Non‐parametric estimation of the case fatality ratio with competing risks data: an application to Severe Acute Respiratory Syndrome (SARS)
Identifieur interne : 001488 ( Pmc/Curation ); précédent : 001487; suivant : 001489Non‐parametric estimation of the case fatality ratio with competing risks data: an application to Severe Acute Respiratory Syndrome (SARS)
Auteurs : Nicholas P. Jewell ; Xiudong Lei ; Azra C. Ghani ; Christl A. Donnelly ; Gabriel M. Leung ; Lai-Ming Ho ; Benjamin J. Cowling ; Anthony J. HedleySource :
- Statistics in Medicine [ 0277-6715 ] ; 2006.
Abstract
For diseases with some level of associated mortality, the case fatality ratio measures the proportion of diseased individuals who die from the disease. In principle, it is straightforward to estimate this quantity from individual follow‐up data that provides times from onset to death or recovery. In particular, in a competing risks context, the case fatality ratio is defined by the limiting value of the sub‐distribution function,
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DOI: 10.1002/sim.2691
PubMed: NONE
PubMed Central: 7169492
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<front><div type="abstract" xml:lang="en"><title>Abstract</title>
<p>For diseases with some level of associated mortality, the case fatality ratio measures the proportion of diseased individuals who die from the disease. In principle, it is straightforward to estimate this quantity from individual follow‐up data that provides times from onset to death or recovery. In particular, in a competing risks context, the case fatality ratio is defined by the limiting value of the sub‐distribution function, <italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
) = Pr(<italic>T</italic>
⩽<italic>t</italic>
and <italic>J</italic>
= 1), associated with death, as <italic>t</italic>
→ ∞, where <italic>T</italic>
denotes the time from onset to death (<italic>J</italic>
= 1) or recovery (<italic>J</italic>
= 2). When censoring is present, however, estimation of <italic>F</italic>
<sub>1</sub>
(∞) is complicated by the possibility of little information regarding the right tail of <italic>F</italic>
<sub>1</sub>
, requiring use of estimators of <italic>F</italic>
<sub>1</sub>
(t<sup>*</sup>
) or <italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
<sup>*</sup>
)/(<italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
<sup>*</sup>
)+<italic>F</italic>
<sub>2</sub>
(<italic>t</italic>
<sup>*</sup>
)) where <italic>t</italic>
<sup>*</sup>
is large, with <italic>F</italic>
<sub>2</sub>
(<italic>t</italic>
) = Pr(<italic>T</italic>
⩽<italic>t</italic>
and <italic>J</italic>
= 2) being the analogous sub‐distribution function associated with recovery. With right censored data, the variability of such estimators increases as <italic>t</italic>
<sup>*</sup>
increases, suggesting the possibility of using estimators at lower values of <italic>t</italic>
<sup>*</sup>
where bias may be increased but overall mean squared error be smaller. These issues are investigated here for non‐parametric estimators of <italic>F</italic>
<sub>1</sub>
and <italic>F</italic>
<sub>2</sub>
. The ideas are illustrated on case fatality data for individuals infected with Severe Acute Respiratory Syndrome (SARS) in Hong Kong in 2003. Copyright © 2006 John Wiley & Sons, Ltd.</p>
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<front><journal-meta><journal-id journal-id-type="nlm-ta">Stat Med</journal-id>
<journal-id journal-id-type="iso-abbrev">Stat Med</journal-id>
<journal-id journal-id-type="doi">10.1002/(ISSN)1097-0258</journal-id>
<journal-id journal-id-type="publisher-id">SIM</journal-id>
<journal-title-group><journal-title>Statistics in Medicine</journal-title>
</journal-title-group>
<issn pub-type="ppub">0277-6715</issn>
<issn pub-type="epub">1097-0258</issn>
<publisher><publisher-name>John Wiley & Sons, Ltd.</publisher-name>
<publisher-loc>Chichester, UK</publisher-loc>
</publisher>
</journal-meta>
<article-meta><article-id pub-id-type="pmc">7169492</article-id>
<article-id pub-id-type="doi">10.1002/sim.2691</article-id>
<article-id pub-id-type="publisher-id">SIM2691</article-id>
<article-categories><subj-group subj-group-type="overline"><subject>Research Article</subject>
</subj-group>
<subj-group subj-group-type="heading"><subject>Research Articles</subject>
</subj-group>
</article-categories>
<title-group><article-title>Non‐parametric estimation of the case fatality ratio with competing risks data: an application to Severe Acute Respiratory Syndrome (SARS)</article-title>
<alt-title alt-title-type="right-running-head">NON‐PARAMETRIC ESTIMATION OF CFR</alt-title>
</title-group>
<contrib-group><contrib id="au1" contrib-type="author" corresp="yes"><name><surname>Jewell</surname>
<given-names>Nicholas P.</given-names>
</name>
<xref ref-type="aff" rid="af1"><sup>1</sup>
</xref>
<address><email>jewell@stat.berkeley.edu</email>
</address>
</contrib>
<contrib id="au2" contrib-type="author"><name><surname>Lei</surname>
<given-names>Xiudong</given-names>
</name>
<address><email>xiudonglei@hotmail.com</email>
</address>
<xref ref-type="aff" rid="af1"><sup>1</sup>
</xref>
</contrib>
<contrib id="au3" contrib-type="author"><name><surname>Ghani</surname>
<given-names>Azra C.</given-names>
</name>
<address><email>azra.ghani@lshtm.ac.uk</email>
</address>
<xref ref-type="aff" rid="af2"><sup>2</sup>
</xref>
</contrib>
<contrib id="au4" contrib-type="author"><name><surname>Donnelly</surname>
<given-names>Christl A.</given-names>
</name>
<address><email>c.donnelly@imperial.ac.uk</email>
</address>
<xref ref-type="aff" rid="af2"><sup>2</sup>
</xref>
</contrib>
<contrib id="au5" contrib-type="author"><name><surname>Leung</surname>
<given-names>Gabriel M.</given-names>
</name>
<address><email>gmleung@hku.hk</email>
</address>
<xref ref-type="aff" rid="af3"><sup>3</sup>
</xref>
</contrib>
<contrib id="au6" contrib-type="author"><name><surname>Ho</surname>
<given-names>Lai‐Ming</given-names>
</name>
<address><email>lmho@hkucc.hku.hk</email>
</address>
<xref ref-type="aff" rid="af3"><sup>3</sup>
</xref>
</contrib>
<contrib id="au7" contrib-type="author"><name><surname>Cowling</surname>
<given-names>Benjamin J.</given-names>
</name>
<address><email>bcowling@hkucc.hku.hk</email>
</address>
<xref ref-type="aff" rid="af3"><sup>3</sup>
</xref>
</contrib>
<contrib id="au8" contrib-type="author"><name><surname>Hedley</surname>
<given-names>Anthony J.</given-names>
</name>
<address><email>hrmrajh@hkucc.hku.hk</email>
</address>
<xref ref-type="aff" rid="af3"><sup>3</sup>
</xref>
</contrib>
</contrib-group>
<aff id="af1"><label><sup>1</sup>
</label>
Division of Biostatistics and Department of Statistics, University of California, Berkeley, U.S.A.</aff>
<aff id="af2"><label><sup>2</sup>
</label>
Department of Infectious Disease Epidemiology, Imperial College, London, U.K.</aff>
<aff id="af3"><label><sup>3</sup>
</label>
Department of Community Medicine, University of Hong Kong, Hong Kong</aff>
<author-notes><corresp id="correspondenceTo"><label>*</label>
Division of Biostatistics and Department of Statistics, University of California, Berkeley, U.S.A.</corresp>
</author-notes>
<pub-date pub-type="epub"><day>15</day>
<month>9</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="ppub"><day>30</day>
<month>4</month>
<year>2007</year>
</pub-date>
<volume>26</volume>
<issue>9</issue>
<issue-id pub-id-type="doi">10.1002/sim.v26:9</issue-id>
<fpage>1982</fpage>
<lpage>1998</lpage>
<history><date date-type="received"><day>21</day>
<month>12</month>
<year>2005</year>
</date>
<date date-type="accepted"><day>13</day>
<month>7</month>
<year>2006</year>
</date>
</history>
<permissions><copyright-statement content-type="article-copyright">Copyright © 2006 John Wiley & Sons, Ltd.</copyright-statement>
<license><license-p>This article is being made freely available through PubMed Central as part of the COVID-19 public health emergency response. It can be used for unrestricted research re-use and analysis in any form or by any means with acknowledgement of the original source, for the duration of the public health emergency.</license-p>
</license>
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<abstract><title>Abstract</title>
<p>For diseases with some level of associated mortality, the case fatality ratio measures the proportion of diseased individuals who die from the disease. In principle, it is straightforward to estimate this quantity from individual follow‐up data that provides times from onset to death or recovery. In particular, in a competing risks context, the case fatality ratio is defined by the limiting value of the sub‐distribution function, <italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
) = Pr(<italic>T</italic>
⩽<italic>t</italic>
and <italic>J</italic>
= 1), associated with death, as <italic>t</italic>
→ ∞, where <italic>T</italic>
denotes the time from onset to death (<italic>J</italic>
= 1) or recovery (<italic>J</italic>
= 2). When censoring is present, however, estimation of <italic>F</italic>
<sub>1</sub>
(∞) is complicated by the possibility of little information regarding the right tail of <italic>F</italic>
<sub>1</sub>
, requiring use of estimators of <italic>F</italic>
<sub>1</sub>
(t<sup>*</sup>
) or <italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
<sup>*</sup>
)/(<italic>F</italic>
<sub>1</sub>
(<italic>t</italic>
<sup>*</sup>
)+<italic>F</italic>
<sub>2</sub>
(<italic>t</italic>
<sup>*</sup>
)) where <italic>t</italic>
<sup>*</sup>
is large, with <italic>F</italic>
<sub>2</sub>
(<italic>t</italic>
) = Pr(<italic>T</italic>
⩽<italic>t</italic>
and <italic>J</italic>
= 2) being the analogous sub‐distribution function associated with recovery. With right censored data, the variability of such estimators increases as <italic>t</italic>
<sup>*</sup>
increases, suggesting the possibility of using estimators at lower values of <italic>t</italic>
<sup>*</sup>
where bias may be increased but overall mean squared error be smaller. These issues are investigated here for non‐parametric estimators of <italic>F</italic>
<sub>1</sub>
and <italic>F</italic>
<sub>2</sub>
. The ideas are illustrated on case fatality data for individuals infected with Severe Acute Respiratory Syndrome (SARS) in Hong Kong in 2003. Copyright © 2006 John Wiley & Sons, Ltd.</p>
</abstract>
<kwd-group kwd-group-type="author-generated"><kwd id="kwd1">case fatality ratio</kwd>
<kwd id="kwd2">competing risks</kwd>
<kwd id="kwd3">inverse probability weighting</kwd>
<kwd id="kwd4">non‐parametric maximum likelihood estimation</kwd>
</kwd-group>
<funding-group><award-group id="funding-0001"><funding-source>University of California, Berkeley</funding-source>
</award-group>
</funding-group>
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