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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article">
<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">JDS1166</article-id>
<article-id pub-id-type="doi">10.6339/25-JDS1166</article-id>
<article-categories><subj-group subj-group-type="heading">
<subject>Statistical Data Science</subject></subj-group></article-categories>
<title-group>
<article-title>Variable Selection with FDR Control for Noisy Data – An Application to Screening Metabolites that Are Associated with Breast Cancer and Colorectal Cancer</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Wang</surname><given-names>Runqiu</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_001">1</xref>
</contrib>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3732-2789</contrib-id>
<name><surname>Dai</surname><given-names>Ran</given-names></name><email xlink:href="mailto:ran.dai@unmc.edu">ran.dai@unmc.edu</email><xref ref-type="aff" rid="j_jds1166_aff_001">1</xref><xref ref-type="corresp" rid="cor1">∗</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Huang</surname><given-names>Ying</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_002">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Neuhouser</surname><given-names>Marian L.</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_002">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Lampe</surname><given-names>Johanna W.</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_002">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Raftery</surname><given-names>Daniel</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_003">3</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Tabung</surname><given-names>Fred K.</given-names></name><xref ref-type="aff" rid="j_jds1166_aff_004">4</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Zheng</surname><given-names>Cheng</given-names></name><email xlink:href="mailto:cheng.zheng@unmc.edu">cheng.zheng@unmc.edu</email><xref ref-type="aff" rid="j_jds1166_aff_001">1</xref><xref ref-type="corresp" rid="cor1">∗</xref>
</contrib>
<aff id="j_jds1166_aff_001"><label>1</label>Department of Biostatistics, <institution>University of Nebraska Medical Center</institution>, Omaha, Nebraska, <country>U.S.A.</country></aff>
<aff id="j_jds1166_aff_002"><label>2</label>Division of Public Health Sciences, <institution>Fred Hutchinson Cancer Center</institution>, Seattle, Washington, <country>U.S.A.</country></aff>
<aff id="j_jds1166_aff_003"><label>3</label>Department of Anesthesiology and Pain Medicine, <institution>University of Washington</institution>, Seattle, Washington, <country>U.S.A.</country></aff>
<aff id="j_jds1166_aff_004"><label>4</label>Department of Internal Medicine, College of Medicine and Comprehensive Cancer Center, <institution>The Ohio State University</institution>, Columbus, Ohio, <country>U.S.A.</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>∗</label>Corresponding author. Email: <ext-link ext-link-type="uri" xlink:href="mailto:ran.dai@unmc.edu">ran.dai@unmc.edu</ext-link> or <ext-link ext-link-type="uri" xlink:href="mailto:cheng.zheng@unmc.edu">cheng.zheng@unmc.edu</ext-link>.</corresp>
</author-notes>
<pub-date pub-type="ppub"><year>2025</year></pub-date><pub-date pub-type="epub"><day>11</day><month>6</month><year>2025</year></pub-date><volume>23</volume><issue>3</issue><fpage>499</fpage><lpage>520</lpage><supplementary-material id="S1" content-type="archive" xlink:href="jds1166_s001.zip" mimetype="application" mime-subtype="x-zip-compressed">
<caption>
<title>Supplementary Material</title>
<p>We provide an additional pdf file that includes additional simulation results and real data analysis. The R codes for the analysis of this paper are available at <ext-link ext-link-type="uri" xlink:href="https://github.com/RunqiuWang22/Variable_Selection_FDR_noisy">https://github.com/RunqiuWang22/Variable_Selection_FDR_noisy</ext-link>.</p>
</caption>
</supplementary-material><history><date date-type="received"><day>29</day><month>6</month><year>2024</year></date><date date-type="accepted"><day>7</day><month>1</month><year>2025</year></date></history>
<permissions><copyright-statement>2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.</copyright-statement><copyright-year>2025</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>The rapidly expanding field of metabolomics presents an invaluable resource for understanding the associations between metabolites and various diseases. However, the high dimensionality, presence of missing values, and measurement errors associated with metabolomics data can present challenges in developing reliable and reproducible approaches for disease association studies. Therefore, there is a compelling need for robust statistical analyses that can navigate these complexities to achieve reliable and reproducible disease association studies. In this paper, we construct algorithms to perform variable selection for noisy data and control the False Discovery Rate when selecting mutual metabolomic predictors for multiple disease outcomes. We illustrate the versatility and performance of this procedure in a variety of scenarios, dealing with missing data and measurement errors. As a specific application of this novel methodology, we target two of the most prevalent cancers among US women: breast cancer and colorectal cancer. By applying our method to the Women’s Health Initiative data, we successfully identify metabolites that are associated with either or both of these cancers, demonstrating the practical utility and potential of our method in identifying consistent risk factors and understanding shared mechanisms between diseases.</p>
</abstract>
<kwd-group>
<label>Keywords</label>
<kwd>cancer</kwd>
<kwd>FDR control</kwd>
<kwd>measurement error</kwd>
<kwd>metabolomics data</kwd>
<kwd>missing data</kwd>
<kwd>variable selection</kwd>
</kwd-group>
<funding-group><funding-statement>This research is partly supported by the National Cancer Institute under grants R01 CA119171, CA277133, and P30 CA015704 and by the National Institute of General Medical Sciences under grant U54 GM115458. The WHI programs are funded by the National Heart, Lung, and Blood Institute, National Institutes of Health, U.S. Department of Health and Human Services through contracts, HHSN268201600018C, HHSN268201600001C, HHSN268201600002C, HHSN268201600003C, and HHSN268201600004C.</funding-statement></funding-group>
</article-meta>
</front>
<back>
<ref-list id="j_jds1166_reflist_001">
<title>References</title>
<ref id="j_jds1166_ref_001">
<mixed-citation publication-type="book"> <string-name><surname>ACS</surname></string-name> (<year>2020</year>). <source><italic>Cancer Facts and Figures 2020</italic></source>. <publisher-name>American Cancer Society</publisher-name>, <publisher-loc>Atlanta, GA</publisher-loc>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_002">
<mixed-citation publication-type="journal"> <string-name><surname>Antoniadis</surname> <given-names>A</given-names></string-name>, <string-name><surname>Fryzlewicz</surname> <given-names>P</given-names></string-name>, <string-name><surname>Letué</surname> <given-names>F</given-names></string-name>, <string-name><surname>Sapatinas</surname> <given-names>T</given-names></string-name> (<year>2010</year>). <article-title>The Dantzig selector in Cox’s proportional hazards model</article-title>. <source><italic>Scandinavian Journal of Statistics</italic></source>, <volume>37</volume>(<issue>4</issue>): <fpage>531</fpage>–<lpage>552</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/j.1467-9469.2009.00685.x" xlink:type="simple">https://doi.org/10.1111/j.1467-9469.2009.00685.x</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_003">
<mixed-citation publication-type="journal"> <string-name><surname>Bae</surname> <given-names>S</given-names></string-name>, <string-name><surname>Ulrich</surname> <given-names>CM</given-names></string-name>, <string-name><surname>Neuhouser</surname> <given-names>ML</given-names></string-name>, <string-name><surname>Malysheva</surname> <given-names>O</given-names></string-name>, <string-name><surname>Bailey</surname> <given-names>LB</given-names></string-name>, <string-name><surname>Xiao</surname> <given-names>L</given-names></string-name>, <etal>et al.</etal> (<year>2014</year>). <article-title>Plasma choline metabolites and colorectal cancer risk in the women’s health initiative observational study</article-title>. <source><italic>Cancer Research</italic></source>, <volume>74</volume>(<issue>24</issue>): <fpage>7442</fpage>–<lpage>7452</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1158/0008-5472.CAN-14-1835" xlink:type="simple">https://doi.org/10.1158/0008-5472.CAN-14-1835</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_004">
<mixed-citation publication-type="journal"> <string-name><surname>Barber</surname> <given-names>RF</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>EJ</given-names></string-name> (<year>2015</year>). <article-title>Controlling the false discovery rate via knockoffs</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>43</volume>(<issue>5</issue>): <fpage>2055</fpage>–<lpage>2085</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/15-AOS1337" xlink:type="simple">https://doi.org/10.1214/15-AOS1337</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_005">
<mixed-citation publication-type="journal"> <string-name><surname>Barber</surname> <given-names>RF</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>EJ</given-names></string-name> (<year>2019</year>). <article-title>A knockoff filter for high-dimensional selective inference</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>47</volume>(<issue>5</issue>): <fpage>2504</fpage>–<lpage>2537</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/18-AOS1765" xlink:type="simple">https://doi.org/10.1214/18-AOS1765</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_006">
<mixed-citation publication-type="journal"> <string-name><surname>Barber</surname> <given-names>RF</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>EJ</given-names></string-name>, <string-name><surname>Samworth</surname> <given-names>RJ</given-names></string-name> (<year>2020</year>). <article-title>Robust inference with knockoffs</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>48</volume>(<issue>3</issue>): <fpage>1409</fpage>–<lpage>1431</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_007">
<mixed-citation publication-type="journal"> <string-name><surname>Bates</surname> <given-names>S</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>E</given-names></string-name>, <string-name><surname>Janson</surname> <given-names>L</given-names></string-name>, <string-name><surname>Wang</surname> <given-names>W</given-names></string-name> (<year>2021</year>). <article-title>Metropolized knockoff sampling</article-title>. <source><italic>Journal of the American Statistical Association</italic></source>, <volume>116</volume>(<issue>535</issue>): <fpage>1413</fpage>–<lpage>1427</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1080/01621459.2020.1729163" xlink:type="simple">https://doi.org/10.1080/01621459.2020.1729163</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_008">
<mixed-citation publication-type="journal"> <string-name><surname>Benjamini</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Hochberg</surname> <given-names>Y</given-names></string-name> (<year>1995</year>). <article-title>Controlling the false discovery rate: A practical and powerful approach to multiple testing</article-title>. <source><italic>Journal of the Royal Statistical Society, Series B, Methodological</italic></source>, <volume>57</volume>(<issue>1</issue>): <fpage>289</fpage>–<lpage>300</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/j.2517-6161.1995.tb02031.x" xlink:type="simple">https://doi.org/10.1111/j.2517-6161.1995.tb02031.x</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_009">
<mixed-citation publication-type="journal"> <string-name><surname>Bogomolov</surname> <given-names>M</given-names></string-name>, <string-name><surname>Heller</surname> <given-names>R</given-names></string-name> (<year>2013</year>). <article-title>Discovering findings that replicate from a primary study of high dimension to a follow-up study</article-title>. <source><italic>Journal of the American Statistical Association</italic></source>, <volume>108</volume>(<issue>504</issue>): <fpage>1480</fpage>–<lpage>1492</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1080/01621459.2013.829002" xlink:type="simple">https://doi.org/10.1080/01621459.2013.829002</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_010">
<mixed-citation publication-type="journal"> <string-name><surname>Bogomolov</surname> <given-names>M</given-names></string-name>, <string-name><surname>Heller</surname> <given-names>R</given-names></string-name> (<year>2018</year>). <article-title>Assessing replicability of findings across two studies of multiple features</article-title>. <source><italic>Biometrika</italic></source>, <volume>105</volume>(<issue>3</issue>): <fpage>505</fpage>–<lpage>516</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1093/biomet/asy029" xlink:type="simple">https://doi.org/10.1093/biomet/asy029</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_011">
<mixed-citation publication-type="journal"> <string-name><surname>Candès</surname> <given-names>E</given-names></string-name>, <string-name><surname>Fan</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Janson</surname> <given-names>L</given-names></string-name>, <string-name><surname>Lv</surname> <given-names>J</given-names></string-name> (<year>2018</year>). <article-title>Panning for gold: ‘Model-x’ knockoffs for high dimensional controlled variable selection</article-title>. <source><italic>Journal of the Royal Statistical Society, Series B, Statistical Methodology</italic></source>, <volume>80</volume>(<issue>3</issue>): <fpage>551</fpage>–<lpage>577</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/rssb.12265" xlink:type="simple">https://doi.org/10.1111/rssb.12265</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_012">
<mixed-citation publication-type="journal"> <string-name><surname>Cappelletti</surname> <given-names>V</given-names></string-name>, <string-name><surname>Iorio</surname> <given-names>E</given-names></string-name>, <string-name><surname>Miodini</surname> <given-names>P</given-names></string-name>, <string-name><surname>Silvestri</surname> <given-names>M</given-names></string-name>, <string-name><surname>Dugo</surname> <given-names>M</given-names></string-name>, <string-name><surname>Daidone</surname> <given-names>MG</given-names></string-name> (<year>2017</year>). <article-title>Metabolic footprints and molecular subtypes in breast cancer</article-title>. <source><italic>Disease Markers</italic></source>, <volume>2017</volume>(<issue>1</issue>): <fpage>7687851</fpage>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_013">
<mixed-citation publication-type="journal"> <string-name><surname>Chen</surname> <given-names>J</given-names></string-name>, <string-name><surname>Hou</surname> <given-names>A</given-names></string-name>, <string-name><surname>Hou</surname> <given-names>TY</given-names></string-name> (<year>2019</year>). <article-title>A prototype knockoff filter for group selection with FDR control</article-title>. <source><italic>Information and Inference</italic></source>, <volume>9</volume>(<issue>2</issue>): <fpage>271</fpage>–<lpage>288</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1093/imaiai/iaz012" xlink:type="simple">https://doi.org/10.1093/imaiai/iaz012</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_014">
<mixed-citation publication-type="journal"> <string-name><surname>Cheung</surname> <given-names>PK</given-names></string-name>, <string-name><surname>Ma</surname> <given-names>MH</given-names></string-name>, <string-name><surname>Tse</surname> <given-names>HF</given-names></string-name>, <string-name><surname>Yeung</surname> <given-names>KY</given-names></string-name>, <string-name><surname>Tsang</surname> <given-names>HC</given-names></string-name>, <string-name><surname>Chu</surname> <given-names>MK</given-names></string-name>, <etal>et al.</etal> (<year>2019</year>). <article-title>The applications of metabolomics in the molecular diagnostics of cancer</article-title>. <source><italic>Expert Review of Molecular Diagnostics</italic></source>, <volume>19</volume>(<issue>9</issue>): <fpage>785</fpage>–<lpage>793</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1080/14737159.2019.1656530" xlink:type="simple">https://doi.org/10.1080/14737159.2019.1656530</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_015">
<mixed-citation publication-type="journal"> <string-name><surname>Chi</surname> <given-names>Z</given-names></string-name> (<year>2008</year>). <article-title>False discovery rate control with multivariate p-values</article-title>. <source><italic>Electronic Journal of Statistics</italic></source>, <volume>2</volume>: <fpage>368</fpage>–<lpage>411</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_016">
<mixed-citation publication-type="chapter"> <string-name><surname>Dai</surname> <given-names>R</given-names></string-name>, <string-name><surname>Barber</surname> <given-names>R</given-names></string-name> (<year>2016</year>). <chapter-title>The knockoff filter for FDR control in group-sparse and multitask regression</chapter-title>. In: <source><italic>Proceedings of The 33rd International Conference on Machine Learning</italic></source> (<string-name><given-names>MF</given-names> <surname>Balcan</surname></string-name>, <string-name><given-names>KQ</given-names> <surname>Weinberger</surname></string-name>, eds.), volume <volume>48</volume> of <series><italic>Proceedings of Machine Learning Research</italic></series>, <fpage>1851</fpage>–<lpage>1859</lpage>. <publisher-name>PMLR</publisher-name>, <publisher-loc>New York, New York, USA</publisher-loc>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_017">
<mixed-citation publication-type="journal"> <string-name><surname>Dai</surname> <given-names>R</given-names></string-name>, <string-name><surname>Zheng</surname> <given-names>C</given-names></string-name> (<year>2023</year>). <article-title>False discovery rate-controlled multiple testing for union null hypotheses: A knockoff-based approach</article-title>. <source><italic>Biometrics</italic></source>, <volume>79</volume>(<issue>4</issue>): <fpage>3497</fpage>–<lpage>3509</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/biom.13848" xlink:type="simple">https://doi.org/10.1111/biom.13848</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_018">
<mixed-citation publication-type="journal"> <string-name><surname>Datta</surname> <given-names>A</given-names></string-name>, <string-name><surname>Zou</surname> <given-names>H</given-names></string-name> (<year>2017</year>). <article-title>Cocolasso for high-dimensional error-in-variables regression</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>45</volume>: <fpage>2400</fpage>–<lpage>2426</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/16-AOS1527" xlink:type="simple">https://doi.org/10.1214/16-AOS1527</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_019">
<mixed-citation publication-type="journal"> <string-name><surname>Garcia</surname> <given-names>RI</given-names></string-name>, <string-name><surname>Ibrahim</surname> <given-names>JG</given-names></string-name>, <string-name><surname>Zhu</surname> <given-names>H</given-names></string-name> (<year>2010</year>). <article-title>Variable selection in the Cox regression model with covariates missing at random</article-title>. <source><italic>Biometrics</italic></source>, <volume>66</volume>(<issue>1</issue>): <fpage>97</fpage>–<lpage>104</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/j.1541-0420.2009.01274.x" xlink:type="simple">https://doi.org/10.1111/j.1541-0420.2009.01274.x</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_020">
<mixed-citation publication-type="journal"> <string-name><surname>Hata</surname> <given-names>N</given-names></string-name>, <string-name><surname>Shigeyasu</surname> <given-names>K</given-names></string-name>, <string-name><surname>Umeda</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Yano</surname> <given-names>S</given-names></string-name>, <string-name><surname>Takeda</surname> <given-names>S</given-names></string-name>, <string-name><surname>Yoshida</surname> <given-names>K</given-names></string-name>, <etal>et al.</etal> (<year>2023</year>). <article-title>ADAR1 is a promising risk stratification biomarker of remnant liver recurrence after hepatic metastasectomy for colorectal cancer</article-title>. <source><italic>Scientific Reports</italic></source>, <volume>13</volume>(<issue>1</issue>): <fpage>2078</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1038/s41598-023-29397-z" xlink:type="simple">https://doi.org/10.1038/s41598-023-29397-z</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_021">
<mixed-citation publication-type="journal"> <string-name><surname>Heller</surname> <given-names>R</given-names></string-name>, <string-name><surname>Bogomolov</surname> <given-names>M</given-names></string-name>, <string-name><surname>Benjamini</surname> <given-names>Y</given-names></string-name> (<year>2014</year>). <article-title>Deciding whether follow-up studies have replicated findings in a preliminary large-scale omics study</article-title>. <source><italic>Proceedings of the National Academy of Sciences</italic></source>, <volume>111</volume>(<issue>46</issue>): <fpage>16262</fpage>–<lpage>16267</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1073/pnas.1314814111" xlink:type="simple">https://doi.org/10.1073/pnas.1314814111</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_022">
<mixed-citation publication-type="journal"> <string-name><surname>Heller</surname> <given-names>R</given-names></string-name>, <string-name><surname>Yekutieli</surname> <given-names>D</given-names></string-name> (<year>2014</year>). <article-title>Replicability analysis for genome-wide association studies</article-title>. <source><italic>Annals of Applied Statistics</italic></source>, <volume>8</volume>(<issue>1</issue>): <fpage>481</fpage>–<lpage>498</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/13-AOAS697" xlink:type="simple">https://doi.org/10.1214/13-AOAS697</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_023">
<mixed-citation publication-type="journal"> <string-name><surname>His</surname> <given-names>M</given-names></string-name>, <string-name><surname>Viallon</surname> <given-names>V</given-names></string-name>, <string-name><surname>Dossus</surname> <given-names>L</given-names></string-name>, <string-name><surname>Gicquiau</surname> <given-names>A</given-names></string-name>, <string-name><surname>Achaintre</surname> <given-names>D</given-names></string-name>, <string-name><surname>Scalbert</surname> <given-names>A</given-names></string-name>, <etal>et al.</etal> (<year>2019</year>). <article-title>Prospective analysis of circulating metabolites and breast cancer in epic</article-title>. <source><italic>BMC Medicine</italic></source>, <volume>17</volume>(<issue>1</issue>): <fpage>178</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1186/s12916-019-1408-4" xlink:type="simple">https://doi.org/10.1186/s12916-019-1408-4</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_024">
<mixed-citation publication-type="journal"> <string-name><surname>Huang</surname> <given-names>D</given-names></string-name>, <string-name><surname>Janson</surname> <given-names>L</given-names></string-name> (<year>2020</year>). <article-title>Relaxing the assumptions of knockoffs by conditioning</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>48</volume>(<issue>5</issue>): <fpage>3021</fpage>–<lpage>3042</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_025">
<mixed-citation publication-type="journal"> <string-name><surname>Johnson</surname> <given-names>BA</given-names></string-name> (<year>2008</year>). <article-title>Variable selection in semiparametric linear regression with censored data</article-title>. <source><italic>Journal of the Royal Statistical Society, Series B, Statistical Methodology</italic></source>, <volume>70</volume>(<issue>2</issue>): <fpage>351</fpage>–<lpage>370</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1111/j.1467-9868.2008.00639.x" xlink:type="simple">https://doi.org/10.1111/j.1467-9868.2008.00639.x</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_026">
<mixed-citation publication-type="journal"> <string-name><surname>Kampman</surname> <given-names>E</given-names></string-name>, <string-name><surname>Thompson</surname> <given-names>R</given-names></string-name>, <string-name><surname>Wiseman</surname> <given-names>M</given-names></string-name>, <string-name><surname>Mitrou</surname> <given-names>G</given-names></string-name>, <string-name><surname>Allen</surname> <given-names>K</given-names></string-name> (<year>2018</year>). <article-title>PO-087 the WCRF/AICR third expert report on diet, nutrition, physical activity and cancer: Updated recommendations</article-title>. <source><italic>ESMO Open</italic></source>, <volume>3</volume>: <fpage>A260</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1136/esmoopen-2018-EACR25.615" xlink:type="simple">https://doi.org/10.1136/esmoopen-2018-EACR25.615</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_027">
<mixed-citation publication-type="journal"> <string-name><surname>Li</surname> <given-names>S</given-names></string-name>, <string-name><surname>Sesia</surname> <given-names>M</given-names></string-name>, <string-name><surname>Romano</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>E</given-names></string-name>, <string-name><surname>Sabatti</surname> <given-names>C</given-names></string-name> (<year>2021</year>). <article-title>Searching for robust associations with a multi-environment knockoff filter</article-title>. <source><italic>Biometrika</italic></source>, <volume>109</volume>(<issue>3</issue>): <fpage>611</fpage>–<lpage>629</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1093/biomet/asab055" xlink:type="simple">https://doi.org/10.1093/biomet/asab055</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_028">
<mixed-citation publication-type="book"> <string-name><surname>Little</surname> <given-names>RJ</given-names></string-name>, <string-name><surname>Rubin</surname> <given-names>DB</given-names></string-name> (<year>2002</year>). <source><italic>Statistical Analysis with Missing Data</italic></source>. <publisher-name>John Wiley &amp; Sons</publisher-name>, <publisher-loc>New York</publisher-loc>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_029">
<mixed-citation publication-type="journal"> <string-name><surname>Liu</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Zheng</surname> <given-names>C</given-names></string-name> (<year>2019</year>). <article-title>Deep latent variable models for generating knockoffs</article-title>. <source><italic>Stat</italic></source>, <volume>8</volume>(<issue>1</issue>): <fpage>e260</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1002/sta4.260" xlink:type="simple">https://doi.org/10.1002/sta4.260</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_030">
<mixed-citation publication-type="journal"> <string-name><surname>Loh</surname> <given-names>PL</given-names></string-name>, <string-name><surname>Wainwright</surname> <given-names>MJ</given-names></string-name> (<year>2012</year>). <article-title>High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>40</volume>(<issue>3</issue>): <fpage>1637</fpage>–<lpage>1664</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/12-AOS1018" xlink:type="simple">https://doi.org/10.1214/12-AOS1018</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_031">
<mixed-citation publication-type="journal"> <string-name><surname>Loktionov</surname> <given-names>A</given-names></string-name> (<year>2020</year>). <article-title>Biomarkers for detecting colorectal cancer non-invasively: DNA, RNA or proteins?</article-title> <source><italic>World Journal of Gastrointestinal Oncology</italic></source>, <volume>12</volume>(<issue>2</issue>): <fpage>124</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.4251/wjgo.v12.i2.124" xlink:type="simple">https://doi.org/10.4251/wjgo.v12.i2.124</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_032">
<mixed-citation publication-type="journal"> <string-name><surname>Machala</surname> <given-names>M</given-names></string-name>, <string-name><surname>Procházková</surname> <given-names>J</given-names></string-name>, <string-name><surname>Hofmanová</surname> <given-names>J</given-names></string-name>, <string-name><surname>Králiková</surname> <given-names>L</given-names></string-name>, <string-name><surname>Slavík</surname> <given-names>J</given-names></string-name>, <string-name><surname>Tylichová</surname> <given-names>Z</given-names></string-name>, <etal>et al.</etal> (<year>2019</year>). <article-title>Colon cancer and perturbations of the sphingolipid metabolism</article-title>. <source><italic>International Journal of Molecular Sciences</italic></source>, <volume>20(23)</volume>: <fpage>6051</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3390/ijms20236051" xlink:type="simple">https://doi.org/10.3390/ijms20236051</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_033">
<mixed-citation publication-type="journal"> <string-name><surname>Miller</surname> <given-names>JW</given-names></string-name>, <string-name><surname>Beresford</surname> <given-names>SA</given-names></string-name>, <string-name><surname>Neuhouser</surname> <given-names>ML</given-names></string-name>, <string-name><surname>Cheng</surname> <given-names>TYD</given-names></string-name>, <string-name><surname>Song</surname> <given-names>X</given-names></string-name>, <string-name><surname>Brown</surname> <given-names>EC</given-names></string-name>, <etal>et al.</etal> (<year>2013</year>). <article-title>Homocysteine, cysteine, and risk of incident colorectal cancer in the women’s health initiative observational cohort</article-title>. <source><italic>The American Journal of Clinical Nutrition</italic></source>, <volume>97</volume>(<issue>4</issue>): <fpage>827</fpage>–<lpage>834</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3945/ajcn.112.049932" xlink:type="simple">https://doi.org/10.3945/ajcn.112.049932</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_034">
<mixed-citation publication-type="journal"> <string-name><surname>Nannini</surname> <given-names>G</given-names></string-name>, <string-name><surname>Meoni</surname> <given-names>G</given-names></string-name>, <string-name><surname>Amedei</surname> <given-names>A</given-names></string-name>, <string-name><surname>Tenori</surname> <given-names>L</given-names></string-name> (<year>2020</year>). <article-title>Metabolomics profile in gastrointestinal cancers: Update and future perspectives</article-title>. <source><italic>World Journal of Gastroenterology</italic></source>, <volume>26</volume>(<issue>20</issue>): <fpage>2514</fpage>–<lpage>2532</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3748/wjg.v26.i20.2514" xlink:type="simple">https://doi.org/10.3748/wjg.v26.i20.2514</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_035">
<mixed-citation publication-type="journal"> <string-name><surname>Neitzel</surname> <given-names>C</given-names></string-name>, <string-name><surname>Demuth</surname> <given-names>P</given-names></string-name>, <string-name><surname>Wittmann</surname> <given-names>S</given-names></string-name>, <string-name><surname>Fahrer</surname> <given-names>J</given-names></string-name> (<year>2020</year>). <article-title>Targeting altered energy metabolism in colorectal cancer: Oncogenic reprogramming, the central role of the tca cycle and therapeutic opportunities</article-title>. <source><italic>Cancers</italic></source>, <volume>12</volume>(<issue>7</issue>): <fpage>1731</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3390/cancers12071731" xlink:type="simple">https://doi.org/10.3390/cancers12071731</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_036">
<mixed-citation publication-type="journal"> <string-name><surname>Ni</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Xie</surname> <given-names>G</given-names></string-name>, <string-name><surname>Jia</surname> <given-names>W</given-names></string-name> (<year>2014</year>). <article-title>Metabonomics of human colorectal cancer: New approaches for early diagnosis and biomarker discovery</article-title>. <source><italic>Journal of Proteome Research</italic></source>, <volume>13</volume>(<issue>9</issue>): <fpage>3857</fpage>–<lpage>3870</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1021/pr500443c" xlink:type="simple">https://doi.org/10.1021/pr500443c</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_037">
<mixed-citation publication-type="journal"> <string-name><surname>Playdon</surname> <given-names>MC</given-names></string-name>, <string-name><surname>Ziegler</surname> <given-names>RG</given-names></string-name>, <string-name><surname>Sampson</surname> <given-names>JN</given-names></string-name>, <string-name><surname>Stolzenberg-Solomon</surname> <given-names>R</given-names></string-name>, <string-name><surname>Thompson</surname> <given-names>HJ</given-names></string-name>, <string-name><surname>Irwin</surname> <given-names>ML</given-names></string-name>, <etal>et al.</etal> (<year>2017</year>). <article-title>Nutritional metabolomics and breast cancer risk in a prospective study</article-title>. <source><italic>The American Journal of Clinical Nutrition</italic></source>, <volume>106</volume>(<issue>2</issue>): <fpage>637</fpage>–<lpage>649</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3945/ajcn.116.150912" xlink:type="simple">https://doi.org/10.3945/ajcn.116.150912</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_038">
<mixed-citation publication-type="journal"> <string-name><surname>Putri</surname> <given-names>SP</given-names></string-name>, <string-name><surname>Nakayama</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Matsuda</surname> <given-names>F</given-names></string-name>, <etal>et al.</etal> (<year>2013</year>). <article-title>Current metabolomics: Practical applications</article-title>. <source><italic>Journal of Bioscience and Bioengineering</italic></source>, <volume>115</volume>(<issue>6</issue>): <fpage>579</fpage>–<lpage>589</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1016/j.jbiosc.2012.12.007" xlink:type="simple">https://doi.org/10.1016/j.jbiosc.2012.12.007</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_039">
<mixed-citation publication-type="journal"> <string-name><surname>Rässler</surname> <given-names>S</given-names></string-name>, <string-name><surname>Rubin</surname> <given-names>DB</given-names></string-name>, <string-name><surname>Zell</surname> <given-names>ER</given-names></string-name> (<year>2013</year>). <article-title>Imputation</article-title>. <source><italic>Wiley Interdisciplinary Reviews: Computational Statistics</italic></source>, <volume>5</volume>: <fpage>20</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1002/wics.1240" xlink:type="simple">https://doi.org/10.1002/wics.1240</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_040">
<mixed-citation publication-type="journal"> <string-name><surname>Romano</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Sesia</surname> <given-names>M</given-names></string-name>, <string-name><surname>Candès</surname> <given-names>E</given-names></string-name> (<year>2020</year>). <article-title>Deep knockoffs</article-title>. <source><italic>Journal of the American Statistical Association</italic></source>, <volume>115</volume>(<issue>532</issue>): <fpage>1861</fpage>–<lpage>1872</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1080/01621459.2019.1660174" xlink:type="simple">https://doi.org/10.1080/01621459.2019.1660174</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_041">
<mixed-citation publication-type="chapter"> <string-name><surname>Rosenbaum</surname> <given-names>M</given-names></string-name>, <string-name><surname>Tsybakov</surname> <given-names>AB</given-names></string-name> (<year>2013</year>). <chapter-title>Improved matrix uncertainty selector</chapter-title>. In: <source><italic>From Probability to Statistics and Back: High-Dimensional Models and Processes – A Festschrift in Honor of Jon A. Wellner</italic></source>, <fpage>276</fpage>–<lpage>290</lpage>. <publisher-name>Institute of Mathematical Statistics</publisher-name>, <publisher-loc>Beachwood, Ohio, USA</publisher-loc>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_042">
<mixed-citation publication-type="journal"> <string-name><surname>Rothwell</surname> <given-names>JA</given-names></string-name>, <string-name><surname>Bešević</surname> <given-names>J</given-names></string-name>, <string-name><surname>Dimou</surname> <given-names>N</given-names></string-name>, <string-name><surname>Breeur</surname> <given-names>M</given-names></string-name>, <string-name><surname>Murphy</surname> <given-names>N</given-names></string-name>, <string-name><surname>Jenab</surname> <given-names>M</given-names></string-name>, <etal>et al.</etal> (<year>2023</year>). <article-title>Circulating amino acid levels and colorectal cancer risk in the European prospective investigation into cancer and nutrition and UK biobank cohorts</article-title>. <source><italic>BMC Medicine</italic></source>, <volume>21</volume>(<issue>1</issue>): <fpage>80</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1186/s12916-023-02739-4" xlink:type="simple">https://doi.org/10.1186/s12916-023-02739-4</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_043">
<mixed-citation publication-type="journal"> <string-name><surname>Sorensen</surname> <given-names>O</given-names></string-name>, <string-name><surname>Frigessi</surname> <given-names>A</given-names></string-name>, <string-name><surname>Thoresen</surname> <given-names>M</given-names></string-name>, <string-name><surname>Glad</surname> <given-names>IK</given-names></string-name> (<year>2015</year>). <article-title>Measurement error in lasso: Impact and likelihood bias correction</article-title>. <source><italic>Statistica Sinica</italic></source>, <volume>25</volume>(<issue>2</issue>): <fpage>809</fpage>–<lpage>829</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_044">
<mixed-citation publication-type="journal"> <string-name><surname>Spector</surname> <given-names>A</given-names></string-name>, <string-name><surname>Janson</surname> <given-names>L</given-names></string-name> (<year>2022</year>). <article-title>Powerful knockoffs via minimizing reconstructability</article-title>. <source><italic>The Annals of Statistics</italic></source>, <volume>50</volume>(<issue>1</issue>): <fpage>252</fpage>–<lpage>276</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/21-AOS2104" xlink:type="simple">https://doi.org/10.1214/21-AOS2104</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_045">
<mixed-citation publication-type="book"> <string-name><surname>Tsiatis</surname> <given-names>AA</given-names></string-name> (<year>2006</year>). <source><italic>Semiparametric Theory and Missing Data</italic></source>. <publisher-name>Springer</publisher-name>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_046">
<mixed-citation publication-type="journal"> <string-name><surname>Valko-Rokytovská</surname> <given-names>M</given-names></string-name>, <string-name><surname>Očenáš</surname> <given-names>P</given-names></string-name>, <string-name><surname>Salayová</surname> <given-names>A</given-names></string-name>, <string-name><surname>Kostecká</surname> <given-names>Z</given-names></string-name> (<year>2021</year>). <article-title>Breast cancer: Targeting of steroid hormones in cancerogenesis and diagnostics</article-title>. <source><italic>International Journal of Molecular Sciences</italic></source>, <volume>22</volume>(<issue>11</issue>): <fpage>5878</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.3390/ijms22115878" xlink:type="simple">https://doi.org/10.3390/ijms22115878</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_047">
<mixed-citation publication-type="journal"> <string-name><surname>Vulcan</surname> <given-names>A</given-names></string-name>, <string-name><surname>Manjer</surname> <given-names>J</given-names></string-name>, <string-name><surname>Ohlsson</surname> <given-names>B</given-names></string-name> (<year>2017</year>). <article-title>High blood glucose levels are associated with higher risk of colon cancer in men: A cohort study</article-title>. <source><italic>BMC Cancer</italic></source>, <volume>17</volume>(<issue>1</issue>): <fpage>1</fpage>–<lpage>8</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1186/s12885-016-3022-6" xlink:type="simple">https://doi.org/10.1186/s12885-016-3022-6</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_048">
<mixed-citation publication-type="journal"> <string-name><surname>Wolfson</surname> <given-names>J</given-names></string-name> (<year>2011</year>). <article-title>EEBoost: A general method for prediction and variable selection based on estimating equations</article-title>. <source><italic>Journal of the American Statistical Association</italic></source>, <volume>106</volume>(<issue>493</issue>): <fpage>296</fpage>–<lpage>305</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1198/jasa.2011.tm10098" xlink:type="simple">https://doi.org/10.1198/jasa.2011.tm10098</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_049">
<mixed-citation publication-type="journal"> <string-name><surname>Xiao</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Xia</surname> <given-names>J</given-names></string-name>, <string-name><surname>Li</surname> <given-names>L</given-names></string-name>, <etal>et al.</etal> (<year>2019</year>). <article-title>Associations between dietary patterns and the risk of breast cancer: A systematic review and meta-analysis of observational studies</article-title>. <source><italic>Breast Cancer Research</italic></source>, <volume>21</volume>(<issue>1</issue>): <fpage>16</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1186/s13058-019-1096-1" xlink:type="simple">https://doi.org/10.1186/s13058-019-1096-1</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_050">
<mixed-citation publication-type="journal"> <string-name><surname>Xu</surname> <given-names>X</given-names></string-name>, <string-name><surname>Gammon</surname> <given-names>MD</given-names></string-name>, <string-name><surname>Zeisel</surname> <given-names>SH</given-names></string-name>, <string-name><surname>Lee</surname> <given-names>YL</given-names></string-name>, <string-name><surname>Wetmur</surname> <given-names>JG</given-names></string-name>, <string-name><surname>Teitelbaum</surname> <given-names>SL</given-names></string-name>, <etal>et al.</etal> (<year>2008</year>). <article-title>Choline metabolism and risk of breast cancer in a population-based study</article-title>. <source><italic>The FASEB Journal</italic></source>, <volume>22</volume>(<issue>6</issue>): <fpage>2045</fpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1096/fj.07-101279" xlink:type="simple">https://doi.org/10.1096/fj.07-101279</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_051">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>L</given-names></string-name>, <string-name><surname>Wang</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Cai</surname> <given-names>H</given-names></string-name>, <string-name><surname>Wang</surname> <given-names>S</given-names></string-name>, <string-name><surname>Shen</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Ke</surname> <given-names>C</given-names></string-name> (<year>2020</year>). <article-title>Application of metabolomics in the diagnosis of breast cancer: A systematic review</article-title>. <source><italic>Journal of Cancer</italic></source>, <volume>11</volume>(<issue>9</issue>): <fpage>2540</fpage>–<lpage>2551</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.7150/jca.37604" xlink:type="simple">https://doi.org/10.7150/jca.37604</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_052">
<mixed-citation publication-type="journal"> <string-name><surname>Yusof</surname> <given-names>AS</given-names></string-name>, <string-name><surname>Isa</surname> <given-names>ZM</given-names></string-name>, <string-name><surname>Shah</surname> <given-names>SA</given-names></string-name> (<year>2012</year>). <article-title>Dietary patterns and risk of colorectal cancer: A systematic review of cohort studies (2000–2011)</article-title>. <source><italic>Asian Pacific Journal of Cancer Prevention</italic></source>, <volume>13</volume>(<issue>9</issue>): <fpage>4713</fpage>–<lpage>4717</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.7314/APJCP.2012.13.9.4713" xlink:type="simple">https://doi.org/10.7314/APJCP.2012.13.9.4713</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_053">
<mixed-citation publication-type="chapter"> <string-name><surname>Zhang</surname> <given-names>C</given-names></string-name>, <string-name><surname>Quinones</surname> <given-names>A</given-names></string-name>, <string-name><surname>Le</surname> <given-names>A</given-names></string-name> (<year>2022</year>). <chapter-title>Metabolic reservoir cycles in cancer</chapter-title>. In: <source><italic>Seminars in Cancer Biology</italic></source>, volume <volume>86</volume>, <fpage>180</fpage>–<lpage>188</lpage>. <publisher-name>Elsevier</publisher-name>.</mixed-citation>
</ref>
<ref id="j_jds1166_ref_054">
<mixed-citation publication-type="journal"> <string-name><surname>Zhao</surname> <given-names>SD</given-names></string-name>, <string-name><surname>Nguyen</surname> <given-names>YT</given-names></string-name> (<year>2020</year>). <article-title>Nonparametric false discovery rate control for identifying simultaneous signals</article-title>. <source><italic>Electronic Journal of Statistics</italic></source>, <volume>14</volume>(<issue>1</issue>): <fpage>110</fpage>–<lpage>142</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1214/20-EJS1726" xlink:type="simple">https://doi.org/10.1214/20-EJS1726</ext-link></mixed-citation>
</ref>
<ref id="j_jds1166_ref_055">
<mixed-citation publication-type="journal"> <string-name><surname>Zhu</surname> <given-names>J</given-names></string-name>, <string-name><surname>Djukovic</surname> <given-names>D</given-names></string-name>, <string-name><surname>Deng</surname> <given-names>L</given-names></string-name>, <string-name><surname>Gu</surname> <given-names>H</given-names></string-name>, <string-name><surname>Himmati</surname> <given-names>F</given-names></string-name>, <string-name><surname>Chiorean</surname> <given-names>EG</given-names></string-name>, <etal>et al.</etal> (<year>2014</year>). <article-title>Colorectal cancer detection using targeted serum metabolic profiling</article-title>. <source><italic>Journal of Proteome Research</italic></source>, <volume>13</volume>(<issue>9</issue>): <fpage>4120</fpage>–<lpage>4130</lpage>. <ext-link ext-link-type="doi" xlink:href="https://doi.org/10.1021/pr500494u" xlink:type="simple">https://doi.org/10.1021/pr500494u</ext-link></mixed-citation>
</ref>
</ref-list>
</back>
</article>
