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

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  • Jorge L. Bazán

    (University of São Paulo
    Pontificia Universidad Católica de Chile/ Avda. Vicuña Mackenna 4860)

  • Victor H. Lachos

    (University of Connecticut)

  • Alex de la Cruz H.

    (Pontificia Universidad Católica del Perú)

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.

Suggested Citation

  • Jorge L. Bazán & Victor H. Lachos & Alex de la Cruz H., 2025. "A New Class of Binary Regression Models for Unbalanced Data with Applications in Medical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(2), pages 699-740, August.
    • Handle: RePEc:spr:sankha:v:87:y:2025:i:2:d:10.1007_s13171-025-00388-8
    DOI: 10.1007/s13171-025-00388-8
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    References listed on IDEAS

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    1. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
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