A Model Free Approach to Combining Biomarkers

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)