Speaker: Ying Kuen Cheung, Columbia Public Health - Ying Kuen Cheung, PhD | Columbia University Mailman School of Public Health
Abstract: Monotonicity is a common and often necessary assumption in biomedical research. In multiplex assays, biomarker expression is expected to have a monotonic association with disease outcome; similarly, in dose-finding studies, the probability of a response or toxicity outcome is expected to increase with dose. In this talk, we present a novel nonparametric framework for multivariable isotonic classification and regression based on the projective Bayes approach, which projects an unconstrained Bayes estimator onto the partial ordering subspace defined by the monotonicity assumption. A key theoretical result establishes that the exact Bayes solution — which maximizes the posterior gain over all monotone classifiers — can be obtained via a sequential update method, reducing what would otherwise be an exponentially complex optimization to a sequence of tractable subproblems. To implement this efficiently, we propose recursive comb algorithms and establish their computational feasibility in high-dimensional settings. We have implemented these methods in an open-source R package. We illustrate our approach using a human papillomavirus (HPV) assay for cervical cancer precursor lesions, demonstrating superior diagnostic accuracy compared to parametric logistic regression and monotone generalized additive models. Simulation studies further demonstrate substantial efficiency gains from leveraging monotonicity constraints as the dimension of the biomarker panel grows.
This will be a free hybrid seminar. To register to attend remotely, please click here: https://cam-ac-uk.zoom.us/meeting/register/6ANeRCzcRaa4rXx-FJVpLA