  Simulation studies are commonly used to evaluate the performance of newly
developed meta-analysis methods. For methodology that is developed for an
aggregated data meta-analysis, researchers often resort to simulation of the
aggregated data directly, instead of simulating individual participant data
from which the aggregated data would be calculated in reality. Clearly,
distributional characteristics of the aggregated data statistics may be derived
from distributional assumptions of the underlying individual data, but they are
often not made explicit in publications. This paper provides the distribution
of the aggregated data statistics that were derived from a heteroscedastic
mixed effects model for continuous individual data. As a result, we provide a
procedure for directly simulating the aggregated data statistics. We also
compare our distributional findings with other simulation approaches of
aggregated data used in literature by describing their theoretical differences
and by conducting a simulation study for three meta-analysis methods:
DerSimonian and Laird's pooled estimate and the Trim & Fill and PET-PEESE
method for adjustment of publication bias. We demonstrate that the choices of
simulation model for aggregated data may have a relevant impact on (the
conclusions of) the performance of the meta-analysis method. We recommend the
use of multiple aggregated data simulation models for investigation of new
methodology to determine sensitivity or otherwise make the individual
participant data model explicit that would lead to the distributional choices
of the aggregated data statistics used in the simulation.
