A Model Free Approach to Combining Biomarkers

Abstract

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.