<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-1751</journal-id>
<journal-title><![CDATA[Revista Colombiana de Estadística]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.Colomb.Estad.]]></abbrev-journal-title>
<issn>0120-1751</issn>
<publisher>
<publisher-name><![CDATA[Departamento de Estadística - Universidad Nacional de Colombia.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-17512018000200137</article-id>
<article-id pub-id-type="doi">10.15446/rce.v41n2.68535</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Using an Anchor to Improve Linear Predictions with Application to Predicting Disease Progression]]></article-title>
<article-title xml:lang="es"><![CDATA[Usando un anclaje para mejorar predicciones lineales con aplicación a la predicción de progresión de enfermedad]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Karanevich]]></surname>
<given-names><![CDATA[Alex G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[He]]></surname>
<given-names><![CDATA[Jianghua]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gajewski]]></surname>
<given-names><![CDATA[Byron J]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of Kansas Medical Center  ]]></institution>
<addr-line><![CDATA[Kansas City ]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>41</volume>
<numero>2</numero>
<fpage>137</fpage>
<lpage>155</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512018000200137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512018000200137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512018000200137&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Linear models are some of the most straightforward and commonly used modelling approaches. Consider modelling approximately monotonic response data arising from a time-related process. If one has knowledge as to when the process began or ended, then one may be able to leverage additional assumed data to reduce prediction error. This assumed data, referred to as the &#8220;anchor&#8221;, is treated as an additional data-point generated at either the beginning or end of the process. The response value of the anchor is equal to an intelligently selected value of the response (such as the upper bound, lower bound, or 99th percentile of the response, as appropriate). The anchor reduces the variance of prediction at the cost of a possible increase in prediction bias, resulting in a potentially reduced overall mean-square prediction error. This can be extremely effective when few individual data-points are available, allowing one to make linear predictions using as little as a single observed data-point. We develop the mathematics showing the conditions under which an anchor can improve predictions, and also demonstrate using this approach to reduce prediction error when modelling the disease progression of patients with amyotrophic lateral sclerosis.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Modelos lineales son los modelos más fáciles de usar y comunes en modelamiento. Si se considera el modelamiento de una respuesta aproximadamente monótona que surge de un proceso relacionado al tiempo y se sabe cuándo el proceso inició o terminó, es posible asumir datos adicionales como palanca para reducir el error de predicción. Estos datos adicionales son llamados de &#8220;anclaje&#8221; y son datos generados antes del inicio o después del final del proceso. El valor de respuesta del anclaje es igual a un valor de respuesta escogido de manera inteligente (como por ejemplo la cota superior, inferior o el percentil 99, según conveniencia). Este anclaje reduce la varianza de la predicción a costo de un posible sesgo en la misma, lo cual resulta en una reducción potencial del error medio de predicción. Lo anterior puede ser extremadamente efectivo cuando hay pocos datos individuales, permitiendo hacer predicciones con muy pocos datos. En este trabajo presentamos en desarrollo matemático demostrando las condiciones bajo las cuales el anclaje puede mejorar predicciones y también demostramos una reducción del error de predicción aplicando el método a la modelación de progresión de enfermedad en pacientes con esclerosis lateral amiotrófica.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Linear models]]></kwd>
<kwd lng="en"><![CDATA[biased regression]]></kwd>
<kwd lng="en"><![CDATA[anchor]]></kwd>
<kwd lng="en"><![CDATA[amyotrophic lateral sclerosis]]></kwd>
<kwd lng="en"><![CDATA[ordinary least squares]]></kwd>
<kwd lng="es"><![CDATA[modelos lineales]]></kwd>
<kwd lng="es"><![CDATA[regresión sesgada]]></kwd>
<kwd lng="es"><![CDATA[anclaje]]></kwd>
<kwd lng="es"><![CDATA[esclerosis lateral amiotrófica]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados ordinarios]]></kwd>
</kwd-group>
</article-meta>
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