Unless I am mistaken, [a/(a+b)]/[b/(a+b)]=a/b.
Then, assuming a+b=1 and a=p(x)=p, [p/(1-p)], which is the left hand side term of the defining equation of the logit model, is a probability ratio as well as an odds ratio.
Risk, as incidence, is defined as the number of occurrences of a certain event (deaths, plane crashes, etc.) per time spent at risk (a.k.a exposure) by a given number of units of observation (people, airlines, etc.).
Coefficients of a logit model, multinomial or not, are basically (conditional) odds ratios or equivalently (conditional) probability ratios. They can be interpreted as (conditional) risks ratios (or relative risks ratios, or relative incidence rates) if logit models are used to estimate models in which time to event or exposure is somehow taken into account. Using logit models to estimate discrete time survival models is an example. I assume that the same is true for the case-control studies referred to by Roger Newson.
Beno�t Laplante
________________________________
De: [email protected] de la part de Michael Ingre
Date: jeu. 2005-04-21 8:22
�: [email protected]
Objet : Re: st: Use of the term 'relative risk ratio'
> At 11:25 21/04/2005, Ronan Conroy wrote:
>> I have a reviewer who is grumbling about the use of 'relative risk
>> ratio' to describe the effect estimates from multinomial logistic
>> regression. And it's the second time this has happened. The reviewer
>> feels that they ought to be called odds ratios, to prevent confusion
>> with relative risks (and that is a good point).
Thanks for bringing this confusing issue up for discussion.
> On 2005-04-21, at 12:56, Roger Newson wrote:
>> The "RRR" of -mlogit- is definitely not a relative risk ratio
I have always assumed that the RRRs from -mlogit- were risk ratios and
not odds ratios - because they say so and because the manual describe
the exponentiated coefficients from -mlogit- as the ratio of two
probabilities/risks (p. 507). The coefficients from the -logit- is (of
course) described as the log of the odds ratio (p. 329).
However, it is easy to see that both produce the same (log) odds
ratios, at least when the outcome is binary.
What is going on here? Why name odds ratios risk ratios?
> At 11:25 21/04/2005, Ronan Conroy wrote:
>> Has anyone else experienced the problem? Is there a more useful way
>> of describing RRRs out there?
How about Relative Odds Ratio (ROR)?
Michael
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