Estimating COVID-19 Prevalence in the United States: A Sample Selection Model Approach

Abstract

the large shares of mild and asymptomatic cases. We developed a methodology that corrects observed positive test rates for non-random sampling to estimate population infection rates across U.S. states from March 31 to April 7. MethodsWe adapted a sample selection model that corrects for non-random testing to estimate population infection rates. The methodology compares how the observed positive case rate vary with changes in the size of the tested population, and applies this gradient to infer total population infection rates. Model identification requires that variation in testing rates be uncorrelated with changes in underlying disease prevalence. To this end, we relied on data on day-to-day changes in completed tests across U.S. states for the period March 31 to April 7, which were primarily influenced by immediate supply-side constraints. We used this methodology to construct predicted infection rates across each state over the sample period. We also assessed the sensitivity of the results to controls for state-specific daily trends in infection rates.

Estimates of COVID-19 Cases across Four Canadian Provinces

“…Consistent with the theoretical framework, we fi nd large estimates of β ranging from -1,093 to -1,391, which implies that the sample selection in testing approaches zero as the number of tests approaches the total population size. We also fi nd alternating signs on coeffi cient 1 2 3,, , consistent with the estimates of the power series approximation developed in Benatia et al (2020 ). Figure 2 presents scatterplots of the relationship between daily changes in per capita testing and the share of positive tests across states and provinces for the three time periods.…”

“…The estimated infection rates in Quebec are similar to those of the United Kingdom (2.7%) and several US states (Pennsylvania, 2.4%; Rhode Island, 2.4%; and Massachusetts, 3.4%). Meanwhile, the rates in Ontario are similar to those in Austria (1.1%), Denmark (1.1%), Vermont (1.4%), Virginia (1.4%), and Idaho (1.5%) in early April (see Benatia et al 2020 ;Ferguson et al 2020 ;Johndrow et al 2020 ;Javan et al 2020 ). Our results are also consistent with recent evidence from serological testing across several US jurisdictions that shows widespread undetected infection by mid-April ( Bendavid et al 2020 ; Conarck and Chang 2020 ; Goodman and Rothfeld 2020 ).…”

“…This article provides new evidence on the population prevalence of COVID-19 in Quebec, Ontario, Alberta, and British Columbia from late March to early May. Our analysis adapts a sample selection model approach developed in Benatia et al (2020 ). We fi nd widespread population that there were 11-12 population infections per diagnosed case.…”

“…In this section, we present the theoretical framework developed in Benatia et al (2020 ) to estimate COVID-19 prevalence. This framework motivates estimating Equation (6).…”

“…In this article, we estimate population infection rates for COVID-19 across four Canadian provinces-Quebec, Ontario, Alberta, and British Columbia-from late March to early May. The analysis is based on the methodology developed in Benatia, Godefroy, and Lewis (2020 ) that corrects observed infection rates among tested individuals for non-random sampling to calculate infection rates in the overall population. 1 To implement the procedure, we estimate the relationship between the number of tests and the share of positive tests.…”