EVALUATING MULTIPLEX DIAGNOSTIC TEST USING PARTIALLY ORDERED BAYES CLASSIFIER

In a diagnostic test using multiplex assay, each individual biomarker is often expected to have monotonic association with the disease outcome and therefore the underlying disease classification rule is partially ordered with respect to the biomarkers. Nonparametric estimation of the classification rule can be accomplished by projecting an unconstrained Bayes estimator onto the partial ordering subspace. However, computing the projection is challenging as it involves performing maximization over a constrained parameter space whose size grows exponentially with the sample size. We introduce a novel sequential update method for projection-based nonparametric estimation of the disease classification rule and propose new recursive algorithms to implement the method. The proposed algorithms yields the exact Bayes solution that maximizes the posterior gain with respect to a classification-type gain function. When compared to an existing algorithm that gives approximate Bayes solution, our algorithms accomplish the same tasks with much reduced elapsed time in simulation study. We apply the sequential update method to evaluate a human papillomavirus test for cervical cancer precursor lesions and derive diagnostic rule that improves accuracy on existing estimation methods including parametric logistic regression and monotone generalized additive models.