As part of my research I have some association data between exposure to a risk factor and a range of health outcomes from published studies. The association is reported in terms of odds ratios. I want to convert this (OR) to risk ratio (RR), but I don't have enough prevalence data (i.e., the proportion of the health outcome among the unexposed/reference group). Any suggestionsons on whether there is alternative way to get RR other than through what I already know (i.e., converting to RR using the OR and prevalence data)?
Suppose
- a = number of exposed cases
- b = number of exposed controls
- c = number of non-exposed cases
- d = number of non-exposed controls
The gold standard formula for converting OR to RR is:
RR = (OR)/(1-Ro+Ro*OR), where Ro = c/c+d, ie, the probability that the non-exposed will develop the outcome/disease.
I assume that in your case the problem is you do not have 'c' and hence Ro can not be calculated.
There is a method to overcome this by some optimisation provided you have the total number of treated (exposed, a+b) and non-treated (non-exposed, c+d). The theory behind it is mostly based on the fact that the (1-p) confidence interval for log OR is log(OR) +_ (plus or minus) z-value*SE where
SE = root of (1/a + 1/b + 1/c + 1/d). The entire mathematical steps are difficult to be written here, but the basic idea is to minimise the sum of squares via optimisation.
Attaching a link to an article by Zhu Wang where both theoretical and practical implementation (in R) is shown.
Hope this was helpful for you
http://cran.r-project.org/web/packages/orsk/vignettes/orsk_demo.pdf
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