Benchmarking the Covid-19 pandemic across countries and states in the USA under heterogeneous testing

Abstract

Scientists and policymakers need to compare the incidence of Covid-19 across territories or periods with various levels of testing. Benchmarking based on the increase in total cases or case fatality rates is one way of comparing the evolution of the pandemic across countries or territories and could inform policy decisions about strategies to control coronavirus transmission. However, comparing cases and fatality rates across regions is challenging due to heterogeneity in testing and health systems. We show two complementary ways of benchmarking across territories and in time. First, we used multivariate regressions to estimate the test-elasticity of Covid-19 case incidence. Cases grow less than proportionally with testing when assessing weekly changes or looking across states in the USA. They tend to be proportional or even more than proportional when comparing the month-to-month evolution of an average country in the pandemic. Our results were robust to various model specifications. Second, we decomposed the growth in cases into test growth and positive test ratio growth to intuitively visualize the components of case growth. We hope these results can help support evidence-based decisions by public officials and help the public discussion when comparing across territories and in time.

Figure 1

Changes in Covid-19 cases per capita relative to changes in the number of tests for countries and states in the USA. Panels show the growth in weekly cases and tests (in logarithms of the per capita rate) for (A) countries and (B) States in the USA that have reported Covid-19 cases. Data compares the week ending April 10th, 2020, with the previous week. (A) β = 0.86; 95% CI 0.57–1.15; p < 0.001; (B) β = 0.17; 95% CI 0.03–0.31; p = 0.02. The Supplementary material shows a higher elasticity for (B) if we restrict logarithmic week-on-week changes of testing rates between − 1 and + 1.5, the range observed in the global sample. In Supplementary Material, Figure S1: β = 0.54, p < 0.0001, 95%CI: 0.36–0.71. Names and abbreviations for countries and US States are included in the Supplementary Material’s Table S5.

Figure 2

Growth Decomposition of Cases: Testing Growth vs. PTR Growth. Week-on-week growth of Testing and PTR across countries and US states. Points are countries (A) or US states (B). In both panels, we plot the growth of tests and PTR between the week ending April 10th and the previous week. The functional form of the previously mentioned growth is the change in the natural logarithm of per capita rates per week. The growth decomposition of cases is the sum of the increase in testing (horizontal axis) and PTR growth (vertical axis). The line is not a regression but represents zero case growth as $\mathrm{\Delta }\ln Cases=\mathrm{\Delta }\ln Tests+\mathrm{\Delta }\ln PTR=0$. While territories above the line have growing cases, territories below the line have decreasing cases. The four quadrants (I to IV) in gray show the various combinations of increasing or decreasing testing and PTR. Notably, quadrants (II) and (IV) include growing and declining cases, depending on the side of the zero-case growth line. For instance, in (B), KY appears with decreasing cases but is associated with fewer tests and more PTR. The opposite combination happened in (A) for Ecuador. For visual purposes, countries in A were restricted to a pop > 5 million people, and US states in (B) exclude WA. Countries are represented by ISO 3 codes and US states by two-digit codes. The supplementary material shows how the USA moved over several weeks in the cross-country plot. Names and abbreviations for countries and US States are included in the Supplementary Material.

Figure 3

Exact decomposition of cases in the United States (a) and the United Kingdom (b).

Figure 4

Exact decomposition of Covid-19 cases, month-on-month (growth in June 2020). The line is not a regression but represents the menu of possibilities of zero case growth. Names and abbreviations for countries and US States are included in the Supplementary Material.