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

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  • 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
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    References listed on IDEAS

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    1. 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.
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