<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.1d3 20150301//EN" "http://jats.nlm.nih.gov/publishing/1.1d3/JATS-journalpublishing1.dtd">
<article article-type="research-article" dtd-version="1.1d3" xml:lang="en" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="nlm-ta">PLoS ONE</journal-id>
<journal-id journal-id-type="publisher-id">plos</journal-id>
<journal-id journal-id-type="pmc">plosone</journal-id>
<journal-title-group>
<journal-title>PLOS ONE</journal-title>
</journal-title-group>
<issn pub-type="epub">1932-6203</issn>
<publisher>
<publisher-name>Public Library of Science</publisher-name>
<publisher-loc>San Francisco, CA USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.1371/journal.pone.0297211</article-id>
<article-id pub-id-type="publisher-id">PONE-D-23-04351</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Research Article</subject>
</subj-group>
<subj-group subj-group-type="Discipline-v3">
<subject>Medicine and health sciences</subject><subj-group><subject>Epidemiology</subject><subj-group><subject>Medical risk factors</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Medicine and health sciences</subject><subj-group><subject>Epidemiology</subject><subj-group><subject>Medical risk factors</subject><subj-group><subject>Traumatic injury risk factors</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Medicine and health sciences</subject><subj-group><subject>Public and occupational health</subject><subj-group><subject>Traumatic injury risk factors</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Medicine and health sciences</subject><subj-group><subject>Critical care and emergency medicine</subject><subj-group><subject>Trauma medicine</subject><subj-group><subject>Traumatic injury</subject><subj-group><subject>Bone fracture</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Medicine and health sciences</subject><subj-group><subject>Public and occupational health</subject><subj-group><subject>Safety</subject><subj-group><subject>Traffic safety</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>People and places</subject><subj-group><subject>Geographical locations</subject><subj-group><subject>North America</subject><subj-group><subject>United States</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>People and places</subject><subj-group><subject>Population groupings</subject><subj-group><subject>Age groups</subject><subj-group><subject>Adults</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>People and places</subject><subj-group><subject>Population groupings</subject><subj-group><subject>Age groups</subject><subj-group><subject>Adults</subject><subj-group><subject>Young adults</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Engineering and technology</subject><subj-group><subject>Civil engineering</subject><subj-group><subject>Transportation infrastructure</subject><subj-group><subject>Roads</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Engineering and technology</subject><subj-group><subject>Transportation</subject><subj-group><subject>Transportation infrastructure</subject><subj-group><subject>Roads</subject></subj-group></subj-group></subj-group></subj-group></article-categories>
<title-group>
<article-title>Female vs. male relative fatality risk in fatal motor vehicle crashes in the US, 1975–2020</article-title>
<alt-title alt-title-type="running-head">Female and male relative fatality risk in vehicle crashes</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes" xlink:type="simple">
<contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0001-6818-5214</contrib-id>
<name name-style="western">
<surname>Abrams</surname>
<given-names>Mitchell Z.</given-names>
</name>
<role content-type="http://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role content-type="http://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role content-type="http://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role content-type="http://credit.niso.org/contributor-roles/investigation/">Investigation</role>
<role content-type="http://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role content-type="http://credit.niso.org/contributor-roles/software/">Software</role>
<role content-type="http://credit.niso.org/contributor-roles/validation/">Validation</role>
<role content-type="http://credit.niso.org/contributor-roles/visualization/">Visualization</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-original-draft/">Writing – original draft</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-review-editing/">Writing – review &amp; editing</role>
<xref ref-type="aff" rid="aff001"><sup>1</sup></xref>
<xref ref-type="corresp" rid="cor001">*</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple">
<name name-style="western">
<surname>Bass</surname>
<given-names>Cameron R.</given-names>
</name>
<role content-type="http://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role content-type="http://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role content-type="http://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
<role content-type="http://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role content-type="http://credit.niso.org/contributor-roles/project-administration/">Project administration</role>
<role content-type="http://credit.niso.org/contributor-roles/resources/">Resources</role>
<role content-type="http://credit.niso.org/contributor-roles/supervision/">Supervision</role>
<role content-type="http://credit.niso.org/contributor-roles/validation/">Validation</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-review-editing/">Writing – review &amp; editing</role>
<xref ref-type="aff" rid="aff002"><sup>2</sup></xref>
</contrib>
</contrib-group>
<aff id="aff001"><label>1</label> <addr-line>Department of Biomedical Engineering, Injury and Orthopedic Biomechanics Laboratory, Duke University, Durham, North Carolina, United States of America</addr-line></aff>
<aff id="aff002"><label>2</label> <addr-line>Department of Biomedical Engineering, Wayne State University, Detroit, Michigan, United States of America</addr-line></aff>
<contrib-group>
<contrib contrib-type="editor" xlink:type="simple">
<name name-style="western">
<surname>Yuan</surname>
<given-names>Quan</given-names>
</name>
<role>Editor</role>
<xref ref-type="aff" rid="edit1"/>
</contrib>
</contrib-group>
<aff id="edit1"><addr-line>Tsinghua University, CHINA</addr-line></aff>
<author-notes>
<fn fn-type="conflict" id="coi001">
<p>The authors have declared that no competing interests exist.</p>
</fn>
<corresp id="cor001">* E-mail: <email xlink:type="simple">mitchell.abrams@duke.edu</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>12</day>
<month>2</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>19</volume>
<issue>2</issue>
<elocation-id>e0297211</elocation-id>
<history>
<date date-type="received">
<day>14</day>
<month>2</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>29</day>
<month>12</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-year>2024</copyright-year>
<copyright-holder>Abrams, Bass</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">
<license-p>This is an open access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">Creative Commons Attribution License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="info:doi/10.1371/journal.pone.0297211"/>
<abstract>
<p>Motor vehicle accidents are the leading cause of death for young adults 18–29 years old worldwide, resulting in nearly 1 million years of life lost annually in the United States. Despite improvements in vehicle safety technologies, young women are at higher risk of dying in car crashes compared with men in matched scenarios. Vehicle crash testing primarily revolves around test dummies representative of the 50th percentile adult male, potentially resulting in these differences in fatality risk for female occupants compared to males. Vehicle occupants involved in fatal car crashes were matched using seating location, vehicle type, airbag deployment, seatbelt usage, and age. The relative risk for fatality (R) between males and females was calculated using a Double Pair Comparison. Young women (20s-40s) are at approximately 20% higher risk of dying in car crashes compared with men of the same age in matched scenarios. In passenger cars, 25-year-old female occupants in passenger car crashes from 1975–2020 exhibit R = 1.201 (95% CI 1.160–1.250) compared to 25-year-old males, and R-1.117 (95% CI 1.040–1.207) for passenger car crashes from 2010–2020. This trend persists across vehicle type, airbag deployment, seatbelt use, and number of vehicles involved in a crash. Known sex-based differences do not explain this large risk differential, suggesting a need for expanded test methodologies and research strategies to address as-yet unexplored sex differences in crash fatalities. These differences should be further investigated to ensure equitable crash protection.</p>
</abstract>
<funding-group>
<award-group id="award001">
<funding-source>
<institution-wrap>
<institution-id institution-id-type="funder-id">http://dx.doi.org/10.13039/100000952</institution-id>
<institution>Paul G. Allen Family Foundation</institution>
</institution-wrap>
</funding-source>
<award-id>571996/12347</award-id>
<principal-award-recipient>
<name name-style="western">
<surname>Bass</surname>
<given-names>Cameron R.</given-names>
</name>
</principal-award-recipient>
</award-group>
<funding-statement>CRB and MZA received funding from the Paul G Allen Family Foundation (<ext-link ext-link-type="uri" xlink:href="https://pgafamilyfoundation.org/" xlink:type="simple">https://pgafamilyfoundation.org/</ext-link>) Grant 571996/12347, Trustees of the University of Pennsylvania/prime. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.</funding-statement>
</funding-group>
<counts>
<fig-count count="5"/>
<table-count count="2"/>
<page-count count="12"/>
</counts>
<custom-meta-group>
<custom-meta id="data-availability">
<meta-name>Data Availability</meta-name>
<meta-value>All FARS data files are available from the National Highway Traffic Safety Administration FTP repository: <ext-link ext-link-type="uri" xlink:href="https://www.nhtsa.gov/file-downloads?p=nhtsa/downloads/FARS/" xlink:type="simple">https://www.nhtsa.gov/file-downloads?p=nhtsa/downloads/FARS/</ext-link>.</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="sec001" sec-type="intro">
<title>Introduction</title>
<p>Motor vehicle accidents are one of the leading causes of mortality worldwide, and the leading cause of death for young adults 18–29 years old [<xref ref-type="bibr" rid="pone.0297211.ref001">1</xref>]. In the United States, mortality from motor vehicle accidents is the 3<sup>rd</sup> leading nationwide cause of unintentional injury death, resulting in over 900,000 years of life lost annually as of 2020 [<xref ref-type="bibr" rid="pone.0297211.ref002">2</xref>]. Motor vehicle fatalities rank in the top 3 causes of death for individuals under the age of 34 [<xref ref-type="bibr" rid="pone.0297211.ref003">3</xref>].</p>
<p>The National Highway Traffic Safety Administration (NHTSA) maintains the Fatality Analysis Reporting System (FARS) [<xref ref-type="bibr" rid="pone.0297211.ref004">4</xref>,<xref ref-type="bibr" rid="pone.0297211.ref005">5</xref>], which tracks all traffic crashes in the USA since 1975 that involve at least one fatality. FARS data are used to inform safety decisions at the local, state, and national levels, and provide key insights into the efficacy of changing vehicle and roadway safety standards [<xref ref-type="bibr" rid="pone.0297211.ref004">4</xref>]. To be included in FARS, a crash must occur on a public road and must result in at least one death within 30 days of the crash. Road fatalities in the US continue to decrease as better advanced safety technologies emerge and become standard features across the board. Occupant fatalities involving vehicles manufactured in the last five or ten years have decreased steadily, down significantly since 1975 (<xref ref-type="fig" rid="pone.0297211.g001">Fig 1A</xref>). Despite improvements, when compared to 15 peer nations, the United States ranks last in reducing the rate of annual vehicle fatalities, and fatalities in 2021 were the highest since 2005 [<xref ref-type="bibr" rid="pone.0297211.ref006">6</xref>,<xref ref-type="bibr" rid="pone.0297211.ref007">7</xref>].</p>
<fig id="pone.0297211.g001" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.g001</object-id>
<label>Fig 1</label>
<caption>
<title>Trends in annual vehicle fatality rates.</title>
<p><bold>(A)</bold> Annual vehicle occupant fatalities involving vehicles manufactured in the prior five or 10 years. Annual fatalities for occupants in “recent-model” vehicles manufactured in the last five or 10 years have been generally declining as vehicle safety technologies have improved. <bold>(B)</bold> Annual vehicle occupant fatalities have decreased overall since 1975, yet fatalities among females have remained largely the same year-to-year.</p>
</caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.g001" xlink:type="simple"/>
</fig>
<p>Overall, evolving crash testing and vehicle standards are estimated to have prevented ~60% of all potential vehicle fatalities in the USA [<xref ref-type="bibr" rid="pone.0297211.ref008">8</xref>,<xref ref-type="bibr" rid="pone.0297211.ref009">9</xref>]. However, the bulk of the fatality reduction is in males (<xref ref-type="fig" rid="pone.0297211.g001">Fig 1B</xref>). Qualitatively, female fatality rates have been relatively stable when compared to the overall trend. While historically males have driven more miles per licensed driver than females, that gap is steadily closing, with decreasing differences in licensure rates and driving exposure [<xref ref-type="bibr" rid="pone.0297211.ref010">10</xref>–<xref ref-type="bibr" rid="pone.0297211.ref012">12</xref>]. Driving exposure for females has increased, and female drivers have been reported to display similar behavioral risk profiles to males when behind the wheel [<xref ref-type="bibr" rid="pone.0297211.ref012">12</xref>–<xref ref-type="bibr" rid="pone.0297211.ref014">14</xref>].</p>
<p>Given these trends, it is important to note that no vehicle crashworthiness test in the US involves an anthropomorphic test device (ATD) representative of the average adult female, despite clear evidence of the increase of female drivers over the last 20 years [<xref ref-type="bibr" rid="pone.0297211.ref015">15</xref>]. The current US regulations only require crash testing with the 50<sup>th</sup> percentile adult male and 5<sup>th</sup> percentile adult female ATD. Prior research has shown that female drivers and vehicle occupants are more likely than males to suffer severe or fatal injuries when involved in a crash severe enough to result in fatality for an occupant involved in the crash [<xref ref-type="bibr" rid="pone.0297211.ref014">14</xref>,<xref ref-type="bibr" rid="pone.0297211.ref016">16</xref>–<xref ref-type="bibr" rid="pone.0297211.ref018">18</xref>]. Female vehicle occupants are at higher risk of Abbreviated Injury Scale (AIS) 2+ (moderate) and 3+ (serious) injuries compared to males when controlling for a variety of factors, particularly to the lower extremities [<xref ref-type="bibr" rid="pone.0297211.ref019">19</xref>,<xref ref-type="bibr" rid="pone.0297211.ref020">20</xref>]. This disparity between men and women in automobile crashes is a major public health issue with implications for automobile design, personnel protection, and governmental regulation. The goal of this paper is to utilize fatal crash data to assess the extent to which a difference in fatality risk exists for male and female occupants under matched crash conditions.</p>
</sec>
<sec id="sec002" sec-type="materials|methods">
<title>Materials and methods</title>
<sec id="sec003">
<title>Data pre-processing</title>
<p>Data were downloaded from the US Department of Transportation–National Highway Traffic Safety Administration Fatality Analysis Reporting System (NHTSA FARS) FTP directory. Data pre-processing was performed using the fars-cleaner package, produced by the authors for this study and freely available as open source software [<xref ref-type="bibr" rid="pone.0297211.ref021">21</xref>,<xref ref-type="bibr" rid="pone.0297211.ref022">22</xref>]. Pre-processing with this package merged changes in the FARS dataset, adjusting outdated and modified codes using the FARS Analytical User Manual as reference [<xref ref-type="bibr" rid="pone.0297211.ref004">4</xref>]. Data preprocessing and analyses were performed using Python (RRID:SCR_008394), pyjanitor, pandas dataframes (RRID:SCR_018214) and Jupyter notebooks (RRID:SCR_018315) parameterized with Papermill [<xref ref-type="bibr" rid="pone.0297211.ref023">23</xref>–<xref ref-type="bibr" rid="pone.0297211.ref027">27</xref>]. Data visualizations were produced with matplotlib (RRID:SCR_008624) [<xref ref-type="bibr" rid="pone.0297211.ref028">28</xref>].</p>
</sec>
<sec id="sec004">
<title>Double pair comparison method</title>
<p>The double pair comparison method developed by Evans isolates specific features of fatality risk in a crash on a comparable basis [<xref ref-type="bibr" rid="pone.0297211.ref029">29</xref>]. One group of vehicle occupants is selected as the subject occupants, and another is selected as the control. The assessment of fatality risk is performed across the control group. To illustrate the use of the double pair method to determine the relative fatality risk of female vs. male drivers, two sets of crashes are selected with a consistent control occupant (for example, male passengers seated in the front right seat of the vehicle) so that
<disp-formula id="pone.0297211.e001">
<alternatives>
<graphic id="pone.0297211.e001g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e001" xlink:type="simple"/>
<mml:math display="block" id="M1">
<mml:mrow><mml:mi mathvariant="bold">A</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(1)</label>
</disp-formula>
<disp-formula id="pone.0297211.e002">
<alternatives>
<graphic id="pone.0297211.e002g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e002" xlink:type="simple"/>
<mml:math display="block" id="M2">
<mml:mrow><mml:mi mathvariant="bold">B</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(2)</label>
</disp-formula>
<disp-formula id="pone.0297211.e003">
<alternatives>
<graphic id="pone.0297211.e003g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e003" xlink:type="simple"/>
<mml:math display="block" id="M3">
<mml:mrow><mml:mi mathvariant="bold">C</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(3)</label>
</disp-formula>
<disp-formula id="pone.0297211.e004">
<alternatives>
<graphic id="pone.0297211.e004g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e004" xlink:type="simple"/>
<mml:math display="block" id="M4">
<mml:mrow><mml:mi mathvariant="bold">D</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(4)</label>
</disp-formula></p>
<p>From these counts, the relative risk of fatality for a female driver vs. the control occupant, <italic>r</italic><sub>1</sub> = <italic>A</italic>/<italic>B</italic>, and the relative risk of fatality for a male driver vs. the control occupant, <italic>r</italic><sub>2</sub> =<italic>C</italic>/<italic>D</italic>, were used to derive the female vs. male relative risk, <italic>R</italic> = <italic>r</italic><sub>1</sub>/<italic>r</italic><sub>2</sub>. In this technique, the control occupants (B and D) are eliminated from the calculation of relative risk, so male and female subject occupants can be compared. The original double pair method determines standard error in the estimates of <italic>R</italic> (Δ<italic>R</italic>):
<disp-formula id="pone.0297211.e005">
<alternatives>
<graphic id="pone.0297211.e005g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e005" xlink:type="simple"/>
<mml:math display="block" id="M5">
<mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:msqrt><mml:msubsup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:mfrac></mml:msqrt>
</mml:math>
</alternatives>
<label>(5)</label>
</disp-formula>
where <italic>σ</italic><sub><italic>μ</italic></sub> is an estimate of “intrinsic uncertainty,” set to either 0.05 or 0.1 [<xref ref-type="bibr" rid="pone.0297211.ref017">17</xref>,<xref ref-type="bibr" rid="pone.0297211.ref029">29</xref>]. The introduction of this constant term forces all variance estimates to be similar, regardless of the pointwise variance in each estimate. Since these are used in the weighted summaries, results may be biased by granting larger weight to samples with more uncertainty. To mitigate this bias, an alternative method was used for describing the variance of the risk ratios [<xref ref-type="bibr" rid="pone.0297211.ref030">30</xref>]. To correct this deficiency, the counts were further stratified using:
<disp-formula id="pone.0297211.e006">
<alternatives>
<graphic id="pone.0297211.e006g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e006" xlink:type="simple"/>
<mml:math display="block" id="M6">
<mml:mrow><mml:mi mathvariant="bold">A</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(6)</label>
</disp-formula>
<disp-formula id="pone.0297211.e007">
<alternatives>
<graphic id="pone.0297211.e007g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e007" xlink:type="simple"/>
<mml:math display="block" id="M7">
<mml:mrow><mml:mi mathvariant="bold">B</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(7)</label>
</disp-formula>
<disp-formula id="pone.0297211.e008">
<alternatives>
<graphic id="pone.0297211.e008g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e008" xlink:type="simple"/>
<mml:math display="block" id="M8">
<mml:mrow><mml:mi mathvariant="bold">C</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(8)</label>
</disp-formula>
<disp-formula id="pone.0297211.e009">
<alternatives>
<graphic id="pone.0297211.e009g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e009" xlink:type="simple"/>
<mml:math display="block" id="M9">
<mml:mrow><mml:mi mathvariant="bold">E</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(9)</label>
</disp-formula>
<disp-formula id="pone.0297211.e010">
<alternatives>
<graphic id="pone.0297211.e010g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e010" xlink:type="simple"/>
<mml:math display="block" id="M10">
<mml:mrow><mml:mi mathvariant="bold">F</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(10)</label>
</disp-formula>
<disp-formula id="pone.0297211.e011">
<alternatives>
<graphic id="pone.0297211.e011g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e011" xlink:type="simple"/>
<mml:math display="block" id="M11">
<mml:mrow><mml:mi mathvariant="bold">G</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mspace width="0.25em"/><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(11)</label>
</disp-formula></p>
<p>Note that the original variables <bold>A</bold>, <bold>B</bold>, <bold>C</bold>, and <bold>D</bold> (Eqs <xref ref-type="disp-formula" rid="pone.0297211.e001">1</xref>–<xref ref-type="disp-formula" rid="pone.0297211.e004">4</xref>) can be derived as the sum of the new counts detailed above (Eqs <xref ref-type="disp-formula" rid="pone.0297211.e006">6</xref>–<xref ref-type="disp-formula" rid="pone.0297211.e011">11</xref>). Now, the relative risk ratio is
<disp-formula id="pone.0297211.e012">
<alternatives>
<graphic id="pone.0297211.e012g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e012" xlink:type="simple"/>
<mml:math display="block" id="M12">
<mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfrac bevelled="true"><mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mfrac bevelled="true"><mml:mrow><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac><mml:mo>.</mml:mo>
</mml:math>
</alternatives>
<label>(12)</label>
</disp-formula></p>
<p>The variance for the log of the relative risk ratio is [<xref ref-type="bibr" rid="pone.0297211.ref030">30</xref>]
<disp-formula id="pone.0297211.e013">
<alternatives>
<graphic id="pone.0297211.e013g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e013" xlink:type="simple"/>
<mml:math display="block" id="M13">
<mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>×</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mo>+</mml:mo><mml:mi>G</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>[</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>E</mml:mi><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mo>+</mml:mo><mml:mi>G</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mo>×</mml:mo><mml:mi>G</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>G</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mfrac>
</mml:math>
</alternatives>
<label>(13)</label>
</disp-formula></p>
<p>Weighted risk ratios (<inline-formula id="pone.0297211.e014"><alternatives><graphic id="pone.0297211.e014g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e014" xlink:type="simple"/><mml:math display="inline" id="M14"><mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math></alternatives></inline-formula>) and weighted estimates of variance (<inline-formula id="pone.0297211.e015"><alternatives><graphic id="pone.0297211.e015g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e015" xlink:type="simple"/><mml:math display="inline" id="M15"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math></alternatives></inline-formula>) are
<disp-formula id="pone.0297211.e016">
<alternatives>
<graphic id="pone.0297211.e016g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e016" xlink:type="simple"/>
<mml:math display="block" id="M16">
<mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi mathvariant="normal">exp</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">ln</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow>
</mml:math>
</alternatives>
<label>(14)</label>
</disp-formula>
<disp-formula id="pone.0297211.e017">
<alternatives>
<graphic id="pone.0297211.e017g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e017" xlink:type="simple"/>
<mml:math display="block" id="M17">
<mml:mi mathvariant="normal">Δ</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo>
</mml:math>
</alternatives>
<label>(15)</label>
</disp-formula></p>
<p>Confidence intervals (95%) are derived with a bootstrap method, sampling with replacement many times and calculating values for <inline-formula id="pone.0297211.e018"><alternatives><graphic id="pone.0297211.e018g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e018" xlink:type="simple"/><mml:math display="inline" id="M18"><mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math></alternatives></inline-formula> and <inline-formula id="pone.0297211.e019"><alternatives><graphic id="pone.0297211.e019g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pone.0297211.e019" xlink:type="simple"/><mml:math display="inline" id="M19"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math></alternatives></inline-formula> for each new sample set [<xref ref-type="bibr" rid="pone.0297211.ref030">30</xref>]. This procedure was replicated 5000 times for each weighted average. Each bootstrap run produces a distribution of results, from which the 95% confidence interval is derived.</p>
<p>Cases were selected with at least two occupants and with at least one fatality in the vehicle. All rollover crashes were excluded. Only fatalities within a passenger car were examined. Fatality was determined as coded within FARS and includes those declared dead at the crash and within 30 days from crash-related causes. Age ranges were examined in five-year periods for subject occupants, while control occupants were grouped as in previous analyses: ages 16–24, 25–34, 35–54, and 55+ [<xref ref-type="bibr" rid="pone.0297211.ref017">17</xref>]. Tables A and B in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref> show the subject breakdown for 1975–2020 with matched airbag deployment in passenger cars (<italic>n</italic> = 249,160 fatalities) and light trucks (<italic>n</italic> = 92,826 fatalities) and 2010–2020 with matched airbag deployment in passenger cars (<italic>n =</italic> 26,221 fatalities). Matched airbag deployment was defined as cases where both the subject and the control occupant experienced the same airbag deployment at their seating position (deployment or no deployment). Cases with unknown airbag deployment were excluded.</p>
<p>Fatal crash cases were grouped by subject occupant seating position (driver seat, front right seat, rear left seat, etc.), seat-belt use, and control occupant seating position and age. In each analysis, a weighted average of the value for <italic>R</italic> was taken within each subject age subset to find the overall risk a subject of that age independent of seating position or control occupant.</p>
<p>Second row passengers were included as subjects for analyses spanning 1975–2020 only. From 2010–2020, there were typically fewer than 15 fatalities in each subset (age, seating position, belt use, airbag) for rear passengers, and in most cases there were 1 or 0 in each subset. This resulted in excessive error due to small <italic>n</italic>, so rear passengers were not considered from 2010–2020.</p>
</sec>
</sec>
<sec id="sec005" sec-type="results">
<title>Results</title>
<p>Female vehicle occupants between ages 20 and 40 are ~20% more likely to die in a crash than males of the same age under matched conditions (Figs <xref ref-type="fig" rid="pone.0297211.g002">2</xref> and <xref ref-type="fig" rid="pone.0297211.g003">3</xref>). This general trend is apparent when isolating vehicle type (passenger car vs. light trucks), seat-belt use (belted vs unbelted), number of vehicles involved (one, two, or three or more vehicles), crash direction (front vs side), and airbag deployment, and persists for females up to age 50. To best illustrate the results produced by the double pair method, consider the case of belted drivers, aged 23–27 years (25-year-old drivers), in passenger cars, using belted front-right seat passengers as a control, matching airbag deployment, in crashes between 2010 and 2020. These results are given in <xref ref-type="table" rid="pone.0297211.t001">Table 1</xref> for each sex/age cohort under these conditions, giving a relative risk of 4.7% higher for 25 year old, belted female drivers with matched airbag deployment compared to 25 year old male drivers under the same conditions (Relative Risk (R) = 1.047; 95% Confidence Interval (CI) = 0.836–1.168).</p>
<fig id="pone.0297211.g002" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.g002</object-id>
<label>Fig 2</label>
<caption>
<title>Relative fatality risk, females vs. males, passenger car fatalities 2010–2020.</title>
<p>Relative fatality risk for all female occupants compared to males (<italic>n</italic> = 25,480; 2010–2020) under matched airbag deployment condition. Young female vehicle occupants are at an increased risk of fatality compared to males until ~40 years old.</p>
</caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.g002" xlink:type="simple"/>
</fig>
<fig id="pone.0297211.g003" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.g003</object-id>
<label>Fig 3</label>
<caption>
<title>Relative fatality risk, females vs. males, passenger car fatalities 1975–2020.</title>
<p>Relative fatality risk for female occupants compared to males (<italic>n</italic> = 249,160; 1975–2020) under matched airbag deployment condition. Young female vehicle occupants (driver, front right passenger, left and right second row passengers) in passenger cars are at an approximately 20% increased risk of fatality compared to males until ~40 years old.</p>
</caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.g003" xlink:type="simple"/>
</fig>
<table-wrap id="pone.0297211.t001" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.t001</object-id>
<label>Table 1</label> <caption><title>Female vs. Male Fatality Risk, Belted 25YO Car Drivers, airbag deployment (Matched), 2010–2020.</title></caption>
<alternatives>
<graphic id="pone.0297211.t001g" mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.t001" xlink:type="simple"/>
<table>
<colgroup>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
</colgroup>
<thead>
<tr>
<th align="center" rowspan="2" style="background-color:#D9D9D9"><break/>Control Occupant Characteristics, Age</th>
<th align="center" colspan="4" style="background-color:#D9D9D9">Fatalities</th>
<th align="center" colspan="3" style="background-color:#D9D9D9">Ratios</th>
</tr>
<tr>
<th align="center" style="background-color:#D9D9D9">A</th>
<th align="center" style="background-color:#D9D9D9">B</th>
<th align="center" style="background-color:#D9D9D9">C</th>
<th align="center" style="background-color:#D9D9D9">D</th>
<th align="center" style="background-color:#D9D9D9">r<sub>1</sub> = A/B</th>
<th align="center" style="background-color:#D9D9D9">r<sub>2</sub> = C/D</th>
<th align="center" style="background-color:#D9D9D9">R = <italic>r</italic><sub><italic>1</italic></sub>/<italic>r</italic><sub><italic>2</italic></sub></th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Male Passenger, 16–24yo</td>
<td align="left">27</td>
<td align="left">34</td>
<td align="left">158</td>
<td align="left">139</td>
<td align="left">0.794</td>
<td align="left">1.137</td>
<td align="left">0.699</td>
</tr>
<tr>
<td align="left">Male Passenger, 25–34yo</td>
<td align="left">59</td>
<td align="left">53</td>
<td align="left">103</td>
<td align="left">110</td>
<td align="left">1.113</td>
<td align="left">0.936</td>
<td align="left">1.189</td>
</tr>
<tr>
<td align="left">Male Passenger, 35–54yo</td>
<td align="left">16</td>
<td align="left">16</td>
<td align="left">24</td>
<td align="left">37</td>
<td align="left">1.0</td>
<td align="left">0.649</td>
<td align="left">1.542</td>
</tr>
<tr>
<td align="left">Male Passenger, 55+yo</td>
<td align="left">1</td>
<td align="left">7</td>
<td align="left">3</td>
<td align="left">8</td>
<td align="left">0.143</td>
<td align="left">0.375</td>
<td align="left">0.381</td>
</tr>
<tr>
<td align="left">Female Passenger, 16–24yo</td>
<td align="left">35</td>
<td align="left">29</td>
<td align="left">133</td>
<td align="left">140</td>
<td align="left">1.207</td>
<td align="left">0.95</td>
<td align="left">1.27</td>
</tr>
<tr>
<td align="left">Female Passenger, 25–34yo</td>
<td align="left">33</td>
<td align="left">41</td>
<td align="left">74</td>
<td align="left">94</td>
<td align="left">0.805</td>
<td align="left">0.787</td>
<td align="left">1.022</td>
</tr>
<tr>
<td align="left">Female Passenger, 35–54yo</td>
<td align="left">13</td>
<td align="left">30</td>
<td align="left">12</td>
<td align="left">23</td>
<td align="left">0.433</td>
<td align="left">0.522</td>
<td align="left">0.831</td>
</tr>
<tr>
<td align="left">Female Passenger, 55+yo</td>
<td align="left">3</td>
<td align="left">40</td>
<td align="left">1</td>
<td align="left">26</td>
<td align="left">0.075</td>
<td align="left">0.038</td>
<td align="left">1.95</td>
</tr>
<tr>
<td align="right" colspan="7">Weighted average R [95% confidence]</td>
<td align="left">1.047<break/>[0.832, 1.267]</td>
</tr>
</tbody>
</table>
</alternatives>
<table-wrap-foot>
<fn id="t001fn001"><p>Control occupants are belted, front-right passengers.</p></fn>
<fn id="t001fn002"><p>Matched airbag deployment refers to cases where the airbag either deploys at both the control and subject occupant seating position, or deploys at neither position.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>Taking the weighted average across the controls presented in <xref ref-type="table" rid="pone.0297211.t001">Table 1</xref> for each set of subject occupants, we produce <xref ref-type="table" rid="pone.0297211.t002">Table 2</xref>, for 25 year old vehicle occupants. Across cases for these occupants, the overall risk (<xref ref-type="table" rid="pone.0297211.t002">Table 2</xref>) is 11.7% (R = 1.117, 95% CI 1.040–1.207) higher risk for females. This value is plotted as the corresponding value in <xref ref-type="fig" rid="pone.0297211.g002">Fig 2</xref>. Repeating this analysis for female occupants at other ages, we find younger females have a higher fatality risk than younger males when driving or sitting in the front passenger seat, regardless of seat-belt use (<xref ref-type="table" rid="pone.0297211.t002">Table 2</xref>). <xref ref-type="fig" rid="pone.0297211.g003">Fig 3</xref> shows the results of repeating this analysis for all crashes from 1975 to 2020. <xref ref-type="fig" rid="pone.0297211.g004">Fig 4</xref> is representative of the confidence interval estimation utilizing the bootstrap method, and shows the distribution of R values.</p>
<fig id="pone.0297211.g004" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.g004</object-id>
<label>Fig 4</label>
<caption>
<title>Bootstrap estimates, females vs. males, passenger car fatalities 1975–2020.</title>
<p>Bootstrap estimates for relative fatality risk for female occupants compared to males under matched airbag deployment condition. 95% confidence intervals are derived from the middle 95% of these estimates.</p>
</caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.g004" xlink:type="simple"/>
</fig>
<table-wrap id="pone.0297211.t002" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.t002</object-id>
<label>Table 2</label> <caption><title>Values of R, fatality risk to 25yo females compared to 25yo males, passenger car occupants, 2010–2020, matched airbag deployment.</title></caption>
<alternatives>
<graphic id="pone.0297211.t002g" mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.t002" xlink:type="simple"/>
<table>
<colgroup>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
</colgroup>
<thead>
<tr>
<th align="center" style="background-color:#D9D9D9">Subject Occupant</th>
<th align="center" style="background-color:#D9D9D9">Female Fatalities</th>
<th align="center" style="background-color:#D9D9D9">Male Fatalities</th>
<th align="center" style="background-color:#D9D9D9">Total Fatalities</th>
<th align="center" style="background-color:#D9D9D9">R</th>
<th align="center" style="background-color:#D9D9D9">95% CI</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Unbelted drivers, airbag deployed</td>
<td align="left">114</td>
<td align="left">427</td>
<td align="left">541</td>
<td align="left">0.987</td>
<td align="left">[0.916, 1.05]</td>
</tr>
<tr>
<td align="left">Unbelted right front passengers, airbag deployed</td>
<td align="left">225</td>
<td align="left">346</td>
<td align="left">571</td>
<td align="left">1.297</td>
<td align="left">[1.050, 1.511]</td>
</tr>
<tr>
<td align="left">Belted drivers, airbag deployed</td>
<td align="left">187</td>
<td align="left">508</td>
<td align="left">695</td>
<td align="left">1.047</td>
<td align="left">[0.832, 1.267]</td>
</tr>
<tr>
<td align="left">Belted right front passengers, airbag deployed</td>
<td align="left">352</td>
<td align="left">385</td>
<td align="left">737</td>
<td align="left">1.143</td>
<td align="left">[0.943, 1.374]</td>
</tr>
<tr>
<td align="left">Unbelted drivers, airbag not deployed</td>
<td align="left">78</td>
<td align="left">226</td>
<td align="left">304</td>
<td align="left">1.255</td>
<td align="left">[1.033, 1.856]</td>
</tr>
<tr>
<td align="left">Unbelted right front passengers, airbag not deployed</td>
<td align="left">87</td>
<td align="left">170</td>
<td align="left">257</td>
<td align="left">0.978</td>
<td align="left">[0.656, 1.439]</td>
</tr>
<tr>
<td align="left">Belted drivers, airbag not deployed</td>
<td align="left">70</td>
<td align="left">196</td>
<td align="left">266</td>
<td align="left">1.292</td>
<td align="left">[1.003, 2.410]</td>
</tr>
<tr>
<td align="left">Belted right front passengers, airbag not deployed</td>
<td align="left">101</td>
<td align="left">163</td>
<td align="left">264</td>
<td align="left">1.095</td>
<td align="left">[0.789, 1.350]</td>
</tr>
<tr>
<td align="right" colspan="4"><bold>Weighted Average</bold></td>
<td align="right">1.117</td>
<td align="right">[1.040, 1.207]</td>
</tr>
</tbody>
</table>
</alternatives>
</table-wrap>
<p>Repeating the analysis for light truck occupants, we find a similar trend as in passenger cars, as shown in <xref ref-type="fig" rid="pone.0297211.g005">Fig 5</xref>. Female occupants in passenger cars and light trucks are at increased risk to males in one and two vehicle crashes (Fig A-D in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref>). There is no difference in fatality risk for females compared to males in crashes involving three or more vehicles (Fig E and Fig F in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref>). Females are at increased risk in frontal impacts and passenger side impacts, but not in driver side impacts (Fig G-I in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref>).</p>
<fig id="pone.0297211.g005" position="float">
<object-id pub-id-type="doi">10.1371/journal.pone.0297211.g005</object-id>
<label>Fig 5</label>
<caption>
<title>Relative fatality risk, females vs. males, light truck fatalities 1975–2020.</title>
<p>Relative fatality risk for female occupants in light trucks compared to males (<italic>n</italic> = 92,826; 1975–2020) under matched airbag deployment condition. Young female vehicle occupants in light trucks (driver, front right passenger, left and right second row passenger) are at an approximately 20% increased risk of fatality compared to males until ~40 years old.</p>
</caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.g005" xlink:type="simple"/>
</fig>
</sec>
<sec id="sec006" sec-type="conclusions">
<title>Discussion</title>
<p>Despite significant advances in vehicle safety since 1975, female vehicle occupants involved in fatal crashes have a higher risk of death compared to males in matched circumstances. These results show that when in a fatal crash, a younger female occupant is approximately 20% more likely to suffer a fatal injury than a male occupant of the same age, regardless of seating position, airbag deployment, or seat-belt usage.</p>
<p>We have investigated several potential covariates that might explain these findings, including number of passengers, number of vehicles involved, and drug/alcohol use. There are no significant differences in the number of occupants in a vehicle between male and female drivers (Mann-Whitney U-test, p&gt;0.90; See Fig J in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref>). While there are slight differences in the proportion of male and female fatalities identified as using drugs or alcohol, the magnitude of these differences is insufficient to account for the 20% increase in risk shown by young female occupants.</p>
<p>The distribution of vehicles driven by females is similar to that for males, with a slightly higher proportion of female drivers using cars with vehicle masses of ~2,500 lb, but both sexes use heavier vehicles at the same rate. While male drivers are more frequently involved in single-car crashes compared to female drivers, the proportion of crashes involving multiple vehicles is similar across sex. The distribution by sex of the number of occupants in a vehicle are similar as well. The lack of a large qualitative difference in these covariates would imply limited effect on the relative risk to drivers. To verify this conclusion, the above analyses were applied to subsets of vehicle occupants involved in one-, two- and multi-vehicle crashes, as well as cases with one, two, or several vehicle occupants.</p>
<p>When examining single vehicle crashes, we continue to find a higher relative risk to female occupants compared to males despite the increased proportion of crashes involving males. This is true for both passenger cars and light trucks. Similarly, there is an increased risk to female occupants in crashes with two vehicles when compared to males, but not in crashes with three or more vehicles. While females are not at higher risk than males in crashes with 3+ vehicles, one- and two-vehicle crashes account for the majority of cases in the FARS dataset (Fig K in <xref ref-type="supplementary-material" rid="pone.0297211.s001">S1 Appendix</xref>).</p>
<p>The results presented here are similar to those presented by Evans in 2001 for FARS data through 1998 [<xref ref-type="bibr" rid="pone.0297211.ref017">17</xref>]. Notably, the inclusion of data from before 2010 in the analysis presented in <xref ref-type="fig" rid="pone.0297211.g003">Fig 3</xref> mainly reduces the error assessment, without qualitatively altering the overall characteristics of the risk curve. While analyses from 1975–2020 include second-row passengers, we excluded this subject class from analyses for 2010–2020 due to small <italic>n</italic>. The small group size (total <italic>n</italic> = 662 for belted and unbelted male and female rear passengers) resulted in large subgroup error estimates, which overly influence the error estimates. This limits the generalizability of the results for recent crash cases. However, the overall trend is apparent for all analyses with substantial group sizes. As overall there are more male fatalities per year than female fatalities, a sufficiently large sample size may be necessary to observe the differential risk presented here.</p>
<p>Physiological/anatomical differences are difficult to explore within the FARS dataset, but may provide an explanation. Current vehicle crashworthiness tests do not use a crash dummy representative of the average adult female [<xref ref-type="bibr" rid="pone.0297211.ref015">15</xref>]. The current US regulations require crash testing primarily with the 50<sup>th</sup> percentile Hybrid III (HIII) adult male ATD, with a few tests adding in the 5<sup>th</sup> percentile adult female as a passenger. Since the 5<sup>th</sup> percentile female ATD is primarily a dimensionally scaled version of the HIII male [<xref ref-type="bibr" rid="pone.0297211.ref031">31</xref>], the physiological and anatomical differences between the sexes may not be completely reproduced in testing methods. For example, a recent study identified differences in positioning female cadaver specimens compared to male specimens during reclined frontal impacts, requiring a forward shift of the belt anchor points to produce comparable kinematics and injuries for specimens of both sexes [<xref ref-type="bibr" rid="pone.0297211.ref032">32</xref>].</p>
<p>These results are not completely consistent with other well-described trends related to sex differences in injury. Females are more likely than males to suffer fractures past the age of 60 due to osteoporosis and to experience bone loss at an earlier age [<xref ref-type="bibr" rid="pone.0297211.ref033">33</xref>], and females tend to have greater age related bone density loss than males [<xref ref-type="bibr" rid="pone.0297211.ref034">34</xref>]. Increased fracture risk in elderly females, therefore, cannot explain the observed trends. Without detailed injury report data (not available within FARS), the cause of death cannot be determined for each case. This information would be valuable in parsing the differences between male and female crash survivability. We posit that there may be unobserved trends in the injury patterns, and therefore outcomes, between male and female occupants. These trends may be the result of unintentional vehicle design issues, or a potentially unexplained lack of biofidelity in the ATDs used in testing.</p>
</sec>
<sec id="sec007" sec-type="supplementary-material">
<title>Supporting information</title>
<supplementary-material id="pone.0297211.s001" mimetype="application/vnd.openxmlformats-officedocument.wordprocessingml.document" position="float" xlink:href="info:doi/10.1371/journal.pone.0297211.s001" xlink:type="simple">
<label>S1 Appendix</label>
<caption>
<title>The supplemental material contains supporting tables (S1 Appendix Table A-D and S1 Appendix Fig A-K).</title>
<p>(DOCX)</p>
</caption>
</supplementary-material>
</sec>
</body>
<back>
<ref-list>
<title>References</title>
<ref id="pone.0297211.ref001"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">World Health Organization. Global status report on road safety 2018. Geneva, Switzerland. 2018.</mixed-citation></ref>
<ref id="pone.0297211.ref002"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Centers for Disease Control and Prevention, National Center for Injury Prevention and Control. WISQARS™—Web-based Injury Statistics Query and Reporting System. Available from: <ext-link ext-link-type="uri" xlink:href="https://www.cdc.gov/injury/wisqars/index.html" xlink:type="simple">https://www.cdc.gov/injury/wisqars/index.html</ext-link>.</mixed-citation></ref>
<ref id="pone.0297211.ref003"><label>3</label><mixed-citation publication-type="book" xlink:type="simple"><name name-style="western"><surname>Webb</surname> <given-names>CN</given-names></name>. <source>Motor vehicle traffic crashes as a leading cause of death in the United States, 2016 and 2017.</source> <publisher-loc>Washington, DC</publisher-loc>: <publisher-name>Administration NHTS;</publisher-name> <year>2020</year> <month>January</month> <volume>2015</volume>. Report No.: DOT HS 812 927.</mixed-citation></ref>
<ref id="pone.0297211.ref004"><label>4</label><mixed-citation publication-type="book" xlink:type="simple"><collab>National Highway Traffic Safety Administration</collab>. <source>Fatality Analysis Reporting System (FARS) Analytical User’s Manual, 1975–2018.</source> <publisher-loc>Washington, DC</publisher-loc>: <publisher-name>Administration NHTS; 2019</publisher-name> <month>September</month> <year>2019</year>. Report No.: DOT HS 812 827.</mixed-citation></ref>
<ref id="pone.0297211.ref005"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">National Highway Traffic Safety Administration. Fatality Analysis Reporting System. Washington, DC 2018.</mixed-citation></ref>
<ref id="pone.0297211.ref006"><label>6</label><mixed-citation publication-type="book" xlink:type="simple"><collab>National Center for Statistics and Analysis</collab>. <source>Early estimate of motor vehicle traffic fatalities in 2021</source> <publisher-loc>Washington, DC</publisher-loc>: <collab>National Highway Traffic Safety Administration</collab>, <year>2022</year> <month>April</month> 2022. Report No.: DOT HS 813 283.</mixed-citation></ref>
<ref id="pone.0297211.ref007"><label>7</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Ahangari</surname> <given-names>H</given-names></name>, <name name-style="western"><surname>Atkinson-Palombo</surname> <given-names>C</given-names></name>, <name name-style="western"><surname>Garrick</surname> <given-names>NW</given-names></name>. <article-title>Progress towards zero, an international comparison: Improvements in traffic fatality from 1990 to 2010 for different age groups in the USA and 15 of its peers.</article-title> <source>J Safety Res.</source> <year>2016</year>;<volume>57</volume>:<fpage>61</fpage>–<lpage>70</lpage>. Epub 2016/05/15. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.jsr.2016.03.006" xlink:type="simple">10.1016/j.jsr.2016.03.006</ext-link></comment> <object-id pub-id-type="pmid">27178081</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref008"><label>8</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Kahane</surname> <given-names>CJ</given-names></name>. <article-title>Lives Saved by Vehicle Safety Technologies and Associated Federal Motor Vehicle Safety Standards, 1960 to 2012 –Passenger Cars and LTVs–With Reviews of 26 FMVSS and the Effectiveness of Their Associated Safety Technologies in Reducing Fatalities, Injuries, and Crashes.</article-title> <source>Washington, DC: Administration NHTS; 2015</source> <month>January</month> <year>2015</year>. Report No.: DOT HS 812 069.</mixed-citation></ref>
<ref id="pone.0297211.ref009"><label>9</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Viano</surname> <given-names>DC</given-names></name>, <name name-style="western"><surname>Parenteau</surname> <given-names>CS</given-names></name>. <article-title>Effectiveness of the revision to FMVSS 301: FARS and NASS-CDS analysis of fatalities and severe injuries in rear impacts.</article-title> <source>Accident Analysis &amp; Prevention.</source> <year>2016</year>;<volume>89</volume>:<fpage>1</fpage>–<lpage>8</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.aap.2015.12.016" xlink:type="simple">10.1016/j.aap.2015.12.016</ext-link></comment> <object-id pub-id-type="pmid">26773695</object-id></mixed-citation></ref>
<ref id="pone.0297211.ref010"><label>10</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Mayhew</surname> <given-names>DR</given-names></name>, <name name-style="western"><surname>Ferguson</surname> <given-names>SA</given-names></name>, <name name-style="western"><surname>Desmond</surname> <given-names>KJ</given-names></name>, <name name-style="western"><surname>Simpson</surname> <given-names>HM</given-names></name>. <article-title>Trends in fatal crashes involving female drivers, 1975–1998.</article-title> <source>Accident Analysis &amp; Prevention.</source> <year>2003</year>;<volume>35</volume>(<issue>3</issue>):<fpage>407</fpage>–<lpage>15</lpage>. Epub 2003/03/20. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/s0001-4575%2802%2900019-2" xlink:type="simple">10.1016/s0001-4575(02)00019-2</ext-link></comment> <object-id pub-id-type="pmid">12643958</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref011"><label>11</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Sivak</surname> <given-names>M.</given-names></name> <article-title>Female Drivers in the United States, 1963–2010: From a Minority to a Majority?</article-title> <source>Traffic Injury Prevention</source>. <year>2013</year>;<volume>14</volume>(<issue>3</issue>):<fpage>259</fpage>–<lpage>60</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1080/15389588.2012.755736" xlink:type="simple">10.1080/15389588.2012.755736</ext-link></comment> <object-id pub-id-type="pmid">23441943</object-id></mixed-citation></ref>
<ref id="pone.0297211.ref012"><label>12</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Fucci</surname> <given-names>NMA</given-names></name>. <article-title>Summary of Travel Trends: 2017 National Household Travel Survey. Washington, DC: Administration FH; 2018</article-title> <source>January</source> <year>2015</year>. Report No.: FHWA-PL-18-019.</mixed-citation></ref>
<ref id="pone.0297211.ref013"><label>13</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Tsai</surname> <given-names>VW</given-names></name>, <name name-style="western"><surname>Anderson</surname> <given-names>CL</given-names></name>, <name name-style="western"><surname>Vaca</surname> <given-names>FE</given-names></name>. <article-title>Young female drivers in fatal crashes: recent trends, 1995–2004</article-title>. <source>Traffic Injury Prevention</source>. <year>2008</year>;<volume>9</volume>(<issue>1</issue>):<fpage>65</fpage>–<lpage>9</lpage>. Epub 2008/03/14. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1080/15389580701729881" xlink:type="simple">10.1080/15389580701729881</ext-link></comment> <object-id pub-id-type="pmid">18338297</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref014"><label>14</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Romano</surname> <given-names>E</given-names></name>, <name name-style="western"><surname>Kelley-Baker</surname> <given-names>T</given-names></name>, <name name-style="western"><surname>Voas</surname> <given-names>RB</given-names></name>. <article-title>Female involvement in fatal crashes: Increasingly riskier or increasingly exposed?</article-title> <source>Accident Analysis &amp; Prevention.</source> <year>2008</year>;<volume>40</volume>(<issue>5</issue>):<fpage>1781</fpage>–<lpage>8</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.aap.2008.06.016" xlink:type="simple">10.1016/j.aap.2008.06.016</ext-link></comment> <object-id pub-id-type="pmid">18760108</object-id></mixed-citation></ref>
<ref id="pone.0297211.ref015"><label>15</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Linder</surname> <given-names>A</given-names></name>, <name name-style="western"><surname>Svensson</surname> <given-names>MY</given-names></name>. <article-title>Road safety: the average male as a norm in vehicle occupant crash safety assessment</article-title>. <source>Interdisciplinary Science Reviews</source>. <year>2019</year>;<volume>44</volume>(<issue>2</issue>):<fpage>140</fpage>–<lpage>53</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1080/03080188.2019.1603870" xlink:type="simple">10.1080/03080188.2019.1603870</ext-link></comment></mixed-citation></ref>
<ref id="pone.0297211.ref016"><label>16</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Evans</surname> <given-names>L.</given-names></name> <article-title>Risk of fatality from physical trauma versus sex and age</article-title>. <source>J Trauma</source>. <year>1988</year>;<volume>28</volume>(<issue>3</issue>):<fpage>368</fpage>–<lpage>78</lpage>. Epub 1988/03/01. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1097/00005373-198803000-00013" xlink:type="simple">10.1097/00005373-198803000-00013</ext-link></comment> <object-id pub-id-type="pmid">3351994</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref017"><label>17</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Evans</surname> <given-names>L.</given-names></name> <article-title>Female compared with male fatality risk from similar physical impacts</article-title>. <source>Journal of Trauma</source>. <year>2001</year>;<volume>50</volume>(<issue>2</issue>):<fpage>281</fpage>–<lpage>8</lpage>. Epub 2001/03/10. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1097/00005373-200102000-00014" xlink:type="simple">10.1097/00005373-200102000-00014</ext-link></comment> <object-id pub-id-type="pmid">11242293</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref018"><label>18</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Bose</surname> <given-names>D</given-names></name>, <name name-style="western"><surname>Segui-Gomez</surname> <given-names>M</given-names></name>, <name name-style="western"><surname>Crandall</surname> <given-names>JR</given-names></name>. <article-title>Vulnerability of female drivers involved in motor vehicle crashes: an analysis of US population at risk.</article-title> <source>Am J Public Health</source>. <year>2011</year>;<volume>101</volume>(<issue>12</issue>):<fpage>2368</fpage>–<lpage>73</lpage>. Epub 2011/10/25. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.2105/AJPH.2011.300275" xlink:type="simple">10.2105/AJPH.2011.300275</ext-link></comment> <object-id pub-id-type="pmid">22021321</object-id>; PubMed Central PMCID: PMC3222446.</mixed-citation></ref>
<ref id="pone.0297211.ref019"><label>19</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Forman</surname> <given-names>J</given-names></name>, <name name-style="western"><surname>Poplin</surname> <given-names>GS</given-names></name>, <name name-style="western"><surname>Shaw</surname> <given-names>CG</given-names></name>, <name name-style="western"><surname>McMurry</surname> <given-names>TL</given-names></name>, <name name-style="western"><surname>Schmidt</surname> <given-names>K</given-names></name>, <name name-style="western"><surname>Ash</surname> <given-names>J</given-names></name>, <etal>et al</etal>. <article-title>Automobile injury trends in the contemporary fleet: Belted occupants in frontal collisions</article-title>. <source>Traffic Inj Prev</source>. <year>2019</year>;<volume>20</volume>(<issue>6</issue>):<fpage>607</fpage>–<lpage>12</lpage>. Epub 20190708. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1080/15389588.2019.1630825" xlink:type="simple">10.1080/15389588.2019.1630825</ext-link></comment> <object-id pub-id-type="pmid">31283362</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref020"><label>20</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Brumbelow</surname> <given-names>ML</given-names></name>, <name name-style="western"><surname>Jermakian</surname> <given-names>JS</given-names></name>. <article-title>Injury risks and crashworthiness benefits for females and males: Which differences are physiological?</article-title> <source>Traffic Inj Prev</source>. <year>2022</year>;<volume>23</volume>(<issue>1</issue>):<fpage>11</fpage>–<lpage>6</lpage>. Epub 20211207. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1080/15389588.2021.2004312" xlink:type="simple">10.1080/15389588.2021.2004312</ext-link></comment> <object-id pub-id-type="pmid">34874809</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref021"><label>21</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Abrams</surname> <given-names>MZ</given-names></name>, <name name-style="western"><surname>Bass</surname> <given-names>CR</given-names></name>. <article-title>fars_cleaner: A Python package for downloading and pre-processing vehicle fatality data in the US</article-title>. <source>Journal of Open Source Software</source>. <year>2022</year>;<volume>7</volume>(<issue>79</issue>):<fpage>4678</fpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.21105/joss.04678" xlink:type="simple">10.21105/joss.04678</ext-link></comment></mixed-citation></ref>
<ref id="pone.0297211.ref022"><label>22</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Abrams</surname> <given-names>M.</given-names></name> <source>mzabrams/fars-cleaner v1.0.1.</source> <year>2020</year>. <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.5281/zenodo.3735486" xlink:type="simple">https://doi.org/10.5281/zenodo.3735486</ext-link>.</mixed-citation></ref>
<ref id="pone.0297211.ref023"><label>23</label><mixed-citation publication-type="journal" xlink:type="simple"><collab>The Pandas Development Team</collab>. <article-title>pandas-dev/pandas: Pandas</article-title>. <source>v1.5.1 ed: Zenodo</source>; <year>2022</year>.</mixed-citation></ref>
<ref id="pone.0297211.ref024"><label>24</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>McKinney</surname> <given-names>W.</given-names></name> <article-title>pandas: a foundational Python library for data analysis and statistics</article-title>. <source>Python for High Performance and Scientific Computing</source>. <year>2011</year>;<volume>14</volume>. mckinney2011pandas.</mixed-citation></ref>
<ref id="pone.0297211.ref025"><label>25</label><mixed-citation publication-type="other" xlink:type="simple">Ma EJ, Barry Z, Zuckerman S, Sailer Z, editors. pyjanitor: A Cleaner API for Cleaning Data. Proceedings of the 18th Python in Science Conference; 2019.</mixed-citation></ref>
<ref id="pone.0297211.ref026"><label>26</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Kluyver</surname> <given-names>T</given-names></name>, <name name-style="western"><surname>Ragan-Kelley</surname> <given-names>B</given-names></name>, <name name-style="western"><surname>Pérez</surname> <given-names>F</given-names></name>, <name name-style="western"><surname>Granger</surname> <given-names>BE</given-names></name>, <name name-style="western"><surname>Bussonnier</surname> <given-names>M</given-names></name>, <name name-style="western"><surname>Frederic</surname> <given-names>J</given-names></name>, <etal>et al</etal>., editors. <article-title>Jupyter Notebooks—a publishing format for reproducible computational workflows.</article-title> <source>ELPUB</source>; <year>2016</year>.</mixed-citation></ref>
<ref id="pone.0297211.ref027"><label>27</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Perez</surname> <given-names>F</given-names></name>, <name name-style="western"><surname>Granger</surname> <given-names>BE</given-names></name>. <article-title>IPython: A System for Interactive Scientific Computing</article-title>. <source>Computing in Science &amp; Engineering</source>. <year>2007</year>;<volume>9</volume>(<issue>3</issue>):<fpage>21</fpage>–<lpage>9</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1109/mcse.2007.53" xlink:type="simple">10.1109/mcse.2007.53</ext-link></comment></mixed-citation></ref>
<ref id="pone.0297211.ref028"><label>28</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Hunter</surname> <given-names>JD</given-names></name>. <article-title>Matplotlib: A 2D Graphics Environment</article-title>. <source>Computing in Science &amp; Engineering</source>. <year>2007</year>;<volume>9</volume>(<issue>3</issue>):<fpage>90</fpage>–<lpage>5</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1109/mcse.2007.55" xlink:type="simple">10.1109/mcse.2007.55</ext-link></comment></mixed-citation></ref>
<ref id="pone.0297211.ref029"><label>29</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Evans</surname> <given-names>L.</given-names></name> <article-title>Double pair comparison—A new method to determine how occupant characteristics affect fatality risk in traffic crashes.</article-title> <source>Accident Analysis &amp; Prevention.</source> <year>1986</year>;<volume>18</volume>(<issue>3</issue>):<fpage>217</fpage>–<lpage>27</lpage>. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/0001-4575%2886%2990006-0" xlink:type="simple">10.1016/0001-4575(86)90006-0</ext-link></comment> <object-id pub-id-type="pmid">3730096</object-id></mixed-citation></ref>
<ref id="pone.0297211.ref030"><label>30</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Cummings</surname> <given-names>P</given-names></name>, <name name-style="western"><surname>McKnight</surname> <given-names>B</given-names></name>, <name name-style="western"><surname>Weiss</surname> <given-names>NS</given-names></name>. <article-title>Matched-pair cohort methods in traffic crash research.</article-title> <source>Accident Analysis &amp; Prevention</source>. <year>2003</year>;<volume>35</volume>(<issue>1</issue>):<fpage>131</fpage>–<lpage>41</lpage>. Epub 2002/12/14. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/s0001-4575%2801%2900108-7" xlink:type="simple">10.1016/s0001-4575(01)00108-7</ext-link></comment> <object-id pub-id-type="pmid">12479904</object-id>.</mixed-citation></ref>
<ref id="pone.0297211.ref031"><label>31</label><mixed-citation publication-type="other" xlink:type="simple">Saul RA, Pritz HB, McFadden J, Backaitis SH, Hallenbeck H, Rhule D, editors. Description and performance of the Hybrid III three-year-old, six-year-old and small female test dummies in restraint system and out-of-position air bag environments. 17th Enhanced Safety of Vehicles Conference; 2001; Amsterdam, The Netherlands2001.</mixed-citation></ref>
<ref id="pone.0297211.ref032"><label>32</label><mixed-citation publication-type="other" xlink:type="simple">Shin J, Donlon JP, Richardson R, Espelien C, Gallaher M, Luong V, et al. Comparison of Pelvis Kinematics and Injuries in Reclined Frontal Impact Sled Tests Between Mid-Size Adult Male and Female PMHS.</mixed-citation></ref>
<ref id="pone.0297211.ref033"><label>33</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Alswat</surname> <given-names>KA</given-names></name>. <article-title>Gender Disparities in Osteoporosis.</article-title> <source>Journal of Clinical Medicine Research</source>. <year>2017</year>;<volume>9</volume>(<issue>5</issue>):<fpage>382</fpage>–<lpage>7</lpage>. Epub 2017/04/11. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.14740/jocmr2970w" xlink:type="simple">10.14740/jocmr2970w</ext-link></comment> <object-id pub-id-type="pmid">28392857</object-id>; PubMed Central PMCID: PMC5380170.</mixed-citation></ref>
<ref id="pone.0297211.ref034"><label>34</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Hannan</surname> <given-names>MT</given-names></name>, <name name-style="western"><surname>Felson</surname> <given-names>DT</given-names></name>, <name name-style="western"><surname>Dawson-Hughes</surname> <given-names>B</given-names></name>, <name name-style="western"><surname>Tucker</surname> <given-names>KL</given-names></name>, <name name-style="western"><surname>Cupples</surname> <given-names>LA</given-names></name>, <name name-style="western"><surname>Wilson</surname> <given-names>PW</given-names></name>, <etal>et al</etal>. <article-title>Risk factors for longitudinal bone loss in elderly men and women: the Framingham Osteoporosis Study</article-title>. <source>J Bone Miner Res</source>. <year>2000</year>;<volume>15</volume>(<issue>4</issue>):<fpage>710</fpage>–<lpage>20</lpage>. Epub 2000/04/26. <comment>doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1359/jbmr.2000.15.4.710" xlink:type="simple">10.1359/jbmr.2000.15.4.710</ext-link></comment> <object-id pub-id-type="pmid">10780863</object-id>.</mixed-citation></ref>
</ref-list>
</back>
</article>