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A Model Free Approach to Combining Biomarkers
Author(s) -
Pfeiffer Ruth M.,
Bur Efstathia
Publication year - 2008
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200710428
Subject(s) - receiver operating characteristic , mathematics , statistics , likelihood ratio test , statistic , linear regression , linear model , biomarker , generalized linear model , biology , biochemistry
For most diseases, single biomarkers do not have adequate sensitivity or specificity for practical purposes. We present an approach to combine several biomarkers into a composite marker score without assuming a model for the distribution of the predictors. Using sufficient dimension reduction techniques, we replace the original markers with a lower‐dimensional version, obtained through linear transformations of markers that contain sufficient information for regression of the predictors on the outcome. We combine the linear transformations using their asymptotic properties into a scalar diagnostic score via the likelihood ratio statistic. The performance of this score is assessed by the area under the receiver‐operator characteristics curve (ROC), a popular summary measure of the discriminatory ability of a single continuous diagnostic marker for binary disease outcomes. An asymptotic chi‐squared test for assessing individual biomarker contribution to the diagnostic score is also derived. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)