  According to Davey et al. (2011) with a total of 22,453 meta-analyses from
the January 2008 Issue of the Cochrane Database of Systematic Reviews, the
median number of studies included in each meta-analysis is only three. In other
words, about a half or more of meta-analyses conducted in the literature
include only two or three studies. While the common-effect model (also referred
to as the fixed-effect model) may lead to misleading results when the
heterogeneity among studies is large, the conclusions based on the
random-effects model may also be unreliable when the number of studies is
small. Alternatively, the fixed-effects model avoids the restrictive assumption
in the common-effect model and the need to estimate the between-study variance
in the random-effects model. We note, however, that the fixed-effects model is
under appreciated and rarely used in practice until recently. In this paper, we
compare all three models and demonstrate the usefulness of the fixed-effects
model when the number of studies is small. In addition, we propose a new
estimator for the unweighted average effect in the fixed-effects model.
Simulations and real examples are also used to illustrate the benefits of the
fixed-effects model and the new estimator.
