Semiparametric methods for the binormal model with multiple biomarkers

Abstract: In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We also discuss adjustment for covariates in this class of models and provide a simple two-stage estimation procedure that can be fit using standard software packages. Some analytical comparisons between analyses using the proposed model with univariate biomarker analyses are given. In addition, the techniques are applied to simulated data as well as data from two cancer biomarker studies.