Flexible regression models for rate differences, risk differences and relative risks

Mark W. Donoghoe*, Ian C. Marschner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)91-108
Number of pages18
JournalInternational Journal of Biostatistics
Issue number1
Publication statusPublished - 1 May 2015


  • B-splines
  • generalized additive models
  • risk models
  • semi-parametric regression


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