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Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: a Case Study of an Influenza Pandemic

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Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: a Case Study of an Influenza Pandemic Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: A Case Study of an Influenza Pandemic Hiroshi Nishiura1*, Don Klinkenberg1, Mick Roberts2, Johan A. P. Heesterbeek1 1 Theoretical Epidemiology, University of Utrecht, Utrecht, The Netherlands, 2 Centre for Mathematical Biology, Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand Abstract Background: The case fatality ratio (CFR), the ratio of deaths from an infectious disease to the number of cases, provides an assessment of virulence. Calculation of the ratio of the cumulative number of deaths to cases during the course of an epidemic tends to result in a biased CFR. The present study develops a simple method to obtain an unbiased estimate of confirmed CFR (cCFR), using only the confirmed cases as the denominator, at an early stage of epidemic, even when there have been only a few deaths. Methodology/Principal Findings: Our method adjusts the biased cCFR by a factor of underestimation which is informed by the time from symptom onset to death. We first examine the approach by analyzing an outbreak of severe acute respiratory syndrome in Hong Kong (2003) with known unbiased cCFR estimate, and then investigate published epidemiological datasets of novel swine-origin influenza A (H1N1) virus infection in the USA and Canada (2009). Because observation of a few deaths alone does not permit estimating the distribution of the time from onset to death, the uncertainty is addressed by means of sensitivity analysis. The maximum likelihood estimate of the unbiased cCFR for influenza may lie in the range of 0.16–4.48% within the assumed parameter space for a factor of underestimation. The estimates for influenza suggest that the virulence is comparable to the early estimate in Mexico. Even when there have been no deaths, our model permits estimating a conservative upper bound of the cCFR. Conclusions: Although one has to keep in mind that the cCFR for an entire population is vulnerable to its variations among sub-populations and underdiagnosis, our method is useful for assessing virulence at the early stage of an epidemic and for informing policy makers and the public. Citation: Nishiura H, Klinkenberg D, Roberts M, Heesterbeek JAP (2009) Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: A Case Study of an Influenza Pandemic. PLoS ONE 4(8): e6852. doi:10.1371/journal.pone.0006852 Editor: Jean Peccoud, Virginia Tech, United States of America Received June 24, 2009; Accepted August 5, 2009; Published August 31, 2009 Copyright: ß 2009 Nishiura et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: H.N. and H.H. were supported by the Netherlands Organization for Scientific Research (NWO, grant 918.56.620 and 851.40.074). M.R. received support from the Marsden Fund under contract MAU0809. He also acknowledges Massey University and the University of Utrecht for supporting his sabbatical period of research in Utrecht. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected] Introduction marker, as was for example the case in a novel swine-origin influenza A (H1N1) virus (S-OIV), does not necessarily indicate When an emerging influenza virus appears in humans, an early that the virus is benign [7]. Another is an epidemiological concern is whether the virus has the potential to cause a approach to quantification of the case fatality ratio (CFR), the devastating pandemic, i.e., the global spread of an infection killing conditional probability of death given infection (or disease; see a substantial number of people. To assess the pandemic potential, below). two critical aspects need to be studied: the transmission potential The CFR in general is vaguely defined as the ratio of deaths to and the clinical severity of the infection [1–3]. It is widely known cases, whose denominator should ideally be the total number of in epidemiology that the former aspect, the transmission potential, infections, but is frequently taken to be only the diagnosed cases can be quantified by the reproduction number, i.e., the average due to the impossibility of counting all infected individuals. number of secondary cases generated by a single primary case Because in the early phase of an outbreak information is often [1,4], by characterizing the heterogeneous patterns of transmission limited to confirmed cases, we concentrate on confirmed cases (e.g. age-specificity) [5], and by measuring other epidemiological only, and refer to the CFR as the confirmed CFR (cCFR) for quantities such as household secondary attack rate. There are two clarity. As the world has experienced a global spread of S-OIV different approaches to assessing the latter aspect of a pandemic, since April 2009, methods have been sought for the real-time the virulence of infection. One is to explore specific genetic assessment of virulence by measuring the cCFR which is a markers of the virus that are known to be associated with severe representative of the epidemiological measurements of virulence influenza (e.g. the PB1 gene) [6], although the absence of a known [2,3]. Nevertheless, a much-used crude estimate of the cCFR, i.e. PLoS ONE | www.plosone.org 1 August 2009 | Volume 4 | Issue 8 | e6852 Early Assessment of Virulence the ratio of the cumulative number of deaths to cases at calendar In the following, the notation used to represent the three time t, tends to yield a biased (and mostly underestimated) cCFR different statistical measurements of cCFR is: (i) bt, which is a due to the time-delay from onset to death [8]; similar estimates of crude, biased estimate of the cCFR calculated at time t; (ii) p, such a biased cCFR for severe acute respiratory syndrome (SARS) which is an unbiased cCFR to be estimated in the present study, have shown how such estimates can vary substantially as an and is the unknown parameter that governed the outbreaks; and epidemic progresses, stabilizing only in the later stages of the (iii) pt, a random variable, which yields an estimator of p (see outbreak [8,9]. In the following we will use the terms biased and below) and is regarded as the realized value in one particular unbiased cCFR when we refer to this particular source of bias. outbreak. First, bt, a crude and biased estimate of cCFR, calculated Improving an early epidemiological assessment of an unbiased at time t, is given by the ratio of the cumulative number of deaths cCFR is therefore crucial for the initial determination of virulence, Dt to the cumulative number of confirmed cases Ct: shaping the level and choices of public health intervention, and providing advice to the general public [10]. To obtain an estimate Dt bt~ ð1Þ of the cCFR, the lesson from the SARS outbreak is that a Ct: statistical technique is required that corrects the underestimation, e.g. a technique addressing censoring [8,11,12]. Nevertheless, in During the outbreak of severe acute respiratory syndrome (SARS) the case of novel S-OIV, an early unbiased estimation of the cCFR in 2002–03, it was shown that this estimator, bt, considerably has appeared particularly challenging. Initial reports from the underestimates the cCFR [8]. This is easily demonstrated by government of Mexico suggested a virulent infection, whereas in relating Ct and Dt to the incidence function ct (i.e. the number of other countries the same virus was perceived as mild [13]. In the new confirmed cases on day t), and the conditional probability USA and Canada there were no deaths attributed to the virus in density function fs of the time from onset to death, given death. the first 10 days following a declaration of a public health First, Ct is the cumulative number of confirmed cases up to time t: emergency by the World Health Organization. Even under similar circumstances at the early stage of the global pandemic, public Xt C ~ c : health officials, policy makers and the general public want to know t i ð2Þ ~ the virulence of an emerging infectious agent. That is, a simple i 0 method for assessing cCFR is called for, even when only a few Second, Dt is the cumulative number of deaths up to time t: deaths have been reported, or even when there has been no report of deaths. Except for another unbiased cCFR estimate in Mexico Xt X? (0.4%, range 0.3–1.5%) [1], this early assessment has been Dt~pt ci{jfj: ð3Þ missing. In the USA, a technical discussion has taken place on the i~0 j~0 crude measurement of the biased cCFR using the cumulative numbers of deaths and confirmed cases so far [10]. As we mentioned above, pt is the realized proportion of confirmed In line with this, an epidemiological method and its practical cases to die from the infection, and is a random variable, which guide for early assessment of virulence are called for. The present would be an unbiased estimator for p. Therefore, bt can be study aims at developing a simple method to assess the virulence of rewritten as an emerging influenza virus at the early stage of the epidemic, Pt P? even when there have been only a few deaths or none at all. The ci{jfj method takes into account the time from the onset of symptoms to i~0 j~0 b ~p 4 death, while differing from previously published statistical methods t t Pt ð Þ which employ censoring techniques [8,11].
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