Using test positivity and reported case rates to estimate state-level COVID-19 prevalence and seroprevalence in the United States

Abstract

Accurate estimates of infection prevalence and seroprevalence are essential for evaluating and informing public health responses and vaccination coverage needed to address the ongoing spread of COVID-19 in each United States (U.S.) state. However, reliable, timely data based on representative population sampling are unavailable, and reported case and test positivity rates are highly biased. A simple data-driven Bayesian semi-empirical modeling framework was developed and used to evaluate state-level prevalence and seroprevalence of COVID-19 using daily reported cases and test positivity ratios. The model was calibrated to and validated using published state-wide seroprevalence data, and further compared against two independent data-driven mathematical models. The prevalence of undiagnosed COVID-19 infections is found to be well-approximated by a geometrically weighted average of the positivity rate and the reported case rate. Our model accurately fits state-level seroprevalence data from across the U.S. Prevalence estimates of our semi-empirical model compare favorably to those from two data-driven epidemiological models. As of December 31, 2020, we estimate nation-wide a prevalence of 1.4% [Credible Interval (CrI): 1.0%-1.9%] and a seroprevalence of 13.2% [CrI: 12.3%-14.2%], with state-level prevalence ranging from 0.2% [CrI: 0.1%-0.3%] in Hawaii to 2.8% [CrI: 1.8%-4.1%] in Tennessee, and seroprevalence from 1.5% [CrI: 1.2%-2.0%] in Vermont to 23% [CrI: 20%-28%] in New York. Cumulatively, reported cases correspond to only one third of actual infections. The use of this simple and easy-to-communicate approach to estimating COVID-19 prevalence and seroprevalence will improve the ability to make public health decisions that effectively respond to the ongoing COVID-19 pandemic.

Fig 1. Conceptual model for relationship between test positivity, prevalence of infection, and testing rate.

(A) Compartmental representation of how the relationships between new infections, undiagnosed and diagnosed prevalence (I_U and I_D) and seroprevalence (SP_U and SP_D) are modeled for each state, given a bias with power n. All observational inputs are the past τ-day averages of number of positive tests N_+,τ(t) and number of tests performed N_test,τ(t), the corresponding test positivity rate P_+,τ(t) and reported case rate C_+,τ(t), and the state population size N. For diagnosed prevalence and seroprevalence, the observational input is the daily reported cases N_+,τ, and the model parameters are the recovery time after diagnosis T_rec and the time from infection to seropositivity T_inf. For undiagnosed prevalence and seroprevalence, our model assumes the test positivity rate is correlated to delayed undiagnosed disease prevalence with a bias parameter b(t) modeled as a negative power function of the testing rate b(t) = [N_test,τ(t)/N]^–n (Eq 2). The additional parameters consist of the power parameter n and the initial (missed) seroprevalence SP_o. The effective rate parameter 1/T_eff is time-dependent, and accounts for both T_inf and ongoing diagnoses so as to not “double count.” Prevalence and seroprevalence are evaluated with a lag time t_lag, assumed equal to half the averaging time τ/2. In (B), the diagonal lines represent different values of the bias parameter. In (C), the relationship between testing rate and bias parameter represented by Eq (4) is illustrated. Here the shaded region represents different powers n ranging from 0.1 (lower bound bias) to 0.9 (upper bound bias), the solid line represents n = ½.

Fig 2. Calibration results of our semi-empirical model for COVID-19 antibody seroprevalence (posterior median and 95% credible intervals for primary random effects model; posterior median only for geometric mean n = ½ model) for each state with state-wide seroprevalence data (reported point estimates and 95% confidence intervals shown).

Open circles represent validation data not used for model calibration; remaining symbols represent calibration data.

Fig 3. Validation of COVID-19 infection prevalence estimates (posterior median for both primary random effects model and simpler geometric mean n = ½ model) for each state in comparison to posterior median estimates and 95% credible intervals from two data-driven epidemiologic models: an extended-SEIR model calibrated to reported cases and confirmed deaths through July 22, 2020 [23] and a semi-mechanistic model calibrated to confirmed deaths through July 20, 2020 by Imperial College [37]).

Fig 4

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 7, 2021. Values based on primary random effects model. Results for the simpler geometric mean model are provided in Fig F in S1 Text. 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).