Estimation of adjusted rate differences using additive negative binomial regression

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 ECME 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 c 2015 John Wiley & Sons, Ltd

Stable computational methods for additive binomial models with application to adjusted risk differences

Risk difference is an important measure of effect size in biostatistics, for both randomised and observational studies. The natural way to adjust risk differences for potential confounders is to use an additive binomial model, which is a binomial generalised linear model with an identity link function. However, implementations of the additive binomial model in commonly used statistical packages can fail to converge to the maximum likelihood estimate (MLE), necessitating the use of approximate methods involving misspecified or inflexible models. A novel computational method is proposed, which retains the additive binomial model but uses the multinomial–Poisson transformation to convert the problem into an equivalent additive Poisson fit. The method allows reliable computation of the MLE, as well as allowing for semi-parametric monotonic regression functions. The performance of the method is examined in simulations and it is used to analyse two datasets from clinical trials in acute myocardial infarction. Source code for implementing the method in R is provided as supplementary material (see Appendix A).Australian Research Counci

logbin: An R Package for Relative Risk Regression Using the Log-Binomial Model

Relative risk regression using a log-link binomial generalized linear model (GLM) is an important tool for the analysis of binary outcomes. However, Fisher scoring, which is the standard method for fitting GLMs in statistical software, may have difficulties in converging to the maximum likelihood estimate due to implicit parameter constraints. logbin is an R package that implements several algorithms for fitting relative risk regression models, allowing stable maximum likelihood estimation while ensuring the required parameter constraints are obeyed. We describe the logbin package and examine its stability and speed for different computational algorithms. We also describe how the package may be used to include flexible semi-parametric terms in relative risk regression models

Combinatorial EM algorithms

The complete-data model that underlies an Expectation-Maximization (EM) algorithm must have a parameter space that coincides with the parameter space of the observed-data model. Otherwise, maximization of the observed-data log-likelihood will be carried out over a space that does not coincide with the desired parameter space. In some contexts, however, a natural complete-data model may be defined only for parameter values within a subset of the observed-data parameter space. In this paper we discuss situations where this can still be useful if the complete-data model can be viewed as a member of a finite family of complete-data models that have parameter spaces which collectively cover the observed-data parameter space. Such a family of complete-data models defines a family of EM algorithms which together lead to a finite collection of constrained maxima of the observed-data log-likelihood. Maximization of the log-likelihood function over the full parameter space then involves identifying the constrained maximum that achieves the greatest log-likelihood value. Since optimization over a finite collection of candidates is referred to as combinatorial optimization, we refer to such a family of EM algorithms as a combinatorial EM (CEM) algorithm. As well as discussing the theoretical concepts behind CEM algorithms, we discuss strategies for improving the computational efficiency when the number of complete-data models is large. Various applications of CEM algorithms are also discussed, ranging from simple examples that illustrate the concepts, to more substantive examples that demonstrate the usefulness of CEM algorithms in practice.20 page(s