The current interest in meta-analysis of count data in which some studies have
zero events (sparse data) has led to re-assessment of commonly used
meta-analysis methods to establish their validity in such scenarios. The general
consensus is that methods which exclude studies with zero events should be
avoided. In the family of parametric methods, random effects models come out
highly recommended. The random effects approach accounts for the variation in
the effect measure between studies by associating the effect measure with a
random effects structure (random slope). It is has been suggested that if a
parameter is associated with a random effects structure and the distribution of
the random effects is misspecified, the estimated parameter can be biased.
However, previous studies have concentrated on misspecification of random
effects in context where the parameter of interest is not associated with the
random effect hence the frequently conveyed message is that misspecification of
the random effects distribution is not a big deal. Considering the importance of
the random effects approach in meta-analysis of sparse data, we used a
simulation study to investigate the impact of misspecification of the
distribution of the random effects is on the parameter of interest, the effect
measure. Our results indicated that relative bias in the estimated effect could
be as high as 30\% and the 95\% confidence interval coverage as low as 0\%.
These results send a clear message that misspecification of the distribution of
random effects is a big deal when dealing with sparse data. We therefore
illustrated a sensitivity analysis and recommend that it should always accompany
a random effects approach in meta-analysis of sparse data.