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

The International Journal of Biostatistics
Mark W Donoghoe, Ian C Marschner

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 ...Continue Reading

References

Oct 26, 2006·Biostatistics·Florian Leitenstorfer, Gerhard Tutz
Feb 18, 2010·Computational Statistics & Data Analysis·Elizabeth J MalloyEllen A Eisen
Sep 15, 2011·Biostatistics·Ian C Marschner, Alexandra C Gillett
Aug 7, 2012·Statistics in Medicine·Stephanie A KovalchikHormuzd A Katki

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Citations

Mar 12, 2019·Research Synthesis Methods·Ilyas BakbergenulyElena Kulinskaya
Apr 14, 2016·Statistics in Medicine·Mark W Donoghoe, Ian C Marschner

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Methods Mentioned

BETA
GAM

Software Mentioned

rm
R
gamlss
eqalign
Lambda
gam
GMBBoost
GMonBoost
mgcv
addreg

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