similar to performing a TND long after a vaccination campaign was completed (0.2% when vaccination rollout in weeks 11\\u0026ndash;22 and TND in weeks 1\\u0026ndash;12 and vaccination rollout in weeks 21\\u0026ndash;32 and TND in weeks 1\\u0026ndash;12) which was similar to exposures with a long time since vaccination, e.g., in people 12 or more months since vaccination which had at least 40% of VE estimates below zero (Figure S28).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec7\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eVE against severe disease\\u003c/h2\\u003e \\u003cp\\u003eThe median protection against severe disease at the end of the historical period ranged from 0.87 to 0.97 and the distribution of median protection was higher when hybrid protection boosted by 30% compared to VP boosted by 30% of IP or IP was boosted by 10% of VP (Table \\u003cspan refid=\\\"MOESM2\\\" class=\\\"InternalRef\\\"\\u003eS2\\u003c/span\\u003e). The distribution of median protection against severe disease increased with increasing number of vaccinations (Table S3) and was lower for those without a prior infection compared to any number of prior infections (Table S4).\\u003c/p\\u003e \\u003cp\\u003eVE against severe disease (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e, right column) in unadjusted models was highest for people 1\\u0026ndash;2 months since vaccination (VE\\u0026thinsp;=\\u0026thinsp;91.1%; CI: 90.8, 91.3) and lowest for people 12 or more months since vaccination (VE\\u0026thinsp;=\\u0026thinsp;42.2%; CI: 40.3, 44.1). For recent vaccination definitions, VE against severe disease had a small range from 87.4% (CI: 87.0, 87.7) for vaccination in the last 2 months to 85.9% (CI: 85.6, 86.2) for vaccination in the last 6 months.\\u003c/p\\u003e \\u003cp\\u003eUnadjusted models underestimated VE against severe disease compared to adjusted models for recent vaccination exposures, with bias ranging from \\u0026minus;\\u0026thinsp;1.3 pp (CI: -1.4, -1.1) for vaccination in the last 2 months to -2.0 pp (CI: -2.2, -1.9) for vaccination in the last 6 months (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, right column). Bias of VE against severe disease for people 1\\u0026ndash;2 months since vaccination was \\u0026minus;\\u0026thinsp;1.4 pp (CI: -1.5, -1.2), increased for people 3\\u0026ndash;4 months since vaccination (Bias=-2.1 pp; CI: -2.2, -1.9) and 5\\u0026ndash;11 months since vaccination (Bias=-4.7 pp; CI: -4.9, -4.4), before decreasing for people 12\\u0026thinsp;+\\u0026thinsp;months (Bias=-2.5 pp; CI: -2.8, -2.3). Bias was similar for people with two (Bias=-2.2 pp; CI: -2.4, -2.0) or three doses (Bias=-2.1 pp; CI: -2.3, -1.8) and higher for people with four (Bias=-4.8 pp; CI: -5.1, -4.5) or five doses (Bias=-4.3 pp; CI: -4.6, -4.0).\\u003c/p\\u003e \\u003cp\\u003eOverall bias for VE against severe disease for those vaccinated in the previous 3 months (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e) was \\u0026minus;\\u0026thinsp;1.8 pp (CI: -2.0, -1.6). Bias for all parameter levels overlapped with those limits, except bias was less when a constant 4% case distribution was assumed (Bias=-2.0 pp; CI: -2.3, -1.7). Other vaccination exposure definitions (Figures S33-S45) also demonstrated differences in bias by variable levels, including by case definition (Figures S33, S35, S38, S41, S44, S45), hybrid protection (Figures S40-S44), and vaccine-induced protection definition (Figures S33, S36, S37, S39-S45).\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cp\\u003eThese microsimulations suggest that, when many people have experienced at least one prior infection, failure to adjust for infection-induced protection does not dramatically change VE estimates from a TND. On the aggregate, across an array of exposure definitions, VE against symptomatic infection and VE against severe disease were underestimated by a maximum of 5.4 percentage points. Biases of between 6 to 8 percentage points in TNDs has been considered minimal enough to use for vaccine policy making,\\u003csup\\u003e38\\u0026ndash;41\\u003c/sup\\u003e and, as has been argued previously, biases toward 0% should not restrict the utility of a VE estimate as a downward biased VE estimate may provide a lower bound.\\u003csup\\u003e13\\u003c/sup\\u003e\\u003c/p\\u003e \\u003cp\\u003eThough, the aggregated results mask some variability. First, for simulation parameters, the bias of VE against symptomatic infection was impacted by the timing of the vaccination rollout and TND. The association between bias and timing varied by exposure, but tended to be lowest when the vaccination rollout and TND were contemporaneous and largest when the vaccination rollout started three months prior to the TND. The increase in bias may be due to increased time since vaccination since vaccination was most likely early in the 12-week vaccination period, indicating vaccine-induced protection waned before the TND. Differential depletion of susceptibles\\u003csup\\u003e14,42\\u003c/sup\\u003e may also be a factor since vaccination is assumed to offer limited protection against infection and higher protection against severe disease.\\u003c/p\\u003e \\u003cp\\u003eSecond, bias for exposure and parameter combinations was as low as -13.2 pp (CI: -18.1, -8.8). In total, 150 exposure and parameter combinations possessed a bias of less \\u0026minus;\\u0026thinsp;8 pp out of 10,752 total combinations (1.4%). One hundred of those were from VE against symptomatic disease simulations where the vaccination rollout occurred before the TND period. The most common exposures with a bias of less than \\u0026minus;\\u0026thinsp;8 pp were 4- or 5-dose VE in 40 parameter combinations. These results suggest recognizing the entire context and all parameters are important to understanding the potential bias.\\u003c/p\\u003e \\u003cp\\u003eThe timing of the vaccination rollout and TND also affected VE against symptomatic infection. VE against symptomatic infection for vaccination in the previous 3 months was approximately 46% with concurrent vaccination rollout and TND, 27% when rollout immediately preceded the TND, and 38% otherwise. These results suggest an impact for VE against COVID-19 symptomatic infection, potentially of 20 percentage points. Since VE against symptomatic infection wanes quickly, understanding the relative timing of the TND and vaccination rollout is critical for estimating VE for all exposures.\\u003c/p\\u003e \\u003cp\\u003eVE against symptomatic infection less than zero (negative VE) was more likely for exposure groups with more months since the last vaccination dose or fewer vaccination doses. Waning of vaccination-induced protection is a potential contributor to negative VE estimates. \\u003csup\\u003e31,45\\u003c/sup\\u003e Vaccinated individuals further from their last vaccination dose or with fewer doses have vaccination-induced protection that has completely or near-completely waned, which is likely driving the negative VE estimates in these exposures. This is especially true for symptomatic infection since waning may mean vaccinated individuals can be at a similar or greater risk of a mild outcome with SARS-CoV-2 infection compared to unvaccinated individuals during the TND since unvaccinated individuals are more likely to have a prior SARS-CoV-2 infection compared to vaccinated individuals,\\u003csup\\u003e12\\u003c/sup\\u003e indicating that unvaccinated people are at greater likelihood of protection unaccounted for in unadjusted analyses compared to vaccinated people. As a comparison, VE against severe disease had no lower confidence limits below zero since VE against severe disease is greater than VE against symptomatic infection and VE against severe disease wanes at a much slower rate than VE against symptomatic infection. Vaccine protection waning and existing infection-induced protection in unvaccinated participants suggest a higher outcome rate may be observed in vaccinated TND participants compared to unvaccinated TND participants, leading to a negative VE estimate. In addition, scenarios where a TND was performed three months after the vaccination rollout had the greatest likelihood of negative VE, further supporting vaccine-induced protection waning as a contributor to negative VE estimates. Bias also can contribute to negative VE,\\u003csup\\u003e15\\u003c/sup\\u003e and we found a positive VE in adjusted analyses of \\u0026lt;\\u0026thinsp;6% could be underestimated in unadjusted analyses enough to bias an estimate below zero. Finally, random variation may also play a role and some exposures from individual parameter sets with a VE against symptomatic infection point estimate above 40% has lower confidence intervals below zero. Therefore, exposure categories further out from the last vaccination possessed a high enough VE estimate to avoid the underestimation from unadjusted models resulting in a negative VE.\\u003c/p\\u003e \\u003cp\\u003eOur finding that VE estimates unadjusted for prior infection remain reliable and thus can be used to inform policy is especially important as prior infection is challenging to accurately measure. For example, adult vaccine effectiveness studies from the US during SARS-CoV-2 Omicron variant circulation found approximately 15% of included patients with prior documented or self-reported laboratory-confirmed SARS-CoV-2 infection during a period when the vast majority of adults in the US had serological evidence of past infection.\\u003csup\\u003e46,47\\u003c/sup\\u003e A number of factors are likely to contribute to this, including asymptomatic or paucisymptomatic infection\\u003csup\\u003e48\\u003c/sup\\u003e that does not prompt testing, a lack of clinical testing despite symptomatic illness, receiving a prior positive test for SARS-CoV-2 in settings not captured in the surveillance network such as a different healthcare system and at-home testing,\\u003csup\\u003e49,50\\u003c/sup\\u003e and imperfect accuracy of SARS-CoV-2 diagnostic assays. In addition, while a binary indication of prior infection may be available via serology in some study platforms, infection-induced protection is likely related to the number of prior infections, variant of prior infection(s), and time since prior infection, none of which are indicated via serology or fully captured by electronic health records or self-reporting.\\u003c/p\\u003e \\u003cp\\u003eThe results also suggest that, when measuring VE for recent vaccination exposures, VE against severe disease is more stable than VE against symptomatic infection due to the slower waning of protection against severe disease. For all evaluated durations of the recent vaccination exposure, unadjusted VE against severe disease ranged from 83.9\\u0026ndash;85.9% whereas VE against symptomatic infection ranged from 21.2\\u0026ndash;46.2% indicating that bias of VE against severe disease was less likely to be influenced by the exposure duration.\\u003c/p\\u003e \\u003cp\\u003eThe lack of a clear function of how infection-induced and vaccine-induced protection combine to become hybrid protection was one of multiple limitations of these simulations. We utilized published meta-analyses that attempted to characterize the waning effectiveness of vaccines\\u003csup\\u003e32\\u003c/sup\\u003e and hybrid protection,\\u003csup\\u003e33,35\\u003c/sup\\u003e but we required additional assumptions for our simulations. There is rich information on antibody titer trajectories\\u003csup\\u003e53,54\\u003c/sup\\u003e but challenges remain for determining the relationship between neutralization titers and protection.\\u003csup\\u003e55\\u003c/sup\\u003e We tried to create realistic simulations that were also succinct and understandable. As a result, we did not incorporate other known sources of bias such as errors in vaccine registry linkage\\u003csup\\u003e56\\u003c/sup\\u003e or correlation between COVID-19 and influenza vaccination.\\u003csup\\u003e39\\u003c/sup\\u003e Another major consequence of creating realistic simulations was the true VE was dependent on the population in each simulation. Therefore, bias in these simulations was not based on a true, underlying parameter.\\u003c/p\\u003e \\u003cp\\u003eIn addition, although we found differences in the bias associated with vaccination doses, this likely was attributable to the timing of the last vaccination dose. Fewer vaccination doses was typically associated with a longer duration since the last vaccination dose. Therefore, in this simulation people with fewer doses possessed less vaccine-induced protection and were more likely to have overall protection levels similar to unvaccinated people.\\u003c/p\\u003e\"},{\"header\":\"Conclusion\",\"content\":\"\\u003cp\\u003eTNDs have been recommended as the most efficient and feasible method for assessing VE.\\u003csup\\u003e57\\u003c/sup\\u003e Effectiveness of vaccinations delivered are based not only on the vaccine formulations and the circulating pathogens, but also on characteristics of the population, including people\\u0026rsquo;s underlying immunity from past infections. Prior SARS-CoV-2 infections, including the number, variant, and timing of past infections, cannot be ascertained with certainty and are more common in unvaccinated compared to vaccinated individuals.\\u003csup\\u003e12\\u003c/sup\\u003e Although VE estimates unadjusted for prior infection are lower than adjusted estimates, the difference was in line with accepted underestimates of VE. Extra care should be taken when performing analyses by number of total vaccine doses as more recent doses have the potential for greater bias when not controlled for past infection and doses further in the past have greater potential to result in negative VE estimates. Ideally, researchers could adjust VE estimates from a TND for prior infection history if data are available, but unadjusted VE estimates from a TND remain useful.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003eDisclaimer: The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the CDC.\\u003c/p\\u003e\\n\\u003cp\\u003eConflicts of interest: The authors declare that they do not have any commercial or other association that might pose a conflict of interest.\\u003c/p\\u003e\\n\\u003cp\\u003eFinancial support: This study was supported by the Centers for Disease Control and Prevention. Dr. Fireman\\u0026rsquo;s time was supported by the Centers for Disease Control and Prevention contract number 75D30120C07765 to Kaiser Foundation Hospitals.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eDeclaration of interests\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors declare no conflicts of interest.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAcknowledgments\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe findings and conclusions in this report are those of the authors and do not necessarily represent the views of the CDC.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eJackson ML, Nelson JC (2013) The test-negative design for estimating influenza vaccine effectiveness. 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Annual Estimates of the Resident Population by Single Year of Age and Sex for the United States: April 1, (2010) \\u003cem\\u003eto July 1, 2020 (NC-EST2020-AGESEX\\u003c/em\\u003e\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e-RES)\\u003c/span\\u003e\\u003cspan address=\\\"http://-RES)\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e. https://www2.census.gov/programs-surveys/popest/datasets/2010-2020/national/asrh/nc-est2020-agesex-res.csv (2021)\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eWiegand RE et al (2023) Estimated SARS-CoV-2 antibody seroprevalence trends and relationship to reported case prevalence from a repeated, cross-sectional study in the 50 states and the District of Columbia, United States\\u0026ndash;October 25, 2020-February 26, 2022. 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Report No. WHO/2019\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e-nCoV/vaccine_effectiveness/measurement/2021.1\\u003c/span\\u003e\\u003cspan address=\\\"http://-nCoV/vaccine_effectiveness/measurement/2021.1\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"nature-portfolio\",\"isNatureJournal\":true,\"hasQc\":false,\"allowDirectSubmit\":false,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Nature Portfolio\",\"twitterHandle\":\"\",\"acdcEnabled\":false,\"dfaEnabled\":false,\"editorialSystem\":\"ejp\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"vaccine effectiveness, test-negative design, prior infection\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4802667/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4802667/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eTest-negative designs (TNDs) are used to assess vaccine effectiveness (VE). Protection from infection-induced immunity may confound the association between case and vaccination status, but collecting reliable infection history can be challenging. If vaccinated individuals have less infection-induced protection than unvaccinated individuals, failure to account for infection history could underestimate VE, though the bias is not well understood. We simulated individual-level SARS-CoV-2 infection and COVID-19 vaccination histories. VE against symptomatic infection and VE against severe disease estimates unadjusted for infection history underestimated VE compared to estimates adjusted for infection history, and unadjusted estimates were more likely to be below 0%. TNDs assessing VE immediately following vaccine rollout introduced the largest bias and potential for negative VE against symptomatic infection. Despite the potential for bias, VE estimates from TNDs without prior infection information are useful because underestimation is rarely more than 8 percentage points.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Bias and negative values of COVID-19 vaccine effectiveness estimates from a test-negative design without controlling for prior SARS-CoV-2 infection\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-08-05 20:17:38\",\"doi\":\"10.21203/rs.3.rs-4802667/v1\",\"editorialEvents\":[],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"nature-communications\",\"isNatureJournal\":true,\"hasQc\":false,\"allowDirectSubmit\":false,\"externalIdentity\":\"NCOMMS\",\"sideBox\":\"Learn more about [Nature Communications](http://www.nature.com/ncomms/)\",\"snPcode\":\"\",\"submissionUrl\":\"https://mts-ncomms.nature.com/\",\"title\":\"Nature Communications\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"ejp\",\"reportingPortfolio\":\"Nature Communications\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"3bcc7184-ad71-4d40-a552-342de8b121d9\",\"owner\":[],\"postedDate\":\"August 5th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[{\"id\":35407028,\"name\":\"Health sciences/Medical research/Epidemiology\"},{\"id\":35407029,\"name\":\"Health sciences/Diseases/Infectious diseases/Viral infection\"}],\"tags\":[],\"updatedAt\":\"2024-11-21T08:06:16+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-4802667\",\"link\":\"https://doi.org/10.1038/s41467-024-54404-w\",\"journal\":{\"identity\":\"nature-communications\",\"isVorOnly\":false,\"title\":\"Nature Communications\"},\"publishedOn\":\"2024-11-20 05:00:00\",\"publishedOnDateReadable\":\"November 20th, 2024\"},\"versionCreatedAt\":\"2024-08-05 20:17:38\",\"video\":\"\",\"vorDoi\":\"10.1038/s41467-024-54404-w\",\"vorDoiUrl\":\"https://doi.org/10.1038/s41467-024-54404-w\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-4802667\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-4802667\",\"identity\":\"rs-4802667\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}