Estimates of SARS-COV-2 Behavior in the COVID-19 Crisis: Addressing Sample-Selection Bias for Public Health Applications

Abstract

This study surveys and assesses the implications from recent empirical studies and reports to highlight the characteristics of SARS-Cov-2 and the COVID-19 crisis, and then proposes a recursive bivariate probit (RBP) model specification and possible applications. The RBP model addresses sample selection bias to estimate key determinants of virus infection given nonrandom testing. Applicable to anonymized case-level or widely available local-area data in the U.S., multiple data sources are shown. With suitable data the model can control for observed (e.g. population density) and unobserved factors to estimate the marginal effects of varying state-prescribed measures and behavioral social distancing. Case-level scoring models may, in addition, eventually assist in clinical diagnostic assessments. Although not proposed to substitute for more random population testing and other methods, results could also be used in advance of more testing. Uncertain assumptions in epidemiological models reflect unclear effects from gradations of social distancing now occurring. Despite many calls for broader testing and targeted quarantining in the U.S., many practical obstacles remain, leaving unknowns, especially across local areas. Differing local transmission rates respond to stronger or weaker social distancing and quarantining. High risks from latent non-quarantining spread warn of potential overwhelming local outbreaks. The insidious nature of SARS-Cov-2 invites complacency, especially in non-hotspot areas. Complacent behaviors can fail to adequately address the public-goods problem, leading to various forms of continued local and macro COVID-19 waves and crises. To assess a worst case scenario, no model projection is needed, only the herd immunity threshold equation, estimates of the reproduction ratio, and the estimated mortality rate. With no ultimately successful countermeasures in treatment, vaccine, and non-pharmaceutical interventions (NPIs), the analysis here suggests an eventual number of deaths much like the 1918 pandemic in U.S. deaths per capita (1.8-2.7 million U.S. deaths) and in the total number of deaths worldwide (around 50 million). This toll also reflects a hypothetical global “surrender” strategy of business-as-usual and no social distancing, which in practice no nation has followed. Some successes across the three broad social countermeasure efforts – which appears most likely, in a mix of outcomes – can lessen the high social costs.