  Rich meta-epidemiological data sets have been collected to explore
associations between intervention effect estimates and study-level
characteristics. Welton et al. proposed models for the analysis of
meta-epidemiological data, but these models are restrictive because they force
heterogeneity among studies with a particular characteristic to be at least as
large as that among studies without the characteristic. In this paper we
present alternative models that are invariant to the labels defining the two
categories of studies. To exemplify the methods, we use a collection of
meta-analyses in which the Cochrane Risk of Bias tool has been implemented. We
first investigate the influence of small trial sample sizes (less than 100
participants), before investigating the influence of multiple methodological
flaws (inadequate or unclear sequence generation, allocation concealment and
blinding). We fit both the Welton et al. model and our proposed label-invariant
model and compare the results. Estimates of mean bias associated with the trial
characteristics and of between-trial variances are not very sensitive to the
choice of model. Results from fitting a univariable model show that
heterogeneity variance is, on average, 88% greater among trials with less than
100 participants. Based on a multivariable model, heterogeneity variance is, on
average, 25% greater among trials with inadequate/unclear sequence generation,
51% greater among trials with inadequate/unclear blinding, and 23% lower among
trials with inadequate/unclear allocation concealment, though the 95% intervals
for these ratios are very wide. Our proposed label-invariant models for
meta-epidemiological data analysis facilitate investigations of between-study
heterogeneity attributable to certain study characteristics.
