Estimating SARS-CoV-2 seroprevalence

Abstract

Governments and public health authorities use seroprevalence studies to guide responses to the COVID-19 pandemic. Seroprevalence surveys estimate the proportion of individuals who have detectable SARS-CoV-2 antibodies. However, serologic assays are prone to misclassification error, and non-probability sampling may induce selection bias. In this paper, non-parametric and parametric seroprevalence estimators are considered that address both challenges by leveraging validation data and assuming equal probabilities of sample inclusion within covariate-defined strata. Both estimators are shown to be consistent and asymptotically normal, and consistent variance estimators are derived. Simulation studies are presented comparing the estimators over a range of scenarios. The methods are used to estimate severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence in New York City, Belgium, and North Carolina.

Keywords: COVID-19; diagnostic tests; estimating equations; seroepidemiologic studies; standardization.

Figure 1.

Panels (a) and (b) represent selection bias in the simulation studies of data generating processes 3 and 4, described in Sections 4.3.1 and 4.3.2, respectively. Circle size is proportional to prevalence. Points are jittered slightly for legibility, and the diagonal lines denote equality between ${\gamma }_j$ (stratum proportion) and $s_j$ (sampling probability).

Figure 2.

Empirical bias of the Rogan–Gladen (${\hat{\pi }}_{RG}$), non-parametric standardized (${\hat{\pi }}_{SRG}$), and logistic regression standardized (${\hat{\pi }}_{SRGM}$) estimators from simulation study for data generating process 3, described in Section 4.3.1. The six facets correspond to a given combination of sensitivity (‘Sens’) and specificity (‘Spec’).

Figure 3.

Bias results from simulation study on data generating process 4, described in Section 4.3.2. Figure layout is as in Figure 2.

Figure 4.

Estimates and corresponding 95% confidence intervals for each of five collection rounds for the New York City seroprevalence study (Stadlbauer et al., 2021), stratified by routine and urgent care groups, described in Section 5.1.

Figure 5.

Estimates and corresponding 95% confidence intervals for each of seven collection rounds for the 2020 Belgian seroprevalence study (Herzog et al., 2022), described in Section 5.2.