The Time Required to Estimate the Case Fatality Ratio of Influenza Using Only the Tip of an Iceberg: Joint Estimation of the Virulence and the Transmission Potential
Identifieur interne : 000A24 ( Pmc/Checkpoint ); précédent : 000A23; suivant : 000A25The Time Required to Estimate the Case Fatality Ratio of Influenza Using Only the Tip of an Iceberg: Joint Estimation of the Virulence and the Transmission Potential
Auteurs : Keisuke Ejima [Japon] ; Ryosuke Omori [Japon, Hong Kong] ; Benjamin J. Cowling [Hong Kong] ; Kazuyuki Aihara [Japon] ; Hiroshi NishiuraSource :
- Computational and Mathematical Methods in Medicine [ 1748-670X ] ; 2012.
Abstract
Estimating the case fatality ratio (CFR) of a novel strain of influenza virus during the early stage of the pandemic is one of key epidemiological tasks to be conducted as rapid research response. Past experience during the epidemics of severe acute respiratory syndrome (SARS) and influenza A (H1N1-2009) posed several technical challenges in estimating the CFR in real time. The present study aimed to develop a simple method to estimate the CFR based on readily available datasets, that is, confirmed cases and deaths, while addressing some of the known technical issues. To assess the reliability and validity of the proposed method, we examined the minimum length of time required for the assigned CFR to be included within the 95% confidence intervals and for the estimated CFR to be below a prespecified cut-off value by means of Monte Carlo simulations. Overall, the smaller the transmission potential was, the longer it took to compare the estimated CFR against the cut-off value. If policymaking and public health response have to be made based on the CFR estimate derived from the proposed method and readily available data, it should be noted that the successful estimation may take longer than a few months.
Url:
DOI: 10.1155/2012/978901
PubMed: 22649483
PubMed Central: 3357941
Affiliations:
- Hong Kong, Japon
- Kyūshū, Préfecture de Fukuoka, Région de Kantō
- Fukuoka, Tokyo
- Université de Kyūshū, Université de Tokyo
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Past experience during the epidemics of severe acute respiratory syndrome (SARS) and influenza A (H1N1-2009) posed several technical challenges in estimating the CFR in real time. The present study aimed to develop a simple method to estimate the CFR based on readily available datasets, that is, confirmed cases and deaths, while addressing some of the known technical issues. To assess the reliability and validity of the proposed method, we examined the minimum length of time required for the assigned CFR to be included within the 95% confidence intervals and for the estimated CFR to be below a prespecified cut-off value by means of Monte Carlo simulations. Overall, the smaller the transmission potential was, the longer it took to compare the estimated CFR against the cut-off value. If policymaking and public health response have to be made based on the CFR estimate derived from the proposed method and readily available data, it should be noted that the successful estimation may take longer than a few months.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Ma, J" uniqKey="Ma J">J Ma</name></author><author><name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P Van Den Driessche</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H Nishiura</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author><author><name sortKey="Riley, S" uniqKey="Riley S">S Riley</name></author><author><name sortKey="Cauchemez, S" uniqKey="Cauchemez S">S Cauchemez</name></author><author><name sortKey="Ghani, Ac" uniqKey="Ghani A">AC 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Comput Math Methods Med</journal-id><journal-id journal-id-type="iso-abbrev">Comput Math Methods Med</journal-id><journal-id journal-id-type="publisher-id">CMMM</journal-id><journal-title-group><journal-title>Computational and Mathematical Methods in Medicine</journal-title></journal-title-group><issn pub-type="ppub">1748-670X</issn><issn pub-type="epub">1748-6718</issn><publisher><publisher-name>Hindawi Publishing Corporation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">22649483</article-id><article-id pub-id-type="pmc">3357941</article-id><article-id pub-id-type="doi">10.1155/2012/978901</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>The Time Required to Estimate the Case Fatality Ratio of Influenza Using Only the Tip of an Iceberg: Joint Estimation of the Virulence and the Transmission Potential</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Ejima</surname><given-names>Keisuke</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Omori</surname><given-names>Ryosuke</given-names></name><xref ref-type="aff" rid="I2"><sup>2</sup></xref><xref ref-type="aff" rid="I3"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Cowling</surname><given-names>Benjamin J.</given-names></name><xref ref-type="aff" rid="I3"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Aihara</surname><given-names>Kazuyuki</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref><xref ref-type="aff" rid="I4"><sup>4</sup></xref></contrib><contrib contrib-type="author"><name><surname>Nishiura</surname><given-names>Hiroshi</given-names></name><xref ref-type="aff" rid="I3"><sup>3, 5</sup></xref><xref ref-type="aff" rid="I5"></xref><xref ref-type="corresp" rid="cor1">*</xref></contrib></contrib-group><aff id="I1"><sup>1</sup>Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</aff><aff id="I2"><sup>2</sup>Department of Biology, Faculty of Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan</aff><aff id="I3"><sup>3</sup>School of Public Health, The University of Hong Kong, Level 6, Core F, Cyberport 3, 100 Cyberport Road, Pokfulam, Hong Kong</aff><aff id="I4"><sup>4</sup>Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan</aff><aff id="I5"><sup>5</sup>PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan</aff><author-notes><corresp id="cor1">*Hiroshi Nishiura: <email>nishiura@hku.hk</email></corresp><fn fn-type="other"><p>Academic Editor: Gerardo Chowell</p></fn></author-notes><pub-date pub-type="ppub"><year>2012</year></pub-date><pub-date pub-type="epub"><day>10</day><month>5</month><year>2012</year></pub-date><volume>2012</volume><elocation-id>978901</elocation-id><history><date date-type="received"><day>19</day><month>1</month><year>2012</year></date><date date-type="rev-recd"><day>21</day><month>2</month><year>2012</year></date><date date-type="accepted"><day>22</day><month>2</month><year>2012</year></date></history><permissions><copyright-statement>Copyright © 2012 Keisuke Ejima et al.</copyright-statement><copyright-year>2012</copyright-year><license xlink:href="https://creativecommons.org/licenses/by/3.0/"><license-p>This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p></license></permissions><abstract><p>Estimating the case fatality ratio (CFR) of a novel strain of influenza virus during the early stage of the pandemic is one of key epidemiological tasks to be conducted as rapid research response. Past experience during the epidemics of severe acute respiratory syndrome (SARS) and influenza A (H1N1-2009) posed several technical challenges in estimating the CFR in real time. The present study aimed to develop a simple method to estimate the CFR based on readily available datasets, that is, confirmed cases and deaths, while addressing some of the known technical issues. To assess the reliability and validity of the proposed method, we examined the minimum length of time required for the assigned CFR to be included within the 95% confidence intervals and for the estimated CFR to be below a prespecified cut-off value by means of Monte Carlo simulations. Overall, the smaller the transmission potential was, the longer it took to compare the estimated CFR against the cut-off value. If policymaking and public health response have to be made based on the CFR estimate derived from the proposed method and readily available data, it should be noted that the successful estimation may take longer than a few months.</p></abstract></article-meta></front><floats-group><fig id="fig1" position="float"><label>Figure 1</label><caption><p>A single simulation run and the joint estimation results of the case fatality ratio and the exponential growth rate. The assigned CFR value is 0.5%, and the exponential growth rate <italic>r</italic> is set at 0.15 per day. ((a) and (b)) Incidence of confirmed cases and deaths as a function of epidemic days. The epidemic day 0 is the date on which an index case is infected. The numbers of confirmed cases and deaths increase exponentially. ((c) and (d)) The maximum likelihood estimates of (c) the exponential growth rate <italic>r</italic> and (d) the case fatality ratio with the 95% confidence intervals. The 95% confidence intervals were computed by employing the profile likelihood. Unfilled circles are the maximum likelihood estimates accompanied by the whiskers extending to lower and upper 95% confidence intervals. The dotted horizontal line shows the assigned parameter value.</p></caption><graphic xlink:href="CMMM2012-978901.001"></graphic></fig><table-wrap id="tab1" position="float"><label>Table 1</label><caption><p>Coverage probability of the case fatality ratio (CFR) for each set of parameter values. </p></caption><table frame="hsides" rules="groups"><tbody><tr><td rowspan="1" colspan="1"><graphic xlink:href="CMMM2012-978901.tab.001"></graphic></td></tr></tbody></table><table-wrap-foot><fn><p>CFR: case fatality ratio (assigned value). All the values were calculated as the proportion of successful simulation runs with the 95% confidence intervals that include the assigned CFR value among the total of 1000 simulation runs. The parameter <italic>r</italic> is the exponential growth rate of infection (per day). <italic>T</italic> is the epidemic date on which the estimation is performed. Those exceeding the coverage probability of 90% are highlighted in dark grey, while the cells with *mark and shaded in light grey represent combinations of parameter values which generate too large numbers of cases and for which we refrained from estimation.</p></fn></table-wrap-foot></table-wrap><table-wrap id="tab2" position="float"><label>Table 2</label><caption><p>Proportion of simulation runs in which the upper 95% confidential interval of CFR (<italic>p</italic>) falls below specified cut-off values. </p></caption><table frame="hsides" rules="groups"><tbody><tr><td rowspan="1" colspan="1"><graphic xlink:href="CMMM2012-978901.tab.002"></graphic></td></tr></tbody></table><table-wrap-foot><fn><p>CFR: case fatality ratio (assigned value). Relative CFR: the ratio of assigned CFR value relative to the cut-off value. The proportion of successful simulation runs with the upper 95% confidence interval below the pre-specified cut-off value is shown. The parameter <italic>r</italic> is the exponential growth rate of infection (per day). <italic>T</italic> is the epidemic date on which the comparison is performed. Those exceeding the proportion of 90% are highlighted in dark grey, while the cells with *mark and shaded in light grey represent combinations of parameter values which generate too large numbers of cases and for which we refrained from estimation.</p></fn></table-wrap-foot></table-wrap></floats-group></pmc><affiliations><list><country><li>Hong Kong</li><li>Japon</li></country><region><li>Kyūshū</li><li>Préfecture de Fukuoka</li><li>Région de Kantō</li></region><settlement><li>Fukuoka</li><li>Tokyo</li></settlement><orgName><li>Université de Kyūshū</li><li>Université de Tokyo</li></orgName></list><tree><noCountry><name sortKey="Nishiura, Hiroshi" sort="Nishiura, Hiroshi" uniqKey="Nishiura H" first="Hiroshi" last="Nishiura">Hiroshi Nishiura</name></noCountry><country name="Japon"><region name="Région de Kantō"><name sortKey="Ejima, Keisuke" sort="Ejima, Keisuke" uniqKey="Ejima K" first="Keisuke" last="Ejima">Keisuke Ejima</name></region><name sortKey="Aihara, Kazuyuki" sort="Aihara, Kazuyuki" uniqKey="Aihara K" first="Kazuyuki" last="Aihara">Kazuyuki Aihara</name><name sortKey="Aihara, Kazuyuki" sort="Aihara, Kazuyuki" uniqKey="Aihara K" first="Kazuyuki" last="Aihara">Kazuyuki Aihara</name><name sortKey="Omori, Ryosuke" sort="Omori, Ryosuke" uniqKey="Omori R" first="Ryosuke" last="Omori">Ryosuke Omori</name></country><country name="Hong Kong"><noRegion><name sortKey="Omori, Ryosuke" sort="Omori, Ryosuke" uniqKey="Omori R" first="Ryosuke" last="Omori">Ryosuke Omori</name></noRegion><name sortKey="Cowling, Benjamin J" sort="Cowling, Benjamin J" uniqKey="Cowling B" first="Benjamin J." last="Cowling">Benjamin J. 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