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Risk = Odds/(1+Odds)
Odds = Risk/(1-Risk)

Odds > Risk (always)
Odds is close to risk if odds and risk are small, and n is much greater than x (n>>x). 
(O~=R for small R).

Risk has a maximum of 1 (100%); Odds has no maximum.
Both Risk and Odds have a minimum of 0; log-risk and log-odds have no minimum.

Further, for a simple 2_by_2 frequency table:
The (unadjusted) Risk Ratio is the ratio of the risks under two different conditions.
The (unadjusted) Odds Ratio is the ratio of the odds under two different conditions.

For rare events RR ~= OR.
Always, OR>RR>1 or OR<RR<1 or OR=RR=1.

Complex regression models for OR (logistic regression; logit link function) 
are more stable than those for RR (log-probability regression; log link function) 
or risk difference (probability regression; identity link function);
due to predicted probabilities above 1 or below 0.  Also, in Case-Control studies, 
where the prevalence is not known, only OR can be reliably estimated; not RR or RD.

This is why OR are so often seen, even though they are difficult to explain.

For meta-analysis and other purposes, there are formulae to convert 
OR to RR, using information about the true prevalence of disease and 
exposure.  I m not sure how useful they are.  The 
assumption in a multiple logistic regression model that there is 
a single fixed OR implies that the RR is not fixed.  
Others may be able to say more.

Finally, I am sure that Nick Cox would want me to remind 
Tim of the statalist FAQ regarding our names.

2.1
"...
3. You are asked to post on Statalist using your full real name. This is a 
long-standing practice on Statalist. Giving full names is one of the ways 
in which we show respect for others. Your chances of eliciting a good reply 
are greatly diminished if you write and conceal your identity. Conversely, 
if you decide just to watch and read on the list, your email identity remains 
entirely up to you."


Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre, King's Health Partners 
(+44) (0) 20 7188 3642.

------------------------------

Date: Thu, 13 Jun 2013 16:06:53 +0800
From: tshmak <tshmak@hku.hk>
Subject: st: RE: prob by using binreg or logit

Dear Carsten, 

There certainly are differences. rr stands for risk ratio. or stands for odds ratio. I assume you know the difference between "odds" and "risk". -binreg- with the rr option assumes that the log of the risk (or probability) is a linear function of the covariates. -logit-, or binreg with the -or- option, assumes that the log of the odds is a linear function of the covariates. That should be enough to lead to differences. 

HTH, 
Tim



- -----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of carsten hinrichsen
Sent: 12 June 2013 23:14
To: statalist@hsphsun2.harvard.edu
Subject: st: prob by using binreg or logit

Dear statalisters,

I am working with survey data and want to find the probability of participation by analyzing the binary variable of participation (yes/no).

As far as I know, I could use binreg with the rr option
or
I could use logit and use the odds to calculate the probability.

I've tried both and get slightly different results. I've been looking through the stata help but can't figure out what the difference is between these to methods. 
So I'm wondering are there different assumptions behind these to methods that I should take into consideration?
And should I prefer one of the methods to the other?

Any help is appreciated.


Kind regards 
Carsten Hinrichsen 		 	   		  


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