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# RE: st: Recovering cell values from odds ratios

 From "Tiago V. Pereira" To statalist@hsphsun2.harvard.edu Subject RE: st: Recovering cell values from odds ratios Date Tue, 31 May 2011 16:09:54 -0300 (BRT)

```Carina is asking for an approach to reconstruct raw 2x2 tables from the
reported odds ratio and its confidence intervals.
--

Carina,

The solution for your problem is easy, and can be found here:

Four-fold table cell frequencies imputation in meta analysis. Carlo Di
Pietrantonj, Issue
Statistics in Medicine, Volume 25, Issue 13, pages 2299?2322, 15 July 2006

I have used it before, and works really well as long as your summary
estimates are reported with some good precision, say, >2 digits (e.g.
1.812).

The approach is very simple, and can be done with a hand calculator. You
can  implement it in Stata as well, and using simple math.

Cheers!

Tiago

*------------------------------------------------------
Thanks for replying, but I think I'm a bit confused, I've attached the
example I'm using:

Cases: 218
Controls: 14748
Total: 14966

Risk factor:      OR:    p:       case exposed(a): control exposed (b):
case unexposed(c): control unexposed(d):

Unconsciousness   3.54   0.77973   48		   3248			170			  11500
Age >65 years     1.69   0.62825   81 		   5483			137			  9265
Female gender     1.66   0.62406   82		   5544			136			  9204

With the method you describe, the p for each comes out as shown above and
consequently the numbers in each group. BUT when I then checked by
recalculating the odds ratio from the numbers given, they all equal 1.
What am I missing?  Thank you!

Carina

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis
Sent: 31 May 2011 12:25
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Recovering cell values from odds ratios

On Tue, May 31, 2011 at 1:06 PM, King, Carina <c.king09@imperial.ac.uk>
wrote:
> I am trying to convert odds ratios back to the raw numbers. I have
information on the number of cases and number of controls, as well as
the odds ratios and confidence intervals.

For that you also need the baseline odds, i.e. the odds of "success"
(the expected number of successes per failure) for the controls. The
odds for the cases are the odds ratio times the baseline odds. You can
transform those odds to probabilities using the formula p = o/(1+o),
where p is probability and o = odds. From there you can compute your
counts by multiplying the probabilities with the number of controls or
cases.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

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