Re: Is constructing a contingency table from odds ratio's (including 95%CI) possible

On Jul 27, 7:50 am, nyika <NDKr...@xxxxxxxxx> wrote:
For a meta analyses i was able to subtract the following information
from an article:
1) the Odds ratio on poor outcome, with 95% confidence intervals
2) the number of patients with treatment and the number of patients
without treatment. (so, also the total number of patients).
I was wondering if anyone knows if it is possible to reconstruct a
contingency table with this information. (is there any software that
can do this? )

regards
ND Kruyt

Let m & n be the two sample sizes, and write the 2 x 2 table as
{{a,m-a},{c,n-c}}. Then the odds ratio is r = a(n-c)/((m-a)c).

Let u be the upper bound for the odds ratio, let z = 1.96 (or
whatever you think was used to get the 95% c.i.). Then the variance
of the log of the odds ratio is v = (log[u/r]/z)^2, which was
presumably arrived at as v = 1/a + 1/(m-a) + 1/c + 1/(n-c).

The easiest way to solve for a & c is to search for a pair of
integers in [1,m-1] & [1,n-1] that come within roundoff error
of satisfying the equations for r & w.

(You might also want to try it with m & n each incremented by 1,
in case they added .5 to all four cells to stabilize the estimate.
Then you would look for pairs of half-integers .5, 1.5, ... .)

.

Relevant Pages