RE: st: Odds ratio

["Mak, Timothy" <timothy.mak07@imperial.ac.uk>]

Hi Rosie and others, 

Perhaps it's too obvious to point out, but of course the odds ratio is a very good approximation for the risk ratio when the probability of the outcome is small. So if that's the case, I believe that's all you need to point out to the reviewers. But if that's not the case, I think it would be useful to give _raw_ probabilities rather than _predicted_ ones. That's common practice in most medical papers, I think. You can then include your odds ratios + CI on the side. I believe most people are more interested in whether your CI crosses 1 or not. It's also quite standard to report the _raw_ odds ratio followed by the adjusted odds ratio in a more involved analyses, or HLM in your case. e.g.: 

		Male	Female	OR			Adjusted OR*
Outcome1	4/45	5/24		xxx(yyy, zzz)	XXX(YYY, ZZZ)
Outcome2	etc	etc		etc			etc

* Adjusted for aaa, bbb, ccc, ddd

Tim

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: 09 April 2010 08:15
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Odds ratio

--- On Fri, 9/4/10, Rosie Chen wrote:
> I am doing HLM analysis, so it is impossible to use the Stata
> syntaxt to calculate the predicted probability. So I will
> just do the calculation by myself in excel. Here is what I
> plan to do: I will calculate  log-odds and then convert
> them into predicted probabilities for individuals with
> characteristics that I am interested in so as to demonstrate
> the magnitude of the effect for a specific variable. 

Sorry for being blunt but that is a very bad idea. There are
very good reasons why Stata isn't giving you those probabilities
directly: These multilevel models take into account group level
variation, while your approach doesn't.

> For example, in order to explain the gender difference in the
> probability of an outcome, I will compute the difference in
> the predicted probability between females and males

I am not so negative about odds ratios as others are: Odds ratios
and risk differences answer subtly different questions. An effect
is a comparison of groups, in your case men and women. That 
comparison can be made in absolute terms (i.e. compute a difference)
or in relative terms (i.e. compute a ratio). Both have their 
advantages and disadvantages. A discussion of that is given in
this paper (if I am allowed some shameless self-promotion):
<http://www.maartenbuis.nl/wp/interactions.html>. 

The key issue with odds ratios is that I would like to have the 
baseline odds present, to help me interpret the odds ratio (which 
in a sense helps to bridge the gap between absolute and relative 
effects). The problem is that by default Stata suppresses those. 
The trick is to add a variable baseline, which is always one, and 
add the -noconstant- option. This trick is discussed in the paper 
I refered to before, and I learned it from: Roger Newson (2003), 
Stata tip 1: The eform() option of regress. The Stata Journal, 
3(4): 445. <http://www.stata-journal.com/article.html?article=st0054>

I am slowely getting used to odds, so the distinction between odds
and probabilities doesn't bother me any more: You can quantify the
likelihood of an event by computing the expected number of success
per 100 trials (100*probability) or by the expected number of 
success per failure (the odds). Just don't mix the two up, as 
sometimes happens when people try to interpret odds ratios as risk
ratios.

Hope this helps,
Maarten

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

http://www.maartenbuis.nl
--------------------------


      

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