A New Class of Binary Regression Models for Unbalanced Data with Applications in Medical Data

Bazán J.L.; Lachos V.H.; de la Cruz H A. · Sankhya A (2025) · DOI: 10.1007/s13171-025-00388-8

Resumen

Imbalanced binary data may be more common than expected in medical trials. In this paper, we propose a new class of link function for binary response based on the cumulative distribution function of the scale mixture of skew-normal distributions, which can be useful for fitting imbalanced binary data. The proposed link class has as special cases several link functions proposed in the literature, such as the probit and Student’s-t link, and we present a Bayesian approach for model fitting. Further, we develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with one example as well as a simulation, which illustrates the potential of the proposed class of links as an alternative for binary regression models when imbalanced binary data is presented. © Indian Statistical Institute 2025.

Instituciones: Pontificia Universidad Católica del Perú