IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v11y2015i1p91-108n8.html
   My bibliography  Save this article

Flexible Regression Models for Rate Differences, Risk Differences and Relative Risks

Author

Listed:
  • Donoghoe Mark W.

    (Department of Statistics, Macquarie University, New South Wales 2109, Australia NHMRC Clinical Trials Centre, University of Sydney, New South Wales 2006, Australia)

  • Marschner Ian C.

    (Department of Statistics, Macquarie University, New South Wales 2109, Australia NHMRC Clinical Trials Centre, University of Sydney, New South Wales 2006, Australia)

Abstract

Generalized additive models (GAMs) based on the binomial and Poisson distributions can be used to provide flexible semi-parametric modelling of binary and count outcomes. When used with the canonical link function, these GAMs provide semi-parametrically adjusted odds ratios and rate ratios. For adjustment of other effect measures, including rate differences, risk differences and relative risks, non-canonical link functions must be used together with a constrained parameter space. However, the algorithms used to fit these models typically rely on a form of the iteratively reweighted least squares algorithm, which can be numerically unstable when a constrained non-canonical model is used. We describe an application of a combinatorial EM algorithm to fit identity link Poisson, identity link binomial and log link binomial GAMs in order to estimate semi-parametrically adjusted rate differences, risk differences and relative risks. Using smooth regression functions based on B-splines, the method provides stable convergence to the maximum likelihood estimates, and it ensures that the estimates always remain within the parameter space. It is also straightforward to apply a monotonicity constraint to the smooth regression functions. We illustrate the method using data from a clinical trial in heart attack patients.

Suggested Citation

  • Donoghoe Mark W. & Marschner Ian C., 2015. "Flexible Regression Models for Rate Differences, Risk Differences and Relative Risks," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 91-108, May.
    • Handle: RePEc:bpj:ijbist:v:11:y:2015:i:1:p:91-108:n:8
    DOI: 10.1515/ijb-2014-0044
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2014-0044
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2014-0044?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    2. Malloy, Elizabeth J. & Spiegelman, Donna & Eisen, Ellen A., 2009. "Comparing measures of model selection for penalized splines in Cox models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2605-2616, May.
    3. Berger, Daniel & Corvalan, Alejandro & Easterly, William & Satyanath, Shanker, 2013. "Do superpower interventions have short and long term consequences for democracy?," Journal of Comparative Economics, Elsevier, vol. 41(1), pages 22-34.
    4. Marschner, Ian C. & Gillett, Alexandra C. & O’Connell, Rachel L., 2012. "Stratified additive Poisson models: Computational methods and applications in clinical epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1115-1130.
    5. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simon N. Wood & Matteo Fasiolo, 2017. "A generalized Fellner‐Schall method for smoothing parameter optimization with application to Tweedie location, scale and shape models," Biometrics, The International Biometric Society, vol. 73(4), pages 1071-1081, December.
    2. Cornelius Fritz & Göran Kauermann, 2022. "On the interplay of regional mobility, social connectedness and the spread of COVID‐19 in Germany," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 400-424, January.
    3. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    4. Umlauf, Nikolaus & Adler, Daniel & Kneib, Thomas & Lang, Stefan & Zeileis, Achim, 2015. "Structured Additive Regression Models: An R Interface to BayesX," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i21).
    5. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    6. Tutz, Gerhard & Berger, Moritz, 2020. "The effect of explanatory variables on income: A tool that allows a closer look at the differences in income," Econometrics and Statistics, Elsevier, vol. 16(C), pages 28-41.
    7. Yixuan Wang & Jianzhu Li & Ping Feng & Rong Hu, 2015. "A Time-Dependent Drought Index for Non-Stationary Precipitation Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5631-5647, December.
    8. Gerhard Tutz & Moritz Berger, 2018. "Tree-structured modelling of categorical predictors in generalized additive regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 737-758, September.
    9. Nathaniel Geiger & Bryan McLaughlin & John Velez, 2021. "Not all boomers: temporal orientation explains inter- and intra-cultural variability in the link between age and climate engagement," Climatic Change, Springer, vol. 166(1), pages 1-20, May.
    10. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    11. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    12. Tommaso Luzzati & Angela Parenti & Tommaso Rughi, 2017. "Spatial error regressions for testing the Cancer-EKC," Discussion Papers 2017/218, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    13. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    14. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    15. Conor Waldock & Bernhard Wegscheider & Dario Josi & Bárbara Borges Calegari & Jakob Brodersen & Luiz Jardim de Queiroz & Ole Seehausen, 2024. "Deconstructing the geography of human impacts on species’ natural distribution," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    16. Chen, Shu & Shao, Dongguo & Tan, Xuezhi & Gu, Wenquan & Lei, Caixiu, 2017. "An interval multistage classified model for regional inter- and intra-seasonal water management under uncertain and nonstationary condition," Agricultural Water Management, Elsevier, vol. 191(C), pages 98-112.
    17. Riccardo De Bin & Vegard Grødem Stikbakke, 2023. "A boosting first-hitting-time model for survival analysis in high-dimensional settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 420-440, April.
    18. Manoel Bittencourt & Renee van Eyden & Monaheng Seleteng, 2013. "Inflation and Economic Growth in the SADC: Some Panel Time-Series Evidence," Working Papers 201354, University of Pretoria, Department of Economics.
    19. Matteo Malavasi & Gareth W. Peters & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang & Georgy Sofronov, 2021. "Cyber Risk Frequency, Severity and Insurance Viability," Papers 2111.03366, arXiv.org, revised Mar 2022.
    20. Joanna Baj-Korpak & Marian Jan Stelmach & Kamil Zaworski & Piotr Lichograj & Marek Wochna, 2022. "Assessment of Motor Abilities and Physical Fitness in Youth in the Context of Talent Identification—OSF Test," IJERPH, MDPI, vol. 19(21), pages 1-19, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:ijbist:v:11:y:2015:i:1:p:91-108:n:8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.