Timely Case-Fatality Risk Estimation

To the Editor: The case-fatality risk (CFR) is one of the key indexes that directly captures the virulence of a disease and is used to determine real-time public health actions.1 In a complete pandemic in which the outcomes of all patients are known (death or cure), the estimation of the CFR is unbiased. However, during the course of an infectious disease, particularly in the early stage when there are few deaths or cures, adequate data are needed to provide a reliable and timely estimate of the CFR. When possible, comprehensive data should be systematically analyzed. For example, Wong2 conducted a systematic review for estimating the CFR of A/H1N1 in 2009, combining data from 33 countries or regions. Notably, before an epidemic is completed, there might be people who will eventually die but are still alive, which results in underestimation due to a delay between the onset of illness and death, ie, censoring. Therefore, good statistical models are needed to overcome this problem. During the early stage of an ongoing epidemic, daily notification data (daily cumulative admissions, cures, and deaths) are usually available in published materials. Based on this type of data, Yoshikura3 recommended using a log–log plot to visually display the ongoing disease patterns. This approach assumes a linear relation between the logarithm of the cumulative confirmed cases and deaths. Chen4 and Yip5 used a cure-death hazard ratio to estimate the CFR for a SARS epidemic. Garske,6 Nishiura,7 and Ejima8 each proposed new methods to adjust the CFR to account for the part that is due to censoring. These methods ultimately introduce a factor to the denominator of the crude CFR measurement. We conducted a Monte Carlo simulation study to assess the performance of the aforementioned six methods at various time points, under scenarios in which the observed timely CFR either was constant or changed over the course of the pandemic. We also used the Lam test to evaluate the constancy of timely CFR and a cure-death hazard ratio plot, which is a graphical method that plots the cumulative death hazard against the cumulative cure hazard, to visually evaluate the progress of the epidemic (eAppendix, https://links.lww.com/EDE/A878). The Yoshikura method underestimated the observed timely CFR, particularly when censoring rate was high (Figure A, B). The Chen method and the Yip method, the non-parametric methods using a cure-death hazard ratio, provided well-approximated estimates, both when the observed timely CFR was constant and when the CFR changed over the course of the epidemic. The Nishiura, Garske, and Ejima methods are parametric methods that incorporate the distribution of time from illness-onset to death. As suggested in sensitivity analysis (eAppendix, https://links.lww.com/EDE/A878), when distributional parameters were mis-specified, the gamma distribution contributed to a larger bias when compared with exponential distribution, which might be introduced by the mis-specification of standard deviation. All methods presented in our study were applied to SARS data in Hong Kong and Beijing in 2003. Applying the Lam test, the CFR was found to remain constant in Hong Kong (Z = 1.034, P = 0.301) but to change considerably in Beijing (Z = 25.485, P < 0.001). Our results showed that in Hong Kong (Figure C), although overestimation was observed on March 21, the Chen and Yip methods were close to the observed timely CFR on April 8 and remained stable thereafter. For Beijing (Figure D), the timely CFR was initially high, with an estimate from the Chen method of 0.49 on April 24, but decreased monotonically to an estimate of 0.10 on June 4 (eAppendix, https://links.lww.com/EDE/A878).FIGURE: A comparison of estimators for the case fatality risk. A, The CFR is constant (n = 1,000). Data were expressed as mean and 95% confidence interval for estimators. B, The CFR changes over the course of epidemic (n = 1,000). C, SARS in Hong Kong, with a cure-death hazard plot (top-right corner). The observed timely CFR was 0.17 on June 30. D, SARS in Beijing, with a cure-death hazard plot. The timely CFR of SARS in Beijing was not constant; therefore, a constant reference line is not provided. The Ejima method generated estimates that were too large to be shown in C and D.Zihang Lu Department of Biostatistics School of Public Health and Tropical Medicine Southern Medical University Guangzhou, China SickKids Research Institute Hospital for Sick Children Toronto, ON, Canada Zheng Chen Department of Biostatistics School of Public Health and Tropical Medicine Southern Medical University Guangzhou, China [email protected]

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