I am familiar with meta analysis and meta regression techniques (using the R package
metafor from Viechtbauer), but I recently stumbled on a problem I can't easily solve. Say we have a disease that can go from mother to the unborn child, and it has been studied already a number of times. Mother and child were tested for the virus right after birth. As an unborn child can impossibly get the virus other than from the mother, one would expect crosstabulations like :
| neg kid | pos kid mother neg | A | C=0 -----------|---------|-------- mother pos | B | D
Obviously using odds ratios (OR) gives errors as one would be dividing by 0. Same for relative risks :
Now the researchers want to test the (senseless) hypothesis whether infection of the child is related to the infection of the mother (which seems very, very obvious). I'm trying to reformulate the hypothesis and come up with something that makes sense, but I can't really find something.
To complicate things, some kids with negative moms actually are positive, probably due to infection in the first week. So I only have a number of studies where C = 0.
Anybody an idea on how to statistically summarize the data of different studies following such a pattern. Links to scientific papers are also more than welcome.