Re: odds ratio to chi square conversionfor meta-anlaysis

Posted by Kornbrot, Diana on Jul 01, 2012; 11:04am
URL: http://spssx-discussion.165.s1.nabble.com/odds-ratio-to-chi-square-conversion-tp5713894p5713929.html

Lets get real
Meta-analysis for 2by2 tables requires ALL 4 cells, for all studies. Do not shoot the messenger
Why?
Because a mean measure of effect size across all studies requires a mean effect size, WEIGHTED by some estimate of standard error of effect size measure.
Total N is simply not sufficient to estimate standard errors of effect sizes.
My  previous example showing different Pearson chi-square for same effect size and total N is an illustration.
For Ln (OR) se^2 = 1/a+1/b+1/c+1/d.
No amount of jiggery-pokery can get round this.

Of course this problem applies just as much to Cohen’s d comparing means for independent groups. Total N does not allow one to give greater weight  to equal n/group studies than to studies with 10* as many observations in 1 group than another. Of course such inappropriate weighting, based on the dubious assumption of all groups having same variance, is extremely prevalent – but that does not mean its a good idea. Unequal n studies are prevalent in health where a disease is rare and so disease group is consderably smaller than control group

Best
Diana

On 30/06/2012 21:38, "R B" <ryan.andrew.black@...> wrote:

Rich,
 
I haven't read the article, but my guess is that they suggested dividing by 1.81 since that value approximates the standard deviation of the standard logistic distribution, which is pi/3.
 
Ryan
 
On Sat, Jun 30, 2012 at 3:46 PM, Rich Ulrich <rich-ulrich@...> wrote:

That's an interesting note.  I'm not sure why it makes
good sense, to divide the ln(OR) by 1.81.  But the
writer does make good sense in suggesting that a
good measure of effect size is log(OR), and what you
need for further information is not the N, but the
standard error. (I think he is suggesting that.)

The original question was about converting an OR
to a chi-squared test, in the context of meta-analysis.
I doubt why anyone should want to do that, except
as an intermediate step to finding the error term --
the chi-squared statistic itself is a *test* statistic, and
is poorly suited for "effect size".  Where it is appropriate,
the OR is a fine measure of effect, and log(OR) is the
version that serves as an interval-scaled measure.

---

Emeritus Professor Diana Kornbrot
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