Adjusted risk difference estimation using a stable and flexible method for additive binomial models

Risk difference is an important measure of effect size in 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. We propose a novel method that retains the additive binomial model but uses the multinomial-Poisson transformation to convert the problem into an equivalent additive Poisson fit. Combined with a stable method for fitting additive Poisson models, this allows reliable computation of the MLE, as well as allowing for semi-parametric monotonic regression functions. We use our method to analyse datasets from two clinical trials in acute myocardial infarction.