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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:

2 by 2 table

Based on this 2x2 table, odds ratio = 0.49 (95%C.I.= 0.25-0.94).

How can we explain this conflict?

Thank you.

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  • $\begingroup$ Do you suppose it might be a coincidence that $1/2.05 = 0.49$? And that $1/1.06 = 0.94$ and $1/3.94 = 0.25$? $\endgroup$ – whuber Sep 1 '17 at 22:00
  • $\begingroup$ 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? $\endgroup$ – Anna Sep 1 '17 at 22:12
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You and the article are just looking at reciprocal ratios.

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

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    $\begingroup$ Thank you. 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? $\endgroup$ – Anna Sep 1 '17 at 22:10

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