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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">JDS1046</article-id>
<article-id pub-id-type="doi">10.6339/22-JDS1046</article-id>
<article-categories><subj-group subj-group-type="heading">
<subject>Data Science in Action</subject></subj-group></article-categories>
<title-group>
<article-title>Propensity Score Modeling in Electronic Health Records with Time-to-Event Endpoints: Application to Kidney Transplantation</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Yu</surname><given-names>Jonathan W.</given-names></name><xref ref-type="aff" rid="j_jds1046_aff_001">1</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Bandyopadhyay</surname><given-names>Dipankar</given-names></name><email xlink:href="mailto:bandyopd@gmail.com">bandyopd@gmail.com</email><xref ref-type="aff" rid="j_jds1046_aff_001">1</xref><xref ref-type="corresp" rid="cor1">∗</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Yang</surname><given-names>Shu</given-names></name><xref ref-type="aff" rid="j_jds1046_aff_002">2</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Kang</surname><given-names>Le</given-names></name><xref ref-type="aff" rid="j_jds1046_aff_001">1</xref>
</contrib>
<contrib contrib-type="author">
<name><surname>Gupta</surname><given-names>Gaurav</given-names></name><xref ref-type="aff" rid="j_jds1046_aff_003">3</xref>
</contrib>
<aff id="j_jds1046_aff_001"><label>1</label>Department of Biostatistics, <institution>Virginia Commonwealth University</institution>, Richmond, VA, <country>USA</country></aff>
<aff id="j_jds1046_aff_002"><label>2</label>Department of Statistics, <institution>North Carolina State University</institution>, Raleigh, NC, <country>USA</country></aff>
<aff id="j_jds1046_aff_003"><label>3</label>Division of Nephrology, <institution>Virginia Commonwealth University</institution>, Richmond, VA, <country>USA</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>∗</label>Corresponding author. <italic>Address of Correspondence</italic>: One Capitol Square, 7th Floor, 830 East Main Street, PO Box 980032, Richmond, VA, 23298-0032, USA. Email: <ext-link ext-link-type="uri" xlink:href="mailto:bandyopd@gmail.com">bandyopd@gmail.com</ext-link>.</corresp>
</author-notes>
<pub-date pub-type="ppub"><year>2022</year></pub-date><pub-date pub-type="epub"><day>20</day><month>4</month><year>2022</year></pub-date><volume>20</volume><issue>2</issue><fpage>188</fpage><lpage>208</lpage><supplementary-material id="S1" content-type="archive" xlink:href="jds1046_s001.zip" mimetype="application" mime-subtype="x-zip-compressed">
<caption>
<title>Supplementary Material</title>
<p>Figures and Tables pertaining to the motivating UNOS data analysis, as well as computing code (in <monospace>R</monospace> and <monospace>SAS</monospace>) and a representative UNOS dataset consisting of a random sample with 19000 observations are available as accompanying supplementary materials associated with this paper.</p>
</caption>
</supplementary-material><history><date date-type="received"><day>20</day><month>7</month><year>2021</year></date><date date-type="accepted"><day>4</day><month>4</month><year>2022</year></date></history>
<permissions><copyright-statement>2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.</copyright-statement><copyright-year>2022</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>For large observational studies lacking a control group (unlike randomized controlled trials, RCT), propensity scores (PS) are often the method of choice to account for pre-treatment confounding in baseline characteristics, and thereby avoid substantial bias in treatment estimation. A vast majority of PS techniques focus on average treatment effect estimation, without any clear consensus on how to account for confounders, especially in a multiple treatment setting. Furthermore, for <italic>time-to event</italic> outcomes, the analytical framework is further complicated in presence of high censoring rates (sometimes, due to non-susceptibility of study units to a disease), imbalance between treatment groups, and clustered nature of the data (where, survival outcomes appear in groups). Motivated by a right-censored kidney transplantation dataset derived from the United Network of Organ Sharing (UNOS), we investigate and compare two recent promising PS procedures, (a) the generalized boosted model (GBM), and (b) the covariate-balancing propensity score (CBPS), in an attempt to decouple the causal effects of treatments (here, study subgroups, such as hepatitis C virus (HCV) positive/negative donors, and positive/negative recipients) on time to death of kidney recipients due to kidney failure, post transplantation. For estimation, we employ a 2-step procedure which addresses various complexities observed in the UNOS database within a unified paradigm. First, to adjust for the large number of confounders on the multiple sub-groups, we fit multinomial PS models via procedures (a) and (b). In the next stage, the estimated PS is incorporated into the likelihood of a semi-parametric cure rate Cox proportional hazard frailty model via inverse probability of treatment weighting, adjusted for multi-center clustering and excess censoring, Our data analysis reveals a more informative and superior performance of the full model in terms of treatment effect estimation, over sub-models that relaxes the various features of the event time dataset.</p>
</abstract>
<kwd-group>
<label>Keywords</label>
<kwd>cure rate</kwd>
<kwd>frailty</kwd>
<kwd>heavy censoring</kwd>
<kwd>inverse probability weighting</kwd>
<kwd>kidney transplantation</kwd>
<kwd>propensity scores</kwd>
</kwd-group>
<funding-group><award-group><funding-source xlink:href="https://doi.org/10.13039/100000002">US National Institutes of Health</funding-source><award-id>R01DE024984</award-id></award-group><funding-statement>Bandyopadhyay’s research was supported by grant R01DE024984 from the US National Institutes of Health. </funding-statement></funding-group>
</article-meta>
</front>
<body/>
<back>
<ref-list id="j_jds1046_reflist_001">
<title>References</title>
<ref id="j_jds1046_ref_001">
<mixed-citation publication-type="journal"> <string-name><surname>Ahmed</surname> <given-names>A</given-names></string-name>, <string-name><surname>Young</surname> <given-names>JB</given-names></string-name>, <string-name><surname>Love</surname> <given-names>TE</given-names></string-name>, <string-name><surname>Levesque</surname> <given-names>R</given-names></string-name>, <string-name><surname>Pitt</surname> <given-names>B</given-names></string-name> (<year>2008</year>). <article-title>A propensity-matched study of the effects of chronic diuretic therapy on mortality and hospitalization in older adults with heart failure</article-title>. <source>International journal of Cardiology</source>, <volume>125</volume>: <fpage>246</fpage>–<lpage>253</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_002">
<mixed-citation publication-type="journal"> <string-name><surname>Ali</surname> <given-names>MS</given-names></string-name>, <string-name><surname>Groenwold</surname> <given-names>RH</given-names></string-name>, <string-name><surname>Pestman</surname> <given-names>WR</given-names></string-name>, <string-name><surname>Belitser</surname> <given-names>SV</given-names></string-name>, <string-name><surname>Roes</surname> <given-names>KC</given-names></string-name>, <string-name><surname>Hoes</surname> <given-names>AW</given-names></string-name>, <etal>et al.</etal> (<year>2014</year>). <article-title>Propensity score balance measures in pharmacoepidemiology: A simulation study</article-title>. <source>Pharmacoepidemiology and Drug Safety</source>, <volume>23</volume>: <fpage>802</fpage>–<lpage>811</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_003">
<mixed-citation publication-type="journal"> <string-name><surname>Austin</surname> <given-names>PC</given-names></string-name> (<year>2009</year>). <article-title>Some methods of propensity-score matching had superior performance to others: Results of an empirical investigation and monte carlo simulations</article-title>. <source>Biometrical Journal</source>, <volume>51</volume>: <fpage>171</fpage>–<lpage>184</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_004">
<mixed-citation publication-type="journal"> <string-name><surname>Austin</surname> <given-names>PC</given-names></string-name>, <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name> (<year>2015</year>). <article-title>Moving towards best practice when using inverse probability of treatment weighting (iptw) using the propensity score to estimate causal treatment effects in observational studies</article-title>. <source>Statistics in Medicine</source>, <volume>34</volume>: <fpage>3661</fpage>–<lpage>3679</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_005">
<mixed-citation publication-type="journal"> <string-name><surname>Barsoum</surname> <given-names>RS</given-names></string-name>, <string-name><surname>William</surname> <given-names>EA</given-names></string-name>, <string-name><surname>Khalil</surname> <given-names>SS</given-names></string-name> (<year>2017</year>). <article-title>Hepatitis C and Kidney disease: A narrative review</article-title>. <source>Journal of Advanced Research</source>, <volume>8</volume>: <fpage>113</fpage>–<lpage>130</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_006">
<mixed-citation publication-type="journal"> <string-name><surname>Bouthot</surname> <given-names>BA</given-names></string-name>, <string-name><surname>Murthy</surname> <given-names>B</given-names></string-name>, <string-name><surname>Schmid</surname> <given-names>CH</given-names></string-name>, <string-name><surname>Levey</surname> <given-names>AS</given-names></string-name>, <string-name><surname>Pereira</surname> <given-names>BJ</given-names></string-name> (<year>1997</year>). <article-title>Long-term follow-up of hepatitis c virus infection among organ transplant recipients: Implications for policies on organ procurement1, 2</article-title>. <source>Transplantation</source>, <volume>63</volume>: <fpage>849</fpage>–<lpage>853</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_007">
<mixed-citation publication-type="other"> <string-name><surname>Bucci</surname> <given-names>JR</given-names></string-name>, <string-name><surname>Lentine</surname> <given-names>KL</given-names></string-name>, <string-name><surname>Agodoa</surname> <given-names>LY</given-names></string-name>, <string-name><surname>Peters</surname> <given-names>T</given-names></string-name>, <string-name><surname>Schnitzler</surname> <given-names>M</given-names></string-name>, <string-name><surname>Abbott</surname> <given-names>K</given-names></string-name> (2004). Outcomes associated with recipient and donor hepatitis C serology status after kidney transplantation in the United States: Analysis of the USRDS/UNOS database. <italic>Clinical Transplants</italic>, 51–61.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_008">
<mixed-citation publication-type="journal"> <string-name><surname>Bucci</surname> <given-names>JR</given-names></string-name>, <string-name><surname>Matsumoto</surname> <given-names>CS</given-names></string-name>, <string-name><surname>Swanson</surname> <given-names>SJ</given-names></string-name>, <string-name><surname>Agodoa</surname> <given-names>LY</given-names></string-name>, <string-name><surname>Holtzmuller</surname> <given-names>KC</given-names></string-name>, <string-name><surname>Peters</surname> <given-names>TG</given-names></string-name>, <etal>et al.</etal> (<year>2002</year>). <article-title>Donor hepatitis C seropositivity: Clinical correlates and effect on early graft and patient survival in adult cadaveric kidney transplantation</article-title>. <source>Journal of the American Society of Nephrology</source>, <volume>13</volume>: <fpage>2974</fpage>–<lpage>2982</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_009">
<mixed-citation publication-type="journal"> <string-name><surname>Burgette</surname> <given-names>JM</given-names></string-name>, <string-name><surname>Preisser</surname> <given-names>JS</given-names></string-name>, <string-name><surname>Rozier</surname> <given-names>RG</given-names></string-name> (<year>2016</year>). <article-title>Propensity score weighting: An application to an Early Head Start dental study</article-title>. <source>Journal of Public Health Dentistry</source>, <volume>76</volume>: <fpage>17</fpage>–<lpage>29</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_010">
<mixed-citation publication-type="journal"> <string-name><surname>Burnham</surname> <given-names>KP</given-names></string-name>, <string-name><surname>Anderson</surname> <given-names>DR</given-names></string-name> (<year>2004</year>). <article-title>Multimodel inference: Understanding AIC and BIC in model selection</article-title>. <source>Sociological Methods &amp; Research</source>, <volume>33</volume>: <fpage>261</fpage>–<lpage>304</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_011">
<mixed-citation publication-type="journal"> <string-name><surname>Cacoub</surname> <given-names>P</given-names></string-name>, <string-name><surname>Comarmond</surname> <given-names>C</given-names></string-name>, <string-name><surname>Domont</surname> <given-names>F</given-names></string-name>, <string-name><surname>Savey</surname> <given-names>L</given-names></string-name>, <string-name><surname>Desbois</surname> <given-names>AC</given-names></string-name>, <string-name><surname>Saadoun</surname> <given-names>D</given-names></string-name> (<year>2016</year>). <article-title>Extrahepatic manifestations of chronic hepatitis C virus infection</article-title>. <source>Therapeutic Advances in Infectious Disease</source>, <volume>3</volume>: <fpage>3</fpage>–<lpage>14</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_012">
<mixed-citation publication-type="journal"> <string-name><surname>Carbognin</surname> <given-names>S</given-names></string-name>, <string-name><surname>Solomon</surname> <given-names>N</given-names></string-name>, <string-name><surname>Yeo</surname> <given-names>F</given-names></string-name>, <string-name><surname>Swanson</surname> <given-names>S</given-names></string-name>, <string-name><surname>Bohen</surname> <given-names>E</given-names></string-name>, <string-name><surname>Koff</surname> <given-names>J</given-names></string-name>, <etal>et al.</etal> (<year>2006</year>). <article-title>Acute renal allograft rejection following pegylated ifn-<italic>α</italic> treatment for chronic hcv in a repeat allograft recipient on hemodialysis: A case report</article-title>. <source>American Journal of Transplantation</source>, <volume>6</volume>: <fpage>1746</fpage>–<lpage>1751</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_013">
<mixed-citation publication-type="journal"> <string-name><surname>Carnegie</surname> <given-names>NB</given-names></string-name>, <string-name><surname>Harada</surname> <given-names>M</given-names></string-name>, <string-name><surname>Hill</surname> <given-names>JL</given-names></string-name> (<year>2016</year>). <article-title>Assessing sensitivity to unmeasured confounding using a simulated potential confounder</article-title>. <source>Journal of Research on Educational Effectiveness</source>, <volume>9</volume>: <fpage>395</fpage>–<lpage>420</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_014">
<mixed-citation publication-type="other"> <string-name><surname>Crump</surname> <given-names>RK</given-names></string-name>, <string-name><surname>Hotz</surname> <given-names>VJ</given-names></string-name>, <string-name><surname>Imbens</surname> <given-names>GW</given-names></string-name>, <string-name><surname>Mitnik</surname> <given-names>OA</given-names></string-name> (2006). Moving the goalposts: Addressing limited overlap in the estimation of average treatment effects by changing the estimand. Working Paper 330. National Bureau of Economic Research. <uri>http://www.nber.org/papers/t0330</uri>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_015">
<mixed-citation publication-type="journal"> <string-name><surname>Crump</surname> <given-names>RK</given-names></string-name>, <string-name><surname>Hotz</surname> <given-names>VJ</given-names></string-name>, <string-name><surname>Imbens</surname> <given-names>GW</given-names></string-name>, <string-name><surname>Mitnik</surname> <given-names>OA</given-names></string-name> (<year>2009</year>). <article-title>Dealing with limited overlap in estimation of average treatment effects</article-title>. <source>Biometrika</source>, <volume>96</volume>: <fpage>187</fpage>–<lpage>199</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_016">
<mixed-citation publication-type="journal"> <string-name><surname>Dharnidharka</surname> <given-names>VR</given-names></string-name>, <string-name><surname>Stevens</surname> <given-names>G</given-names></string-name>, <string-name><surname>Howard</surname> <given-names>RJ</given-names></string-name> (<year>2005</year>). <article-title>En-bloc kidney transplantation in the United states: An analysis of united network of organ sharing (UNOS) data from 1987 to 2003</article-title>. <source>American Journal of Transplantation</source>, <volume>5</volume>: <fpage>1513</fpage>–<lpage>1517</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_017">
<mixed-citation publication-type="journal"> <string-name><surname>Dow</surname> <given-names>JK</given-names></string-name>, <string-name><surname>Endersby</surname> <given-names>JW</given-names></string-name> (<year>2004</year>). <article-title>Multinomial probit and multinomial logit: A comparison of choice models for voting research</article-title>. <source>Electoral Studies</source>, <volume>23</volume>: <fpage>107</fpage>–<lpage>122</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_018">
<mixed-citation publication-type="journal"> <string-name><surname>D’Amour</surname> <given-names>A</given-names></string-name>, <string-name><surname>Ding</surname> <given-names>P</given-names></string-name>, <string-name><surname>Feller</surname> <given-names>A</given-names></string-name>, <string-name><surname>Lei</surname> <given-names>L</given-names></string-name>, <string-name><surname>Sekhon</surname> <given-names>J</given-names></string-name> (<year>2021</year>). <article-title>Overlap in observational studies with high-dimensional covariates</article-title>. <source>Journal of Econometrics</source>, <volume>221</volume>: <fpage>644</fpage>–<lpage>654</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_019">
<mixed-citation publication-type="journal"> <string-name><surname>Feng</surname> <given-names>S</given-names></string-name>, <string-name><surname>Wolfe</surname> <given-names>RA</given-names></string-name>, <string-name><surname>Port</surname> <given-names>FK</given-names></string-name> (<year>2005</year>). <article-title>Frailty survival model analysis of the national deceased donor kidney transplant dataset using poisson variance structures</article-title>. <source>Journal of the American Statistical Association</source>, <volume>100</volume>: <fpage>728</fpage>–<lpage>735</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_020">
<mixed-citation publication-type="journal"> <string-name><surname>Friedman</surname> <given-names>J</given-names></string-name>, <string-name><surname>Hastie</surname> <given-names>T</given-names></string-name>, <string-name><surname>Tibshirani</surname> <given-names>R</given-names></string-name> (<year>2000</year>). <article-title>Additive logistic regression: A statistical view of boosting</article-title>. <source>The Annals of Statistics</source>, <volume>28</volume>: <fpage>337</fpage>–<lpage>407</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_021">
<mixed-citation publication-type="journal"> <string-name><surname>Gill</surname> <given-names>J</given-names></string-name>, <string-name><surname>Cho</surname> <given-names>YW</given-names></string-name>, <string-name><surname>Danovitch</surname> <given-names>GM</given-names></string-name>, <string-name><surname>Wilkinson</surname> <given-names>A</given-names></string-name>, <string-name><surname>Lipshutz</surname> <given-names>G</given-names></string-name>, <string-name><surname>Pham</surname> <given-names>P-T</given-names></string-name>, <etal>et al.</etal> (<year>2008</year>). <article-title>Outcomes of dual adult kidney transplants in the United States: An analysis of the OPTN/UNOS database</article-title>. <source>Transplantation</source>, <volume>85</volume>: <fpage>62</fpage>–<lpage>68</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_022">
<mixed-citation publication-type="journal"> <string-name><surname>Gill</surname> <given-names>J</given-names></string-name>, <string-name><surname>Shah</surname> <given-names>T</given-names></string-name>, <string-name><surname>Hristea</surname> <given-names>I</given-names></string-name>, <string-name><surname>Chavalitdhamrong</surname> <given-names>D</given-names></string-name>, <string-name><surname>Anastasi</surname> <given-names>B</given-names></string-name>, <string-name><surname>Takemoto</surname> <given-names>S</given-names></string-name>, <etal>et al.</etal> (<year>2009</year>). <article-title>Outcomes of simultaneous heart–kidney transplant in the us: A retrospective analysis using optn/unos data</article-title>. <source>American Journal of Transplantation</source>, <volume>9</volume>: <fpage>844</fpage>–<lpage>852</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_023">
<mixed-citation publication-type="journal"> <string-name><surname>Golub</surname> <given-names>GH</given-names></string-name>, <string-name><surname>Welsch</surname> <given-names>JH</given-names></string-name> (<year>1969</year>). <article-title>Calculation of Gaussian quadrature rules</article-title>. <source>Mathematics of Computation</source>, <volume>23</volume>: <fpage>221</fpage>–<lpage>230</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_024">
<mixed-citation publication-type="other"> <string-name><surname>Greifer</surname> <given-names>N</given-names></string-name> (2020). cobalt: Covariate balance tables and plots. <uri>https://CRAN.R-project.org/package=cobalt</uri>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_025">
<mixed-citation publication-type="journal"> <string-name><surname>Gupta</surname> <given-names>G</given-names></string-name>, <string-name><surname>Kang</surname> <given-names>L</given-names></string-name>, <string-name><surname>Yu</surname> <given-names>JW</given-names></string-name>, <string-name><surname>Limkemann</surname> <given-names>AJ</given-names></string-name>, <string-name><surname>Garcia</surname> <given-names>V</given-names></string-name>, <string-name><surname>Bandyopadhyay</surname> <given-names>D</given-names></string-name>, <etal>et al.</etal> (<year>2017</year>). <article-title>Long-term outcomes and transmission rates in hepatitis c virus-positive donor to hepatitis c virus-negative kidney transplant recipients: Analysis of united states national data</article-title>. <source>Clinical Transplantation</source>, <volume>31</volume>: <fpage>e13055</fpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_026">
<mixed-citation publication-type="journal"> <string-name><surname>Hansen</surname> <given-names>LP</given-names></string-name> (<year>1982</year>). <article-title>Large sample properties of generalized method of moments estimators</article-title>. <source>Econometrica: Journal of the Econometric Society</source>, <volume>50</volume>: <fpage>1029</fpage>–<lpage>1054</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_027">
<mixed-citation publication-type="journal"> <string-name><surname>Harder</surname> <given-names>VS</given-names></string-name>, <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name>, <string-name><surname>Anthony</surname> <given-names>JC</given-names></string-name> (<year>2010</year>). <article-title>Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research</article-title>. <source>Psychological methods</source>, <volume>15</volume>: <fpage>234</fpage>–<lpage>249</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_028">
<mixed-citation publication-type="journal"> <string-name><surname>He</surname> <given-names>P</given-names></string-name>, <string-name><surname>Kong</surname> <given-names>G</given-names></string-name>, <string-name><surname>Su</surname> <given-names>Z</given-names></string-name> (<year>2013</year>). <article-title>Estimating the survival functions for right-censored and interval-censored data with piecewise constant hazard functions</article-title>. <source>Contemporary Clinical Trials</source>, <volume>35</volume>: <fpage>122</fpage>–<lpage>127</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_029">
<mixed-citation publication-type="journal"> <string-name><surname>Hernán</surname> <given-names>MA</given-names></string-name>, <string-name><surname>Robins</surname> <given-names>JM</given-names></string-name> (<year>2006</year>). <article-title>Estimating causal effects from epidemiological data</article-title>. <source>Journal of Epidemiology &amp; Community Health</source>, <volume>60</volume>: <fpage>578</fpage>–<lpage>586</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_030">
<mixed-citation publication-type="journal"> <string-name><surname>Hirano</surname> <given-names>K</given-names></string-name>, <string-name><surname>Imbens</surname> <given-names>GW</given-names></string-name> (<year>2001</year>). <article-title>Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization</article-title>. <source>Health Services and Outcomes Research Methodology</source>, <volume>2</volume>: <fpage>259</fpage>–<lpage>278</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_031">
<mixed-citation publication-type="journal"> <string-name><surname>Huang</surname> <given-names>R</given-names></string-name>, <string-name><surname>Xu</surname> <given-names>R</given-names></string-name>, <string-name><surname>Dulai</surname> <given-names>PS</given-names></string-name> (<year>2020</year>). <article-title>Sensitivity analysis of treatment effect to unmeasured confounding in observational studies with survival and competing risks outcomes</article-title>. <source>Statistics in Medicine</source>, <volume>39</volume>: <fpage>3397</fpage>–<lpage>3411</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_032">
<mixed-citation publication-type="journal"> <string-name><surname>Imai</surname> <given-names>K</given-names></string-name>, <string-name><surname>King</surname> <given-names>G</given-names></string-name>, <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name> (<year>2008</year>). <article-title>Misunderstandings between experimentalists and observationalists about causal inference</article-title>. <source>Journal of the Royal Statistical Society: Series A (Statistics in Society)</source>, <volume>171</volume>: <fpage>481</fpage>–<lpage>502</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_033">
<mixed-citation publication-type="journal"> <string-name><surname>Imai</surname> <given-names>K</given-names></string-name>, <string-name><surname>Ratkovic</surname> <given-names>M</given-names></string-name> (<year>2014</year>). <article-title>Covariate balancing propensity score</article-title>. <source>Journal of the Royal Statistical Society: Series B (Statistical Methodology)</source>, <volume>76</volume>: <fpage>243</fpage>–<lpage>263</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_034">
<mixed-citation publication-type="journal"> <string-name><surname>Imbens</surname> <given-names>GW</given-names></string-name> (<year>2000</year>). <article-title>The role of the propensity score in estimating dose-response functions</article-title>. <source>Biometrika</source>, <volume>87</volume>: <fpage>706</fpage>–<lpage>710</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_035">
<mixed-citation publication-type="journal"> <string-name><surname>Kamal</surname> <given-names>L</given-names></string-name>, <string-name><surname>Jonathan</surname> <given-names>WY</given-names></string-name>, <string-name><surname>Reichman</surname> <given-names>TW</given-names></string-name>, <string-name><surname>Kang</surname> <given-names>L</given-names></string-name>, <string-name><surname>Bandyopadhyay</surname> <given-names>D</given-names></string-name>, <string-name><surname>Kumar</surname> <given-names>D</given-names></string-name>, <etal>et al.</etal> (<year>2020</year>). <article-title>Impact of induction immunosuppression strategies in simultaneous liver/kidney transplantation</article-title>. <source>Transplantation</source>, <volume>104</volume>: <fpage>395</fpage>–<lpage>403</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_036">
<mixed-citation publication-type="journal"> <string-name><surname>Kang</surname> <given-names>JD</given-names></string-name>, <string-name><surname>Schafer</surname> <given-names>JL</given-names></string-name>, <etal>et al.</etal> (<year>2007</year>). <article-title>Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data</article-title>. <source>Statistical Science</source>, <volume>22</volume>: <fpage>523</fpage>–<lpage>539</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_037">
<mixed-citation publication-type="journal"> <string-name><surname>Kucirka</surname> <given-names>L</given-names></string-name>, <string-name><surname>Singer</surname> <given-names>A</given-names></string-name>, <string-name><surname>Ros</surname> <given-names>R</given-names></string-name>, <string-name><surname>Montgomery</surname> <given-names>R</given-names></string-name>, <string-name><surname>Dagher</surname> <given-names>N</given-names></string-name>, <string-name><surname>Segev</surname> <given-names>D</given-names></string-name> (<year>2010</year>). <article-title>Underutilization of hepatitis C-positive kidneys for hepatitis C-positive recipients</article-title>. <source>American Journal of Transplantation</source>, <volume>10</volume>: <fpage>1238</fpage>–<lpage>1246</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_038">
<mixed-citation publication-type="journal"> <string-name><surname>Lawless</surname> <given-names>J</given-names></string-name>, <string-name><surname>Zhan</surname> <given-names>M</given-names></string-name> (<year>1998</year>). <article-title>Analysis of interval-grouped recurrent-event data using piecewise constant rate functions</article-title>. <source>Canadian Journal of Statistics</source>, <volume>26</volume>: <fpage>549</fpage>–<lpage>565</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_039">
<mixed-citation publication-type="journal"> <string-name><surname>Lee</surname> <given-names>BK</given-names></string-name>, <string-name><surname>Lessler</surname> <given-names>J</given-names></string-name>, <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name> (<year>2010</year>). <article-title>Improving propensity score weighting using machine learning</article-title>. <source>Statistics in Medicine</source>, <volume>29</volume>: <fpage>337</fpage>–<lpage>346</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_040">
<mixed-citation publication-type="journal"> <string-name><surname>Li</surname> <given-names>F</given-names></string-name>, <string-name><surname>Morgan</surname> <given-names>KL</given-names></string-name>, <string-name><surname>Zaslavsky</surname> <given-names>AM</given-names></string-name> (<year>2018</year>). <article-title>Balancing covariates via propensity score weighting</article-title>. <source>Journal of the American Statistical Association</source>, <volume>113</volume>: <fpage>390</fpage>–<lpage>400</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_041">
<mixed-citation publication-type="journal"> <string-name><surname>Li</surname> <given-names>L</given-names></string-name>, <string-name><surname>Greene</surname> <given-names>T</given-names></string-name> (<year>2013</year>). <article-title>A weighting analogue to pair matching in propensity score analysis</article-title>. <source>The International Journal of Biostatistics</source>, <volume>9</volume>: <fpage>215</fpage>–<lpage>234</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_042">
<mixed-citation publication-type="journal"> <string-name><surname>Lin</surname> <given-names>DY</given-names></string-name>, <string-name><surname>Wei</surname> <given-names>L-J</given-names></string-name> (<year>1989</year>). <article-title>The robust inference for the Cox proportional hazards model</article-title>. <source>Journal of the American statistical Association</source>, <volume>84</volume>: <fpage>1074</fpage>–<lpage>1078</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_043">
<mixed-citation publication-type="journal"> <string-name><surname>Liu</surname> <given-names>L</given-names></string-name>, <string-name><surname>Huang</surname> <given-names>X</given-names></string-name> (<year>2008</year>). <article-title>The use of Gaussian quadrature for estimation in frailty proportional hazards models</article-title>. <source>Statistics in Medicine</source>, <volume>27</volume>: <fpage>2665</fpage>–<lpage>2683</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_044">
<mixed-citation publication-type="journal"> <string-name><surname>Loh</surname> <given-names>W-Y</given-names></string-name> (<year>2011</year>). <article-title>Classification and regression trees</article-title>. <source>Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery</source>, <volume>1</volume>: <fpage>14</fpage>–<lpage>23</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_045">
<mixed-citation publication-type="journal"> <string-name><surname>Lunceford</surname> <given-names>JK</given-names></string-name>, <string-name><surname>Davidian</surname> <given-names>M</given-names></string-name> (<year>2004</year>). <article-title>Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study</article-title>. <source>Statistics in Medicine</source>, <volume>23</volume>: <fpage>2937</fpage>–<lpage>2960</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_046">
<mixed-citation publication-type="journal"> <string-name><surname>Ma</surname> <given-names>X</given-names></string-name>, <string-name><surname>Wang</surname> <given-names>J</given-names></string-name> (<year>2020</year>). <article-title>Robust inference using inverse probability weighting</article-title>. <source>Journal of the American Statistical Association</source>, <volume>115</volume>: <fpage>1851</fpage>–<lpage>1860</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_047">
<mixed-citation publication-type="journal"> <string-name><surname>Maller</surname> <given-names>RA</given-names></string-name>, <string-name><surname>Zhou</surname> <given-names>S</given-names></string-name> (<year>1992</year>). <article-title>Estimating the proportion of immunes in a censored sample</article-title>. <source>Biometrika</source>, <volume>79</volume>: <fpage>731</fpage>–<lpage>739</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_048">
<mixed-citation publication-type="journal"> <string-name><surname>Maluf</surname> <given-names>DG</given-names></string-name>, <string-name><surname>Fisher</surname> <given-names>RA</given-names></string-name>, <string-name><surname>King</surname> <given-names>AL</given-names></string-name>, <string-name><surname>Gibney</surname> <given-names>EM</given-names></string-name>, <string-name><surname>Mas</surname> <given-names>VR</given-names></string-name>, <string-name><surname>Cotterell</surname> <given-names>AH</given-names></string-name>, <etal>et al.</etal> (<year>2007</year>). <article-title>Hepatitis C virus infection and kidney transplantation: Predictors of patient and graft survival</article-title>. <source>Transplantation</source>, <volume>83</volume>: <fpage>853</fpage>–<lpage>857</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_049">
<mixed-citation publication-type="journal"> <string-name><surname>Mao</surname> <given-names>H</given-names></string-name>, <string-name><surname>Li</surname> <given-names>L</given-names></string-name>, <string-name><surname>Yang</surname> <given-names>W</given-names></string-name>, <string-name><surname>Shen</surname> <given-names>Y</given-names></string-name> (<year>2018</year>). <article-title>On the propensity score weighting analysis with survival outcome: Estimands, estimation, and inference</article-title>. <source>Statistics in Medicine</source>, <volume>37</volume>: <fpage>3745</fpage>–<lpage>3763</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_050">
<mixed-citation publication-type="journal"> <string-name><surname>McCaffrey</surname> <given-names>DF</given-names></string-name>, <string-name><surname>Griffin</surname> <given-names>BA</given-names></string-name>, <string-name><surname>Almirall</surname> <given-names>D</given-names></string-name>, <string-name><surname>Slaughter</surname> <given-names>ME</given-names></string-name>, <string-name><surname>Ramchand</surname> <given-names>R</given-names></string-name>, <string-name><surname>Burgette</surname> <given-names>LF</given-names></string-name> (<year>2013</year>). <article-title>A tutorial on propensity score estimation for multiple treatments using generalized boosted models</article-title>. <source>Statistics in Medicine</source>, <volume>32</volume>: <fpage>3388</fpage>–<lpage>3414</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_051">
<mixed-citation publication-type="journal"> <string-name><surname>McCaffrey</surname> <given-names>DF</given-names></string-name>, <string-name><surname>Ridgeway</surname> <given-names>G</given-names></string-name>, <string-name><surname>Morral</surname> <given-names>AR</given-names></string-name> (<year>2004</year>). <article-title>Propensity score estimation with boosted regression for evaluating causal effects in observational studies</article-title>. <source>Psychological Methods</source>, <volume>9</volume>: <fpage>403</fpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_052">
<mixed-citation publication-type="journal"> <string-name><surname>Mirzaee</surname> <given-names>M</given-names></string-name>, <string-name><surname>Azmandian</surname> <given-names>J</given-names></string-name>, <string-name><surname>Zeraati</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mahmoodi</surname> <given-names>M</given-names></string-name>, <string-name><surname>Mohammad</surname> <given-names>K</given-names></string-name>, <string-name><surname>Etminan</surname> <given-names>A</given-names></string-name>, <etal>et al.</etal> (<year>2014</year>). <article-title>Short-term and long-term survival of kidney allograft: Cure model analysis</article-title>. <source>Iranian Journal of Kidney Diseases</source>, <volume>8</volume>: <fpage>225</fpage>–<lpage>230</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_053">
<mixed-citation publication-type="journal"> <string-name><surname>Morgan</surname> <given-names>C</given-names></string-name> (<year>2018</year>). <article-title>Reducing bias using propensity score matching</article-title>. <source>Journal of Nuclear Cardiology</source>, <volume>25</volume>: <fpage>404</fpage>–<lpage>406</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_054">
<mixed-citation publication-type="journal"> <string-name><surname>Neuhäuser</surname> <given-names>M</given-names></string-name>, <string-name><surname>Thielmann</surname> <given-names>M</given-names></string-name>, <string-name><surname>Ruxton</surname> <given-names>GD</given-names></string-name> (<year>2018</year>). <article-title>The number of strata in propensity score stratification for a binary outcome</article-title>. <source>Archives of Medical Science</source>, <volume>14</volume>: <fpage>695</fpage>–<lpage>700</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_055">
<mixed-citation publication-type="book"> <string-name><surname>Nocedal</surname> <given-names>J</given-names></string-name>, <string-name><surname>Wright</surname> <given-names>S</given-names></string-name> (<year>2006</year>). <source>Numerical Optimization</source>. <publisher-name>Springer Science &amp; Business Media</publisher-name>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_056">
<mixed-citation publication-type="journal"> <string-name><surname>Ojo</surname> <given-names>AO</given-names></string-name>, <string-name><surname>Meier-Kriesche</surname> <given-names>H-U</given-names></string-name>, <string-name><surname>Hanson</surname> <given-names>JA</given-names></string-name>, <string-name><surname>Leichtman</surname> <given-names>A</given-names></string-name>, <string-name><surname>Magee</surname> <given-names>JC</given-names></string-name>, <string-name><surname>Cibrik</surname> <given-names>D</given-names></string-name>, <etal>et al.</etal> (<year>2001</year>). <article-title>The impact of simultaneous pancreas-kidney transplantation on long-term patient survival1</article-title>. <source>Transplantation</source>, <volume>71</volume>: <fpage>82</fpage>–<lpage>89</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_057">
<mixed-citation publication-type="journal"> <string-name><surname>Owen</surname> <given-names>A</given-names></string-name> (<year>1991</year>). <article-title>Empirical likelihood for linear models</article-title>. <source>The Annals of Statistics</source>, <volume>19</volume>: <fpage>1725</fpage>–<lpage>1747</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_058">
<mixed-citation publication-type="journal"> <string-name><surname>Pereira</surname> <given-names>BG</given-names></string-name>, <string-name><surname>Wright</surname> <given-names>T</given-names></string-name>, <string-name><surname>Schmid</surname> <given-names>C</given-names></string-name>, <string-name><surname>Levey</surname> <given-names>A</given-names></string-name>, <string-name><surname>Group</surname> <given-names>NEOBHCS</given-names></string-name>, <etal>et al.</etal> (<year>1995</year>). <article-title>A controlled study of hepatitis c transmission by organ transplantation</article-title>. <source>The Lancet</source>, <volume>345</volume>: <fpage>484</fpage>–<lpage>487</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_059">
<mixed-citation publication-type="journal"> <string-name><surname>Pinheiro</surname> <given-names>JC</given-names></string-name>, <string-name><surname>Bates</surname> <given-names>DM</given-names></string-name> (<year>1995</year>). <article-title>Approximations to the log-likelihood function in the nonlinear mixed-effects model</article-title>. <source>Journal of computational and Graphical Statistics</source>, <volume>4</volume>: <fpage>12</fpage>–<lpage>35</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_060">
<mixed-citation publication-type="other"> <string-name><surname>Ridgeway</surname> <given-names>G</given-names></string-name>, <string-name><surname>McCaffrey</surname> <given-names>D</given-names></string-name>, <string-name><surname>Morral</surname> <given-names>A</given-names></string-name>, <string-name><surname>Griffin</surname> <given-names>BA</given-names></string-name>, <string-name><surname>Burgette</surname> <given-names>L</given-names></string-name>, <string-name><surname>Cefalu</surname> <given-names>M</given-names></string-name> (2020). twang: Toolkit for Weighting and Analysis of Nonequivalent Groups. URL<uri>https://CRAN.R-project.org/package=twang</uri>. R package version 1.6.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_061">
<mixed-citation publication-type="book"> <string-name><surname>Rosenbaum</surname> <given-names>PR</given-names></string-name> (<year>2010</year>). <source>Design of Observational Studies</source>. <publisher-name>Springer</publisher-name>, <publisher-loc>New York, NY</publisher-loc>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_062">
<mixed-citation publication-type="journal"> <string-name><surname>Rosenbaum</surname> <given-names>PR</given-names></string-name>, <string-name><surname>Rubin</surname> <given-names>DB</given-names></string-name> (<year>1983</year>). <article-title>The central role of the propensity score in observational studies for causal effects</article-title>. <source>Biometrika</source>, <volume>70</volume>: <fpage>41</fpage>–<lpage>55</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_063">
<mixed-citation publication-type="journal"> <string-name><surname>Rubin</surname> <given-names>DB</given-names></string-name> (<year>2005</year>). <article-title>Causal inference using potential outcomes: Design, modeling</article-title>. <source>decisions. Journal of the American Statistical Association</source>, <volume>100</volume>: <fpage>322</fpage>–<lpage>331</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_064">
<mixed-citation publication-type="journal"> <string-name><surname>Scott</surname> <given-names>DR</given-names></string-name>, <string-name><surname>Wong</surname> <given-names>JK</given-names></string-name>, <string-name><surname>Spicer</surname> <given-names>TS</given-names></string-name>, <string-name><surname>Dent</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mensah</surname> <given-names>FK</given-names></string-name>, <string-name><surname>McDonald</surname> <given-names>S</given-names></string-name>, <etal>et al.</etal> (<year>2010</year>). <article-title>Adverse impact of hepatitis c virus infection on renal replacement therapy and renal transplant patients in Australia and New Zealand</article-title>. <source>Transplantation</source>, <volume>90</volume>: <fpage>1165</fpage>–<lpage>1171</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_065">
<mixed-citation publication-type="journal"> <string-name><surname>Setodji</surname> <given-names>CM</given-names></string-name>, <string-name><surname>McCaffrey</surname> <given-names>DF</given-names></string-name>, <string-name><surname>Burgette</surname> <given-names>LF</given-names></string-name>, <string-name><surname>Almirall</surname> <given-names>D</given-names></string-name>, <string-name><surname>Griffin</surname> <given-names>BA</given-names></string-name> (<year>2017</year>). <article-title>The right tool for the job: Choosing between covariate balancing and generalized boosted model propensity scores</article-title>. <source>Epidemiology</source>, <volume>28</volume>: <fpage>802</fpage>–<lpage>811</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_066">
<mixed-citation publication-type="journal"> <string-name><surname>Singh</surname> <given-names>N</given-names></string-name>, <string-name><surname>Neidlinger</surname> <given-names>N</given-names></string-name>, <string-name><surname>Djamali</surname> <given-names>A</given-names></string-name>, <string-name><surname>Leverson</surname> <given-names>G</given-names></string-name>, <string-name><surname>Voss</surname> <given-names>B</given-names></string-name>, <string-name><surname>Sollinger</surname> <given-names>HW</given-names></string-name>, <etal>et al.</etal> (<year>2012</year>). <article-title>The impact of hepatitis c virus donor and recipient status on long-term kidney transplant outcomes: University of wisconsin experience</article-title>. <source>Clinical Transplantation</source>, <volume>26</volume>: <fpage>684</fpage>–<lpage>693</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_067">
<mixed-citation publication-type="journal"> <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name> (<year>2010</year>). <article-title>Matching methods for causal inference: A review and a look forward</article-title>. <source>Statistical Science</source>, <volume>25</volume>: <fpage>1</fpage>–<lpage>21</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_068">
<mixed-citation publication-type="journal"> <string-name><surname>Stuart</surname> <given-names>EA</given-names></string-name>, <string-name><surname>Lee</surname> <given-names>BK</given-names></string-name>, <string-name><surname>Leacy</surname> <given-names>FP</given-names></string-name> (<year>2013</year>). <article-title>Prognostic score–based balance measures can be a useful diagnostic for propensity score methods in comparative effectiveness research</article-title>. <source>Journal of Clinical Epidemiology</source>, <volume>66</volume>: <fpage>S84</fpage>–<lpage>S90</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_069">
<mixed-citation publication-type="journal"> <string-name><surname>Sy</surname> <given-names>JP</given-names></string-name>, <string-name><surname>Taylor</surname> <given-names>JM</given-names></string-name> (<year>2000</year>). <article-title>Estimation in a cox proportional hazards cure model</article-title>. <source>Biometrics</source>, <volume>56</volume>: <fpage>227</fpage>–<lpage>236</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_070">
<mixed-citation publication-type="journal"> <string-name><surname>Testa</surname> <given-names>G</given-names></string-name>, <string-name><surname>Siegler</surname> <given-names>M</given-names></string-name> (<year>2014</year>). <article-title>Increasing the supply of kidneys for transplantation by making living donors the preferred source of donor kidneys</article-title>. <source>Medicine</source>, <volume>93</volume>: <fpage>e318</fpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_071">
<mixed-citation publication-type="other"> <string-name><surname>Vaughan</surname> <given-names>AS</given-names></string-name>, <string-name><surname>Kelley</surname> <given-names>CF</given-names></string-name>, <string-name><surname>Luisi</surname> <given-names>N</given-names></string-name>, <string-name><surname>del Rio</surname> <given-names>C</given-names></string-name>, <string-name><surname>Sullivan</surname> <given-names>PS</given-names></string-name>, <string-name><surname>Rosenberg</surname> <given-names>ES</given-names></string-name> (2015). An application of propensity score weighting to quantify the causal effect of rectal sexually transmitted infections on incident HIV among men who have sex with men. <italic>BMC Medical Research Methodology</italic>, 15.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_072">
<mixed-citation publication-type="journal"> <string-name><surname>Wei</surname> <given-names>F</given-names></string-name>, <string-name><surname>Liu</surname> <given-names>J</given-names></string-name>, <string-name><surname>Liu</surname> <given-names>F</given-names></string-name>, <string-name><surname>Hu</surname> <given-names>H</given-names></string-name>, <string-name><surname>Ren</surname> <given-names>H</given-names></string-name>, <string-name><surname>Hu</surname> <given-names>P</given-names></string-name> (<year>2014</year>). <article-title>Interferon-based anti-viral therapy for hepatitis c virus infection after renal transplantation: An updated meta-analysis</article-title>. <source>PLoS One</source>, <volume>9</volume>: <fpage>e90611</fpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_073">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>S</given-names></string-name> (<year>2018</year>). <article-title>Propensity score weighting for causal inference with clustered data</article-title>. <source>Journal of Causal Inference</source>. <comment>doi.org/10.1515/jci–2017–0027</comment>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_074">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>S</given-names></string-name>, <string-name><surname>Ding</surname> <given-names>P</given-names></string-name> (<year>2018</year>). <article-title>Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores</article-title>. <source>Biometrika</source>, <volume>105</volume>: <fpage>487</fpage>–<lpage>493</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_075">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>S</given-names></string-name>, <string-name><surname>Imbens</surname> <given-names>GW</given-names></string-name>, <string-name><surname>Cui</surname> <given-names>Z</given-names></string-name>, <string-name><surname>Faries</surname> <given-names>DE</given-names></string-name>, <string-name><surname>Kadziola</surname> <given-names>Z</given-names></string-name> (<year>2016</year>). <article-title>Propensity score matching and subclassification in observational studies with multi-level treatments</article-title>. <source>Biometrics</source>, <volume>72</volume>: <fpage>1055</fpage>–<lpage>1065</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_076">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>S</given-names></string-name>, <string-name><surname>Pieper</surname> <given-names>K</given-names></string-name>, <string-name><surname>Cools</surname> <given-names>F</given-names></string-name> (<year>2020</year>). <article-title>Semiparametric estimation of structural failure time model in continuous-time processes</article-title>. <source>Biometrika</source>, <volume>107</volume>: <fpage>123</fpage>–<lpage>136</lpage>.</mixed-citation>
</ref>
<ref id="j_jds1046_ref_077">
<mixed-citation publication-type="journal"> <string-name><surname>Yang</surname> <given-names>S</given-names></string-name>, <string-name><surname>Tsiatis</surname> <given-names>AA</given-names></string-name>, <string-name><surname>Blazing</surname> <given-names>M</given-names></string-name> (<year>2018</year>). <article-title>Modeling survival distribution as a function of time to treatment discontinuation: A dynamic treatment regime approach</article-title>. <source>Biometrics</source>, <volume>74</volume>: <fpage>900</fpage>–<lpage>909</lpage>.</mixed-citation>
</ref>
</ref-list>
</back>
</article>
