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The Use of Double Poisson Regression for Count Data in Health and Life Science—A Narrative Review

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  • Sebastian Appelbaum

    (Department of Psychology and Psychotherapy, Witten/Herdecke University, Alfred-Herrhausen-Str. 50, 58448 Witten, Germany
    Center for Clinical Trials, Department of Medicine, Faculty of Health, Witten/Herdecke University, 58448 Witten, Germany)

  • Julia Stronski

    (Department of Psychology and Psychotherapy, Witten/Herdecke University, Alfred-Herrhausen-Str. 50, 58448 Witten, Germany)

  • Uwe Konerding

    (Department of Psychology and Psychotherapy, Witten/Herdecke University, Alfred-Herrhausen-Str. 50, 58448 Witten, Germany
    Trimberg Research Academy, Otto-Friedrich-Universität Bamberg, An der Weberei 5, 96047 Bamberg, Germany)

  • Thomas Ostermann

    (Department of Psychology and Psychotherapy, Witten/Herdecke University, Alfred-Herrhausen-Str. 50, 58448 Witten, Germany)

Abstract

Count data are present in many areas of everyday life. Unfortunately, such data are often characterized by over- and under-dispersion. In 1986, Efron introduced the Double Poisson distribution to account for this problem. The aim of this work is to examine the application of this distribution in regression analyses performed in health-related literature by means of a narrative review. The databases Science Direct, PBSC, Pubmed PsycInfo, PsycArticles, CINAHL and Google Scholar were searched for applications. Two independent reviewers extracted data on Double Poisson Regression Models and their applications in the health and life sciences. From a total of 1644 hits, 84 articles were pre-selected and after full-text screening, 13 articles remained. All these articles were published after 2011 and most of them targeted epidemiological research. Both over- and under-dispersion was present and most of the papers used the generalized additive models for location, scale, and shape (GAMLSS) framework. In summary, this narrative review shows that the first steps in applying Efron’s idea of double exponential families for empirical count data have already been successfully taken in a variety of fields in the health and life sciences. Approaches to ease their application in clinical research should be encouraged.

Suggested Citation

  • Sebastian Appelbaum & Julia Stronski & Uwe Konerding & Thomas Ostermann, 2025. "The Use of Double Poisson Regression for Count Data in Health and Life Science—A Narrative Review," Stats, MDPI, vol. 8(4), pages 1-12, October.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:4:p:90-:d:1763273
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    References listed on IDEAS

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    1. Théo Denis & Joseph Lanfranchi, 2025. "A New Empirical Model of the Determinants of Sickness and the Choice Between Presenteeism and Absence," LABOUR, CEIS, vol. 39(1), pages 61-87, March.
    2. Croux, C. & Gijbels, I. & Prosdocimi, I., 2010. "Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models," Other publications TiSEM a188c2bc-8a96-44c9-b1e6-0, Tilburg University, School of Economics and Management.
    3. Croux, C. & Gijbels, I. & Prosdocimi, I., 2010. "Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models," Discussion Paper 2010-104, Tilburg University, Center for Economic Research.
    4. Jana Schmidt & Mandy Vogel & Tanja Poulain & Wieland Kiess & Christian Hirsch & Dirk Ziebolz & Rainer Haak, 2022. "Association of Oral Health Conditions in Adolescents with Social Factors and Obesity," IJERPH, MDPI, vol. 19(5), pages 1-14, March.
    5. Maike Hohberg & Peter Pütz & Thomas Kneib, 2020. "Treatment effects beyond the mean using distributional regression: Methods and guidance," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-29, February.
    6. I. Gijbels & I. Prosdocimi & G. Claeskens, 2010. "Nonparametric estimation of mean and dispersion functions in extended generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 580-608, November.
    7. Kimberly F. Sellers & Darcy S. Morris, 2017. "Underdispersion models: Models that are “under the radar”," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(24), pages 12075-12086, December.
    8. Tammy Harris & Zhao Yang & James W. Hardin, 2012. "Modeling underdispersed count data with generalized Poisson regression," Stata Journal, StataCorp LLC, vol. 12(4), pages 736-747, December.
    9. Sebastian Appelbaum & Thomas Ostermann & Uwe Konerding, 2025. "Maximum likelihood estimation of parameters for double poisson regression: a simulation study," Computational Statistics, Springer, vol. 40(8), pages 4635-4673, November.
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