I am doing a meta-analysis where I calculate an overall prevalence value for multiple studies. I have submitted my manuscript to a journal. I used sample size as one of the risk of bias criteria, where a low sample size represents an underpowered study.
I received the reviewers' comments and one comment mentioned that a low sample size does not invalidate the prevalence estimate (i.e., the prevalence remains valid even if the sample size is low). I am wondering, why is this the case?
If one or more of the estimates from the primary studies is imprecise then that will be taken into account in the meta-analysis as the procedure used is inverse variance weighting which takes precision into account. If you use random effects models then the weights become more nearly equal so small studies do then have greater influence. In the limit when $\tau^2$ vastly exceeds the individual variances then the weights tend to equality. So as long as you trust the study in other respects including it is fine but it may not have much effect on your overall estimate anyway.
