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

Jorge L. Bazán (), Victor H. Lachos () and Alex de la Cruz H. ()
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Jorge L. Bazán: University of São Paulo
Victor H. Lachos: University of Connecticut
Alex de la Cruz H.: Pontificia Universidad Católica del Perú

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 2, No 14, 699-740

Abstract: Abstract 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.

Keywords: Bayesian inference; Binary response; Medical data; Scale mixtures of skew-normal distributions; Unbalanced data; C11; C25; I10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-025-00388-8

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