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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">1680-743X</issn>
      <issn pub-type="ppub">1680-743X</issn>
      <publisher>
        <publisher-name>SOSRUC</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">090206</article-id>
      <article-id pub-id-type="doi">10.6339/JDS.201104_09(2).0006</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Quantifying Treatment Effects When Flexibly Modeling Individual Change in a Nonlinear Mixed Effects Model</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Gallop</surname>
            <given-names>Robert J.</given-names>
          </name>
          <xref ref-type="aff" rid="j_JDS_aff_000"/>
        </contrib>
        <aff id="j_JDS_aff_000">West Chester University</aff>
        <contrib contrib-type="author">
          <name>
            <surname>Dimidjian</surname>
            <given-names>Sona</given-names>
          </name>
          <xref ref-type="aff" rid="j_JDS_aff_001"/>
        </contrib>
        <aff id="j_JDS_aff_001">University of Colorado at Boulder</aff>
        <contrib contrib-type="author">
          <name>
            <surname>Atkins</surname>
            <given-names>David C.</given-names>
          </name>
          <xref ref-type="aff" rid="j_JDS_aff_002"/>
        </contrib>
        <aff id="j_JDS_aff_002">University of Washington</aff>
        <contrib contrib-type="author">
          <name>
            <surname>Muggeo</surname>
            <given-names>Vito</given-names>
          </name>
          <xref ref-type="aff" rid="j_JDS_aff_003"/>
        </contrib>
        <aff id="j_JDS_aff_003">University of Palermo</aff>
      </contrib-group>
      <volume>9</volume>
      <issue>2</issue>
      <fpage>221</fpage>
      <lpage>241</lpage>
      <permissions>
        <ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/>
      </permissions>
      <abstract>
        <p>Abstract: A core task in analyzing randomized clinical trials based on longitudinal data is to find the best way to describe the change over time for each treatment arm. We review the implementation and estimation of a flexible piecewise Hierarchical Linear Model (HLM) to model change over time. The flexible piecewise HLM consists of two phases with differing rates of change. The breakpoints between these two phases, as well as the rates of change per phase are allowed to vary between treatment groups as well as individuals. While this approach may provide better model fit, how to quantify treatment differences over the longitudinal period is not clear. In this paper, we develop a procedure for summarizing the longitudinal data for the flexible piecewise HLM on the lines of Cook et al. (2004). We focus on quantifying the overall treatment efficacy using the area under the curve (AUC) of the individual flexible piecewise HLM models. Methods are illustrated through data from a placebo-controlled trial in the treatment of depression comparing psychotherapy and pharmacotherapy.</p>
      </abstract>
      <kwd-group>
        <label>Keywords</label>
        <kwd>Area under the curve (AUC)</kwd>
        <kwd>breakpoint</kwd>
        <kwd>Hierarchical Linear model</kwd>
        <kwd>random effects</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
