Supplemental Methods.

Table A. State-wide seroprevalence calibration data. Table B. State-wide seroprevalence validation data. Table C. Posterior distributions and convergence diagnostic of n and SP_o for individual states (random effects). Table D. Primary model posterior estimates of prevalence (undiagnosed and total) and seroprevalence as of December 31, 2020. Table E. Geometric mean model posterior estimates of prevalence (undiagnosed and total) and seroprevalence as of December 31, 2020. Table F. International seroprevalence data. Fig A. Posterior distributions of the power parameter n and the seroprevalence offset SP_o for individual states using the primary random effects model. The fixed effect is denoted by “F.E.,” and the vertical dashed line represents its posterior median. For the simpler geometric mean model, the power parameter is fixed at n = ½, and the F.E. posterior median [CrI] for SP_o is 0.90 [0.38–1.50]. Fig B. Scatter plot of seroprevalence predictions (posterior median for primary random effects model) versus calibration data (reported point estimate and 95% CI). The solid line represents equality, the dashed line is +/- one residual standard error, and the dotted line is the 95% CrI residual error. The adjusted R² is calculated from a linear model based on the log-transformed posterior medians and the observed point estimates. Results for the simpler geometric mean (n = ½) model are similar, with residual SE of 1.33-fold, 95% CrI range of 3.01-fold, and adjusted R² = 0.78. Fig C. Scatter plot of seroprevalence predictions (posterior median for primary random effects model) versus validation data (reported point estimate and 95% CI). The solid line represents equality, the dashed line is +/- one residual standard error, and the dotted line is the 95% CrI residual error. The adjusted R² is calculated from a linear model based on the log-transformed posterior medians and the observed point estimates. Results for the simpler geometric mean (n = ½) model are similar, with residual SE of 1.39-fold, 95% CrI range of 3.62-fold, and adjusted R² = 0.77. Fig D. Scatter plot of active infection prevalence predictions from semi-empirical model (posterior median for primary random effects model) versus those from epidemiologic models (posterior median and 95% CrI). The solid line represents equality. The residual standard error (RSE) and adjusted R² are from the comparison of natural log-transformed median predictions. Results for the simpler geometric mean (n = ½) model are similar, with RSEs of 1.71-fold and 2.01-fold, 95% CrI ranges of 1.77-fold and 2.01-fold, and adjusted R² values = 0.73 and 0.71, for the Extended SEIR and Imperial models, respectively. Fig E. Boxplots (box = IQR, line = median, whiskers = 95% CrI) of posterior estimate of infection prevalence (A) and seroprevalence (B) across states and for the U.S. overall as of December 31, 2020, using the primary random effects model. In (B), for comparison, cumulative reported cases are shown with a 14-day lag to allow time for seroconversion (error bars denote range of 7–21 day lags). Fig F. A) Map of estimated undiagnosed (A) and total (B) prevalence and transmission trends and overall seroprevalence (C) as of December 31, 2020, based on data through January 15, 2021. Values based on the simpler geometric mean model (see Fig 4 for primary random effects model predictions). The maps were generated using the R package usmap https://cran.r-project.org/web/packages/usmap/index.html (GPL-3), which uses shape files from the U.S. Census Bureau (the link provided in documentation is here: https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html). Fig G. Boxplots (box = IQR, line = median, whiskers = 95% CrI) of posterior estimate of infection prevalence (A) and seroprevalence (B) across states and for the U.S. overall as of December 31, 2020, using the simpler geometric mean model. In (B), for comparison, cumulative reported cases are shown with a 14-day lag to allow time for seroconversion (error bars denote range of 7–21 day lags). Fig H. Bias estimates from primary random effects model. A, B) Comparison of test positivity (14-day average) and semi-empirical prevalence estimates (median and 95% CrI) across all states (A) or across the U.S. in aggregate (B) from April 1-December 31, 2020. Diagonal lines denote different levels of positivity bias, as illustrated in Fig 1A. C, D) Comparison of cumulative reported cases, with 14-day lag to allow for conversion to seropositivity, and semi-empirical seropositivity estimates (median and 95% CrI) across all states (C) or across the U.S. in aggregate (D) from April 1-December 31, 2020. Diagonal lines denote different levels of cumulative case under-reporting. Results for the simpler geometric mean (n = ½) model are similar. Fig I. Examples of five states where the trends in reported case rates and positivity rates diverged (i.e., one increasing, the other decreasing). For each state, the top panel is the active infection (total diagnosed and undiagnosed) prevalence as predicted by the semi-empirical model (posterior median and 95% CrI), the second panel is the active undiagnosed infection prevalence, whereas the bottom three panels show the reported case, positivity, and testing rates, each averaged over the previous 14 days. Fig J. Application of semi-empirical model using random effects posterior distributions from U.S. states to other nations/countries. COVID-19 antibody seroprevalence estimates (posterior median and 95% credible intervals) for each nation/country with state-wide seroprevalence data (Table F, reported point estimates and 95% confidence intervals shown). Fig K. Conceptual model of undiagnosed prevalence (Eqs 7–9). Assuming a time interval between infection and seropositivity = T_inf, each time point t, we can subdivide the undiagnosed infection prevalence I_U into T_inf “subcompartments” I_U,m (m = 1…T_inf). The number of undiagnosed individuals who are diagnosed each day is I_U ✕ Λ (diagnosis considered sampling without replacement of I_U). The number of undiagnosed individuals who become newly undiagnosed seropositive (entering SP_U the next day) is simply the number in the last subcompartment multiplied by another factor of (1 –Λ) to account for the fraction that get diagnosed that day. Fig L. Sensitivity of parameter estimates to changing averaging time τ from 14 to 7 or 28 days. A) Posterior distributions of power parameter n; B) posterior distributions of seroprevalence offset SP_o. Fig M. Sensitivity of seroprevalence predictions to changing averaging time τ from 14 to 7 or 28 days. All predictions are posterior medians. Fig N. Sensitivity of undiagnosed prevalence predictions to changing averaging time τ from 14 to 7 or 28 days. All predictions are posterior medians. Fig O. Sensitivity of total prevalence predictions to changing averaging time τ from 14 to 7 or 28 days. All predictions are posterior medians.

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