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The relationship between the cumulative numbers of cases and deaths reveals the confirmed case fatality ratio of a novel influenza A (H1N1) virus.

When a novel influenza virus emerges, it is crucial to gain an understanding of the virulence at the very early stage of a pandemic. If a high mortality is predicted, then corresponding countermeasures can be chosen and implemented, and the extent of the pandemic in the presence and absence of interventions is subsequently estimated. In the ongoing pandemic involving the influenza A (H1N1) virus 2009, such an early assessment was initially made based on confirmed cases whose risk of death was estimated at up to 0.5% (1–3). Although it later appeared that the risk of death among all symptomatic cases with medical attendance (i.e., symptomatic case fatality ratio [sCFR]) ranged from approximately 0.02–0.05% (4,5), a ratio which is more useful for the assessment of virulence and prediction of the mortality impact, epidemiological interpretation of minimally available data during the very early stages of the pandemic in the present study involves confirmed cases alone. Yoshikura (6) recently reported a linear relationship between the logarithms of the cumulative numbers of confirmed cases and deaths. In general, a log-log plot enables the relationship between two items to be interpreted and the relevant parameters estimated, given that an underlying power law mechanism exists (such as that observed for the individual contact heterogeneity of infectious diseases (7)). To facilitate epidemiological understanding of the underlying mechanisms behind the empirically observed linear relationship in a bottom-up fashion, a mechanistic statistical model is needed. This article aims to explicitly clarify the relationship between the cumulative numbers of confirmed cases and deaths, to apply this relationship to estimate the confirmed case fatality ratio of the 2009 H1N1 pandemic virus, and to compare the estimates between different countries. Let the cumulative numbers of confirmed cases and deaths by calendar time t be Ct and Dt, respectively. Based on a wellknown mechanistic relationship (1), the expectation of Dt given Ct is written as