  Standard random-effects meta-analysis methods perform poorly when applied to
few studies only. Such settings however are commonly encountered in practice.
It is unclear, whether or to what extent small-sample-size behaviour can be
improved by more sophisticated modeling.
  We consider several likelihood-based inference methods. Confidence intervals
are based on normal or Student-t approximations. We extract an empirical data
set of 40 meta-analyses from recent reviews published by the German Institute
for Quality and Efficiency in Health Care (IQWiG). Methods are then compared
empirically as well as in a simulation study, considering odds-ratio and risk
ratio effect sizes.
  Empirically, a majority of the identified meta-analyses include only 2
studies. In the simulation study, coverage probability is, in the presence of
heterogeneity and few studies, below the nominal level for all frequentist
methods based on normal approximation, in particular when sizes in
meta-analyses are not balanced, but improve when confidence intervals are
adjusted. Bayesian methods result in better coverage than the frequentist
methods with normal approximation in all scenarios. Credible intervals are
empirically and in the simulation study wider than unadjusted confidence
intervals, but considerably narrower than adjusted ones. Confidence intervals
based on the generalized linear mixed models are in general, slightly narrower
than those from other frequentist methods. Certain methods turned out
impractical due to frequent numerical problems.
  In the presence of between-study heterogeneity, especially with unbalanced
study sizes, caution is needed in applying meta-analytical methods to few
studies, as either coverage probabilities might be compromised, or intervals
are inconclusively wide. Bayesian estimation with a sensibly chosen prior for
between-trial heterogeneity may offer a promising compromise.
