Abstract:
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In early detection of disease, a single biomarker often has inadequate classification performance, making it important to identify new biomarkers to combine with the existing marker for improved performance. A biologically natural method for combining biomarkers is to use logic rules, e.g., the OR/AND rules. In our motivating example of early detection of pancreatic cancer, the established biomarker CA19-9 is only present in a subclass of cancers; it is of interest to identify new biomarkers present in the other subclasses and declare disease when either marker is positive. While there has been research on developing biomarker combinations using the OR/AND rules, inference regarding the incremental value of the new marker within this framework is lacking and challenging due to statistical non-regularity. In this article, we aim to answer the inferential question of whether combining the new biomarker achieves better classification performance than using the existing biomarker alone, based on a nonparametrically estimated OR rule that maximizes the weighted average of sensitivity and specificity. We propose and compare various procedures for testing the incremental value of the new
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