# Can odds ratio be in different direction to rate ratio?

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?

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?

Thank you.

• Do you suppose it might be a coincidence that $1/2.05 = 0.49$? And that $1/1.06 = 0.94$ and $1/3.94 = 0.25$?
– whuber
Sep 1 '17 at 22:00
• Thank you. I thought about this but I was confused by the authors explicitly stating that "exposure to erythromycin ... was associated with a 2-fold increased risk of pyloric stenosis (adjusted rate ratio, 2.05; 95% confidence interval, 1.06-3.97) (Table 2)." Is it a mistake in their reporting?
– Anna
Sep 1 '17 at 22:12

$$(9/7129)/(795/306096) = 0.49$$ $$(795/306096)/(9/7129) = 2.06$$