A Bayesian (meta-)regression model for treatment effects on the risk difference scale

In clinical settings, the absolute risk reduction due to treatment that can be expected in a particular patient is of key interest. However, logistic regression, the default regression model for trials with a binary outcome, produces estimates of the effect of treatment measured as a difference in log odds. We explored options to estimate treatment effects directly as a difference in risk, specifically in the network meta-analysis setting. We propose a novel Bayesian (meta-)regression model for binary outcomes on the additive risk scale. The model allows treatment effects, covariate effects, interactions and variance parameters to be estimated directly on the linear scale of clinical interest. We compared effect estimates from this model to (1) a previously proposed additive risk model by Warn, Thompson and Spiegelhalter ("WTS model") and (2) backtransforming the predictions from a logistic model to the natural scale after regression. The models were compared in a network meta-analysis of 20 hepatitis C trials, as well as in the analysis of simulated single trial settings. The resulting estimates diverged, in particular for small sample sizes or true risks close to 0% or 100%. Researchers should be aware that modelling untransformed risk can yield very different results from default logistic models. The treatment effect in participants with such extreme predicted risks weighed more heavily on the overall treatment effect estimate from our proposed model compared to the WTS model. In our network meta-analysis, this sensitivity of our proposed model was needed to detect all information in the data.