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

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  • Donoghoe Mark W.
  • Marschner Ian C.

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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