# Improving case fatality ratio estimates in ongoing pandemics through case-to-death time distribution analysis

## TL;DR

This paper introduces a new method to estimate case fatality ratios during pandemics by accounting for delays between case confirmation and death.

## Contribution

A novel distributed-delay method is proposed to improve real-time CFR estimation by incorporating case-to-death time distributions.

## Key findings

- The distributed-delay method recovers true CFR earlier than traditional methods in simulations.
- The method outperforms Baud’s and Generalized Baud’s methods in various outbreak scenarios.
- A negative association was found between eventual CFR and expected case-to-death time in COVID-19 data.

## Abstract

The case fatality ratio (CFR) is a vital metric for assessing the disease severity of novel pathogens. The widely used direct method of CFR estimation—the ratio of total confirmed deaths to total confirmed cases—is inherently simplistic, as it fails to account for the essential time lag between case confirmation to death, and reporting delays. These limitations often lead to biased CFR estimates, particularly in the early stages of outbreaks. This study introduces a novel approach—the distributed-delay method that, like the direct method, utilizes publicly available aggregate time-series data on cases and deaths. It estimates CFR by flexibly incorporating a case-to-death time distribution without requiring a priori assumptions on distribution parameters. Using a fitting approach to forecast case fatalities based on known or assumed case-to-death time distributions, the method consistently recovers true CFR much earlier than the direct method under various simulation settings. These settings reflect variability in disease severity, uncertainties in case-to-death time parameters, and limited knowledge of case-to-death time distributions. It outperforms other methods such as Baud’s, which assumes a non-zero constant case-to-death time, and the Generalized Baud’s method, which allows for a direct comparison with our new approach. While evaluations based on empirical data are challenging, our conclusions are supported by CFR estimates obtained using empirical COVID-19 data from 34 countries. As an added value, this analysis also demonstrates a significant negative association between eventual CFR and the expected case-to-death time within the context of COVID-19 data. Our study highlights the complexities of inferring real-time CFR from aggregate time-series case and death data, highlighting that refining this method can lead to accurate real-time CFR estimations for actual outbreaks.

The online version contains supplementary material available at 10.1038/s41598-025-89441-y.