Potential Biases in Estimating Absolute and Relative Case-Fatality Risks during Outbreaks

Abstract

Estimating the case-fatality risk (CFR)-the probability that a person dies from an infection given that they are a case-is a high priority in epidemiologic investigation of newly emerging infectious diseases and sometimes in new outbreaks of known infectious diseases. The data available to estimate the overall CFR are often gathered for other purposes (e.g., surveillance) in challenging circumstances. We describe two forms of bias that may affect the estimation of the overall CFR-preferential ascertainment of severe cases and bias from reporting delays-and review solutions that have been proposed and implemented in past epidemics. Also of interest is the estimation of the causal impact of specific interventions (e.g., hospitalization, or hospitalization at a particular hospital) on survival, which can be estimated as a relative CFR for two or more groups. When observational data are used for this purpose, three more sources of bias may arise: confounding, survivorship bias, and selection due to preferential inclusion in surveillance datasets of those who are hospitalized and/or die. We illustrate these biases and caution against causal interpretation of differential CFR among those receiving different interventions in observational datasets. Again, we discuss ways to reduce these biases, particularly by estimating outcomes in smaller but more systematically defined cohorts ascertained before the onset of symptoms, such as those identified by forward contact tracing. Finally, we discuss the circumstances in which these biases may affect non-causal interpretation of risk factors for death among cases.

Fig 1. Illustration of delayed reporting bias in an exponentially growing epidemic.

In an ongoing epidemic, there will typically be a delay between the reporting of a case and the reporting of the death of that case, if the infected person dies. Thus, at any moment, there will be some cases reported who will die of the infection but who have not yet died, or whose deaths have not yet been reported. Simple division of the number of deaths reported by week w (green), by the number of cases reported by week w (blue) will underestimate the CFR because the numerator does not include all those cases in the denominator who will eventually die. With a reporting delay of 3 weeks for deaths compared to cases, the reported deaths curve will be shifted 3 weeks to the right, relative to the curve of the total number of cases reported by week w who will die (red). If the epidemic doubling time is 2 weeks, as shown here, the underestimate of CFR will be by a factor of about 2^3/2 ≈ 2.8, with the exponent being the number of epidemic doubling times that pass between case reporting and death reporting. In reality, there will be a distribution of reporting delays rather than a fixed delay, making this a heuristic rather than exact approach. The problem is ameliorated in an epidemic that grows more slowly or less than exponentially. For more details, see references in Table 1.