Estimation of standardized real-time fatality rate for ongoing epidemics

Abstract

Background: The fatality rate is a crucial metric for guiding public health policies during an ongoing epidemic. For COVID-19, the age structure of the confirmed cases changes over time, bringing a substantial impact on the real-time estimation of fatality. A 'spurious decrease' in fatality rate can be caused by a shift in confirmed cases towards younger ages even if the fatalities remain unchanged across different ages.

Methods: To address this issue, we propose a standardized real-time fatality rate estimator. A simulation study is conducted to evaluate the performance of the estimator. The proposed method is applied for real-time fatality rate estimation of COVID-19 in Germany from March 2020 to May 2022.

Findings: The simulation results suggest that the proposed estimator can provide an accurate trend of disease fatality in all cases, while the existing estimator may convey a misleading signal of the actual situation when the changes in temporal age distribution take place. The application to Germany data shows that there was an increment in the fatality rate at the implementation of the 'live with COVID' strategy.

Conclusions: As many countries have chosen to coexist with the coronavirus, frequent examination of the fatality rate is of paramount importance.

Fig 1. Simulation settings in scenarios I–IV.

Top panel: temporal age distributions of confirmed cases, where $q_t^{*\left(1\right)}$, $q_t^{*\left(2\right)}$, and $q_t^{*\left(3\right)}$ represent the proportion of young, middle and old age groups, respectively. Bottom panel: patterns of the temporal age-specific fatality rates, where $p_t^{\left(1\right)}$, $p_t^{\left(2\right)}$ and $p_t^{\left(3\right)}$ represent the fatality rates of the young, middle and old age groups, respectively.

Fig 2. Simulation results under scenarios I–IV.

Top panel: empirical averages of the age-specific real-time fatality estimates ${\mathbf{\text{rtaCFR}}}_t^{\left(j\right)},j=1,2,3$, overlayed with the true age-specific fatality rates. Bottom panel: the underlying overall fatality rate $\tilde{p}$, and empirical averages of the estimates rtaCFR_t and srtaCFR_t.

Fig 3. The daily numbers of confirmed cases and deaths in Germany.

Fig 4. Estimation of the real-time fatality rates for the COVID-19 data in Germany.

Left panel: Age-specific fatality rates for groups (1) 0 − 20 years old, (2) 20 − 60 years old, and (3) 60+ years old. Right panel: traditional CFR, rtaCFR_t and srtaCFR_t.

Fig 5. Sensitivity analysis.

Fig 6. Temporal age distribution of the confirmed cases in Germany.