Combining multiple biomarkers to linearly maximize the diagnostic accuracy under ordered multi-class setting

Either in clinical study or biomedical research, it is a common practice to combine multiple biomarkers to improve the overall diagnostic performance. Despite the fact there exist a large number of statistical methods for biomarker combination under binary classification, research on this topic under multi-class setting is sparse. The overall diagnostic accuracy, i.e. the sum of correct classification rates, directly measures the classification accuracy of the combined biomarkers. Hence the overall accuracy can serve as an important objective function for biomarker combination, especially when the combined biomarkers are used for the purpose of making medical diagnosis. In this paper, we address the problem of combining multiple biomarkers to directly maximize the overall diagnostic accuracy by presenting several grid search methods and derivation-based methods. A comprehensive simulation study was conducted to compare the performances of these methods. An ovarian cancer data set is analyzed in the end.