Relative risk not making sense for meta-analysis I am doing a meta-analysis and struggling with the relative risk values. Looking at the forest plot and the RR for some relative risks I can tell it is incorrect. i.e first study rr should be 0.33. I have entered numbers from other metaanalysis and it seems to generate the right RR, so how come it doesn't seem to be working with my studies. Some of the RR is right but some off. 

 A: As clearly stated in the Cochrane Handbook (https://handbook-5-1.cochrane.org/chapter_9/9_4_4_1_mantel_haenszel_methods.htm):

The Mantel-Haenszel methods (Mantel 1959, Greenland 1985) are the
  default fixed-effect methods of meta-analysis programmed in RevMan.
  When data are sparse, either in terms of event rates being low or
  study size being small, the estimates of the standard errors of the
  effect estimates that are used in the inverse variance methods may be
  poor. Mantel-Haenszel methods use a different weighting scheme that
  depends upon which effect measure (e.g. risk ratio, odds ratio, risk
  difference) is being used. They have been shown to have better
  statistical properties when there are few events. As this is a common
  situation in Cochrane reviews, the Mantel-Haenszel method is generally
  preferable to the inverse variance method. In other situations the two
  methods give similar estimates.

I recommend you to switch to another method, and you can also switch to Peto's odds ratio for such sparse events. Check here for additional info from Cochrane https://handbook-5-1.cochrane.org/chapter_9/9_4_4_meta_analysis_of_dichotomous_outcomes.htm, and here for the very comprehensive meta R package https://cran.r-project.org/web/packages/meta/meta.pdf.
A: The reason is that a 'continuity correction' is applied in those studies where you are seeing a discrepancy. This correction involves adding 0.5 to the number of events and 1 to the total. For example, in the first study:
> round((1.5 / 4) / (11.5 / 12), 2)
[1] 0.39

You actually have a very common (not sparse) outcome (i.e., often the number of events is equal to the total). Still, as suggested by @Joe_74, I would consider switching to a different method for analyzing these data (e.g., the Mantel-Haenszel method or using a logistic mixed-effects model). 
