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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">JDS</journal-id>
<journal-title-group><journal-title>Journal of Data Science</journal-title></journal-title-group>
<issn pub-type="epub">1683-8602</issn><issn pub-type="ppub">1680-743X</issn><issn-l>1680-743X</issn-l>
<publisher>
<publisher-name>School of Statistics, Renmin University of China</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">JDS1224</article-id>
<article-id pub-id-type="doi">10.6339/26-JDS1224</article-id>
<article-categories><subj-group subj-group-type="heading">
<subject>Data Science in Action</subject></subj-group></article-categories>
<title-group>
<article-title>Relative Growth Modeling of Anthropometric Outcomes</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8169-1605</contrib-id>
<name><surname>Williamson</surname><given-names>John M.</given-names></name><xref ref-type="aff" rid="j_jds1224_aff_001">1</xref>
</contrib>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3176-6570</contrib-id>
<name><surname>Lin</surname><given-names>Hung-Mo</given-names></name><email xlink:href="mailto:hung-mo.lin@yale.edu">hung-mo.lin@yale.edu</email><xref ref-type="aff" rid="j_jds1224_aff_002">2</xref><xref ref-type="corresp" rid="cor1">∗</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname><given-names>Molin</given-names></name><xref ref-type="aff" rid="j_jds1224_aff_003">3</xref>
</contrib>
<aff id="j_jds1224_aff_001"><label>1</label>McKing Consulting Corporation, Atlanta, GA 30341, <institution>University</institution>, <country>USA</country></aff>
<aff id="j_jds1224_aff_002"><label>2</label>Department of Anesthesiology and Yale Center for Analytical Sciences, <institution>Yale University</institution>, New Haven, CT 06520-8051, <country>USA</country></aff>
<aff id="j_jds1224_aff_003"><label>3</label>Department of Epidemiology and Biostatistics, <institution>Harvard T.H. Chan School of Public Health</institution>, and Channing Division of Network Medicine, Harvard Medical School and Brigham and Women’s Hospital, Boston, MA 02115, <country>USA</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>∗</label>Corresponding author. Email: <ext-link ext-link-type="uri" xlink:href="mailto:hung-mo.lin@yale.edu">hung-mo.lin@yale.edu</ext-link>.</corresp>
</author-notes>
<pub-date pub-type="ppub"><year>2026</year></pub-date><pub-date pub-type="epub"><day>3</day><month>4</month><year>2026</year></pub-date><volume content-type="ahead-of-print">0</volume><issue>0</issue><fpage>1</fpage><lpage>15</lpage><supplementary-material id="S1" content-type="archive" xlink:href="jds1224_s001.zip" mimetype="application" mime-subtype="x-zip-compressed">
<caption>
<title>Supplementary Material</title>
<p>The data set, WHO growth curves, and the SAS IML programs can be downloaded from</p>
<p><uri>https://github.com/Hungmolin/Relative-growth-modeling-of-anthropometric-outcomes.git</uri>. A complete list of the files is described in README.txt.</p>
</caption>
</supplementary-material><history><date date-type="received"><day>2</day><month>6</month><year>2025</year></date><date date-type="accepted"><day>22</day><month>2</month><year>2026</year></date></history>
<permissions><copyright-statement>2026 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.</copyright-statement><copyright-year>2026</copyright-year>
<license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>Open access article under the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">CC BY</ext-link> license.</license-p></license></permissions>
<abstract>
<p>Traditionally z-scores specified from the WHO population growth curves have been used to describe a child’s growth in relation to his age- and sex-matched population distribution. We propose a new regression approach that offers a straightforward interpretation of the relative growth in terms of the original anthropometric variable. We create a hybrid data set consisting of the observations from the study of interest and counterpart pseudo-population observations imputed from the WHO population growth curves matched to each study participant. We then fit linear and quantile regression models to the hybrid data incorporating demographic variables (usually age and biological sex) corresponding to the growth curves of demographically-similar individuals, a study versus population indicator, and its interactions with demographic variables. We further control for confounding variables from the study by adding their interactions with the study indicator variable. The interaction terms between the study indicator and the demographic variables age and biologic sex can be interpreted as relative growth parameters that depict the differences in means (or quantiles) between the study participants and their pseudo-population counterparts of the original anthropometric variables, rather than the associated z-scores. We use anthropometric growth data from a prospective birth cohort study conducted in Uganda for illustration.</p>
</abstract>
<kwd-group>
<label>Keywords</label>
<kwd>linear regression</kwd>
<kwd>population life tables</kwd>
<kwd>quantile regression</kwd>
</kwd-group>
<funding-group><funding-statement>HML was partially supported by the National Health Institute under CTSA Grant UL1 TR001863.</funding-statement></funding-group>
</article-meta>
</front>
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