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Abstract
Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identitylink Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this; however, standard modelfitting methods are often unable to cope with the constrained parameter space arising from the nonnegativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation–conditional maximisation–either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semiparametric regression functions. We illustrate the method using a placebocontrolled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method.
Original language  English 

Pages (fromto)  31663178 
Number of pages  13 
Journal  Statistics in Medicine 
Volume  35 
Issue number  18 
DOIs  
Publication status  Published  15 Aug 2016 
Keywords
 ECME algorithm
 negative binomial regression
 overdispersion
 rate difference
 semiparametric regression
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Projects
 1 Finished

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