My question is whether it is plausible to have "Rate Ratio" showing an increased risk while "Odds Ratio" (based on the same data) showing decreased risk?
I have an example in this article: http://jamanetwork.com/journals/jamapediatrics/fullarticle/203581
The article reported a rate ratio of 2.05 (95%C.I.= 1.06-3.97) for "any use of erythromycin" (Table 2 in the article). Constructing the 2x2 table, gives the following:
Based on this 2x2 table, odds ratio = 0.49 (95%C.I.= 0.25-0.94).
How can we explain this conflict?