Estimating the Case Fatality Ratio for COVID-19 using a Time-Shifted Distribution Analysis

Abstract

Estimating the case fatality ratio (CFR) for COVID-19 is an important aspect of public health. However, calculating CFR accurately is problematic early in a novel disease outbreak, due to uncertainties regarding the time course of disease and difficulties in diagnosis and reporting of cases. In this work, we present a simple method for calculating the case fatality ratio using only public case and death data over time by exploiting the correspondence between the time distributions of cases and deaths. The time-shifted distribution (TSD) analysis generates two parameters of interest: the delay time between reporting of cases and deaths and the case fatality ratio. These parameters converge reliably over time once the exponential growth phase has finished. Analysis is performed for early COVID 19 outbreaks in many countries, and we discuss corrections to CFR values using excess-death and seroprevalence data to estimate the infection fatality ratio (IFR). While CFR values range from 0.2-20% in different countries, estimates for IFR are mostly around 0.5-0.8% for countries that experienced moderate outbreaks and 1-3% for severe outbreaks. The simplicity and transparency of TSD analysis enhance its usefulness in characterizing a new disease as well as the state of the health and reporting systems.

Modelling COVID-19 outbreaks in USA with distinct testing, lockdown speed and fatigue rates

“…Indeed, our gamma distributed delay (mean μ = 21) of days after infection until death and fitted true cumulative case totals with ascertainment rate ρ ( t ), together estimate IFR ranging from as low as 0.001 (Guam, CI 0.0010–0.0014) to as high as 0.0283 (New Jersey, CI 0.024-0.035). There were outbreaks from mild to severe toll; with the fit IFR for the USA being 0.012 (CI 0.0108–0.0133) as of 21 June (cut-off date for deaths associated with infections on or before 31 May), similar to estimates from a different retrospective study [10].…”

“…In this way, our minimal number of identifiable parameter values can be compared among the states representing crucial control quantities, such as lockdown speed and fatigue half-life, and via analytically derived relations, we link outbreak size as inversely proportional to population (self) quarantine rate. We also provide estimates of commonly used quantifiers of outbreak severity, epidemic trajectory and effectiveness of control measures, such as infection fatality ratio (IFR) and the ratio of (estimated) true cases to reported cases, accounting for common sources of error in their prediction [9,10]. By estimating these quantities for all states and territories under one modelling framework we provide a comprehensive overview of the first wave outbreak in the USA.…”

Modeling COVID-19 outbreaks in United States with distinct testing, lockdown speed and fatigue rates

“…Indeed, our gamma distributed delay (mean µ = 21) of days after infection until death and fitted true cumulative case totals with ascertainment rate ρ ( t ), together estimate IFR ranging from as low as 0.001 (Guam) to as high as .0156 (Rhode Island). There were outbreaks from mild to severe toll; with the fit IFR for the United states being 0.009 ( CI .007 - .011) as of June 21 (cut-off date for deaths associated with infections on or before May 31), similar to estimates from a different retrospective study [14].…”

“…Indeed, the ratio of true cumulative cases to reported cases across states ranged from as low as low as 2.99 (Rhode Island) to as high as 17.88 (the US Virgin Islands) with a value of 6.62 ( CI 5.54-8.20), in line with CDC estimates [3]. Our fit IFR, both for every state and for the entire United states, works to counter both a common source of overestimation and a common source of underestimation [14], [6]. Indeed, our gamma distributed delay (mean µ = 21) of days after infection until death and fitted true cumulative case totals with ascertainment rate ρ ( t ), together estimate IFR ranging from as low as 0.001 (Guam) to as high as .0156 (Rhode Island).…”

“…In this way, our minimal number of identifiable parameter values can be compared among the states representing crucial control quantities, such as lockdown speed and fatigue, and via analytically derived relations, we link outbreak size as inversely proportional to population quarantine rate. We also provide estimates of commonly used quantifiers of outbreak severity, epidemic trajectory and effectiveness of control measures, such as Infection Fatality Ratio (IFR) and the ratio of (estimated) true cases to reported cases, accounting for common sources of error in their prediction [14], [6]. By estimating these quantities for all states and territories under one modeling framework we provide a comprehensive overview of the first wave outbreak in the United States.…”