title: Estimation of adjusted rate differences using additive negative binomial regression.
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 identity-link 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 model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity 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 semi-parametric regression functions. We illustrate the method using a placebo-controlled 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. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Statistics, Macquarie University, Sydney, 2109, New South Wales, Australia.|NHMRC Clinical Trials Centre, University of Sydney, Sydney, 2006, New South Wales, Australia.
authors.forename: Mark W
authors.identifier: 0000-0003-0212-6443
authors.initials: MW
authors.lastname: Donoghoe
authors.affiliation: Department of Statistics, Macquarie University, Sydney, 2109, New South Wales, Australia.|NHMRC Clinical Trials Centre, University of Sydney, Sydney, 2006, New South Wales, Australia.
authors.forename: Ian C
authors.initials: IC
authors.lastname: Marschner
mesh_terms: D056808:Biostatistics; D003924:Diabetes Mellitus, Type 2 / Q000188:drug therapy; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D012044:Regression Analysis
keywords: ECME algorithm; negative binomial regression; overdispersion; rate difference; semi-parametric regression