Assessing the incremental value of new biomarkers based on OR rules

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 biomarker and constructing its confidence interval, using bootstrap, cross-validation, and a novel fuzzy p-value-based technique. We compare the performance of different methods via extensive simulation studies and apply them to the pancreatic cancer example.