Comment on article by Browne and Draper

As stated by the authors, the use of multilevel models has grown substantially over the last few years. However, as listed in the first paragraph of section 1, there are a number of competing methods proposed for their estimation, both Bayesian and likelihood based. Within the Bayesian framework there is of course the added issue of the choice of prior distributions for the various model parameters. It is worth noting here that the increased use of Bayesian methods over the last decade or so has not necessarily been due to a philosophical shift, but rather a desire to fit complex models, with software such as WinBUGS enabling users to do this. Many of these users want their ‘data to dominate’ and therefore want all prior distributions to be non-informative. However, this is rarely straightforward and in hierarchical models it is the choice of prior distribution for the hierarchical variance parameters that has been shown to be most crucial, particularly in small samples. In earlier work we conducted a simulation study on the choice of prior distribution for the variance component (between study variance) in a meta-analysis of aggregated data (Lambert et al. 2005). One of the advantages of using aggregated data is that models are quicker to fit and we were able to compare 13 different prior distributions for 9 different scenarios. When the number of level 2 units is large the choice of prior distribution becomes less important. However, for many real applications in medicine one would expect the number of level 2 units to be small, for example meta-analysis (Sutton and Abrams 2001) and cluster randomised trials (Turner et al. 2001). It is to the situations where there are only a small number of level 2 units that I wish to address most of my comments.