Combining Multiple Biomarker Models in Logistic Regression

In medical research, there is great interest in developing methods for combining biomarkers. We argue that selection of markers should also be considered in the process. Traditional model/variable selection procedures ignore the underlying uncertainty after model selection. In this work, we propose a novel model-combining algorithm for classification in biomarker studies. It works by considering weighted combinations of various logistic regression models; five different weighting schemes are considered in the article. The weights and algorithm are justified using decision theory and risk-bound results. Simulation studies are performed to assess the finite-sample properties of the proposed model-combining method. It is illustrated with an application to data from an immunohistochemical study in prostate cancer.