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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.
Original language | English |
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Pages (from-to) | 91-108 |
Number of pages | 18 |
Journal | International Journal of Biostatistics |
Volume | 11 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 May 2015 |
Keywords
- B-splines
- generalized additive models
- risk models
- semi-parametric regression
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Dive into the research topics of 'Flexible regression models for rate differences, risk differences and relative risks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Binary regression with additive predictors: new statistical theory with healthcare applications
Marschner, I., Gebski, V., Newton, J. & MQRES, M.
1/01/11 → 30/09/16
Project: Research