Modelling the effect of baseline risk in meta-analysis: a review from the perspective of errors-in-variables regression

In meta-analysis of clinical trials, investigating the relationship between the baseline risk and the treatment benefit is often of interest in order to explain the between trials heterogeneity with respect to treatment effect. The relationship is commonly described with a linear model taking into account the fact that the latent baseline risk is estimated from a finite sample and thus subjected to measurement error. Depending on the specific assumption about the latent baseline risks, two different classes of methods can be pursued. In the literature, it is commonly assumed that the latent baseline risks are sampled from a (normal) distribution. Such methods are often criticised for needing a distribution. Here, we propose the use of methods that require no distributional assumption on the baseline risks. A number of alternative methods are reviewed and are illustrated via simulation and by application to a published meta-analysis data.