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        <title type="main" level="a">Longitudinal profile of a set of biomarkers in predicting Covid-19 mortality using joint models</title>
        <author>
          <persName n="1" ref="https://orcid.org/0000-0002-6481-990X" type="ORCID">
            <forename>Matteo</forename>
            <surname>Di Maso</surname>
            <placeName type="affiliation">University of Milan, Italy</placeName>
          </persName>
          <persName n="2" ref="https://orcid.org/0000-0002-4542-4996" type="ORCID">
            <forename>Monica</forename>
            <surname>Ferraroni</surname>
            <placeName type="affiliation">University of Milan, Italy</placeName>
          </persName>
          <persName n="3">
            <forename>Pasquale</forename>
            <surname>Ferrante</surname>
            <placeName type="affiliation">University of Milan, Italy</placeName>
          </persName>
          <persName n="4" ref="https://orcid.org/0000-0002-3199-9369" type="ORCID">
            <forename>Serena</forename>
            <surname>Delbue</surname>
            <placeName type="affiliation">University of Milan, Italy</placeName>
          </persName>
          <persName n="5" ref="https://orcid.org/0000-0001-9358-011X" type="ORCID">
            <forename>Federico</forename>
            <surname>Ambrogi</surname>
            <placeName type="affiliation">University of Milan, Italy</placeName>
          </persName>
        </author>
        <respStmt>
          <resp>This is a section of <title>ASA 2021 Statistics and Information Systems for Policy Evaluation  </title>(DOI: <idno type="DOI">10.36253/978-88-5518-461-8</idno>) by </resp>
          <name>Alessandra Petrucci, Bruno Bertaccini, Luigi Fabbris</name>
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      <publicationStmt>
        <publisher>Firenze University Press</publisher>
        <pubPlace>Firenze</pubPlace>
        <date when="2021">2021</date>
        <idno type="DOI">https://doi.org/10.36253/978-88-5518-461-8.36</idno>
        <availability>
          <p>Available for academic research purposes</p>
          <p>Open Access</p>
          <p>Copyright Author(s)</p>
          <licence source="text" target="https://creativecommons.org/licenses/by/4.0/legalcode">
            <p>Content licence CC BY 4.0</p>
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          <licence source="metadata" target="https://creativecommons.org/publicdomain/zero/1.0/legalcode">
            <p>Metadata licence CC0 1.0</p>
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        <p>This is original content, published for academic research purposes</p>
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      <abstract xml:lang="en">
        <p>In survival analysis, time-varying covariates are endogenous when their measurements are directly related to the event status and incomplete information occur at random points during the follow-up. Consequently, the time-dependent Cox model leads to biased estimates. Joint models (JM) allow to correctly estimate these associations combining a survival and longitudinal sub-models by means of a shared parameter (i.e., random effects of the longitudinal sub-model are inserted in the survival one). This study aims at showing the use of JM to evaluate the association between a set of inflammatory biomarkers and Covid-19 mortality.
During Covid-19 pandemic, physicians at Istituto Clinico di Città Studi in Milan collected biomarkers (endogenous time-varying covariates) to understand what might be used as prognostic factors for mortality. Furthermore, in the first epidemic outbreak, physicians did not have standard clinical protocols for management of Covid-19 disease and measurements of biomarkers were highly incomplete especially at the baseline. Between February and March 2020, a total of 403 COVID-19 patients were admitted. Baseline characteristics included sex and age, whereas biomarkers measurements, during hospital stay, included log-ferritin, log-lymphocytes, log-neutrophil granulocytes, log-C-reactive protein, glucose and LDH. A Bayesian approach using Markov chain Monte Carlo algorithm were used for fitting JM. Independent and non-informative priors for the fixed effects (age and sex) and for shared parameters were used.
Hazard ratios (HR) from a (biased) time-dependent Cox and joint models for log-ferritin levels were 2.10 (1.67-2.64) and 1.73 (1.38-2.20), respectively. In multivariable JM, doubling of biomarker levels resulted in a significantly increase of mortality risk for log-neutrophil granulocytes, HR=1.78 (1.16-2.69); for log-C-reactive protein, HR=1.44 (1.13-1.83); and for LDH, HR=1.28 (1.09-1.49). Increasing of 100 mg/dl of glucose resulted in a HR=2.44 (1.28-4.26). Age, however, showed the strongest effect with mortality risk starting to rise from 60 years.</p>
      </abstract>
      <textClass>
        <keywords>
          <list>
            <item>Endogenous time-varying covariates</item>
            <item>Time-dependent Cox model</item>
            <item>Joint models</item>
            <item>Inflammatory biomarkers</item>
            <item>Covid-19 mortality</item>
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      <p>It is available online at https://doi.org/10.36253/978-88-5518-461-8.36<ref target="https://doi.org/10.36253/978-88-5518-461-8.36" /></p>
      <div>
        <listBibl>
          <head>References</head>
          <bibl n="60727">Rizopoulos D. (2012). Joint Models for Longitudinal and Time-to-Event Data. With Application in R. Boca Raton: Chapman &amp;amp; Hall/CRC.</bibl>
          <bibl n="60728">Therneau T., Grambsch P. (2000). Modeling Survival Data: Extending the Cox Model. Springer-Verlag, New York (NY).</bibl>
          <bibl n="60729">van Houwelingen HC., Putter H. (2012). Dynamic Prediction in Clinical Survival Analysis. Boca Raton: Chapman &amp;amp; Hall/CRC.</bibl>
          <bibl n="60730">Rizopoulos D. (2016). The R Package JMbayes for Fitting Joint Models for Longitudinal and Time-to-Event Data using MCMC. J Stat Softw. 72(7), pp. 1-45.</bibl>
          <bibl n="60731">Putter H. (2015). dynpred: Companion Package to &amp;quot;Dynamic Prediction in Clinical Survival Analysis&amp;quot;. R package version 0.1.2. &amp;lt;https://CRAN.Rproject.org/package=dynpred&amp;gt;.</bibl>
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