Single biomarkers often have inadequate classification performance in early detection of disease, making it important to identify new biomarkers to combine with the existing marker for improved performance.

One method for combining biomarkers that appears to have a sound biological basis is to use logic rules, e.g., the OR/AND rules. In a 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; furthermore, such research is hindered by challenges due to statistical non-regularity. In this talk I will present a recent development on 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. I will propose 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. Finally, I will use numerical studies and the pancreatic cancer example to illustrate the performance of the proposed methods.