# Swopping exposed and unexposed groups in calculating OR

I am comparing the OR’s of a number of studies which are comparing the effect of laparoscopic (keyhole) surgery vs Open surgery on post-op infection.

A few of the studies treat ‘Laparoscopic’ as the exposure and find OR’s < 1 (protective against infection), while others use ‘Open’ as the exposure and find OR’s > 1 (risk factor for infection).

How could I convert the OR’s of those studies that treat ‘Open’ as the exposure to use ‘Laparoscopic’ as the exposure? My gut tells me to simple invert (1/OR) the OR values and the bounds of the CI…

That is correct. It is easy to see if you write it as a standard 2-by-2 table like

``````      Outcome
Exp   Yes  No
L   a   b
O   c   d
``````

and are familiar with how to calculate an OR from such a table. The OR comparing exposed with non-exposed for the outcome ‘Yes’ in the 2-by-2 table can be calculated as `ad/(bc)` if ‘L’ is the exposure. If ‘O’ is the exposure you may rewrite the 2-by-2 table as

``````      Outcome
Exp   Yes  No
O   c   d
L   a   b
``````

from which the OR is correspondingly `cb/(da) = 1/(ad/(bc))`.

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Thank you for the response.

Could I apply this method to the upper and lower bounds of the confidence interval too?

Yes, this applies also to the confidence bounds.

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