PROC GENMOD link option values for binomial distribution

[TomHsiung]

Hi, everyone

Recently I have been learning logistic regression. I know that PROC GENMOD could be used to do a logistic regression with the option link = logit. However, with the link = logit I can only get the odds ratio. I am more interested in the relative risk and what I found via Google is the same PROC GENMOD but with an option of link = log.

So, my question is: Does the PROC GENMOD still do a logistic regression with the option of link = log? If yes, what is the math behind it? If not, then what is the mathematical mode it uses? Thanks

[StatDave · Accepted solution]

Yes, using the log link you model the log of the event probability and then exponentiation of parameters can be used to estimate relative risks. But using the log link can result in estimation problems because the log link does not keep predicted values restricted to the valid probability range. However, you can also estimate relative risks using a logistic model followed by use of the NLMeans macro. These and other approaches are covered in this note. 

[TomHsiung]

And after some google later, I found the link = log is a model called "log-binomial regression" (https://stats.stackexchange.com/questions/581678/what-is-the-difference-between-a-logistic-regressio... )

The thread says,

Logistic regression always produces estimates of 𝑝𝑖 that are between 0 and 1. This is not true for log-binomial regression;

I guess this is the reason why few people use the log-binomial regression to model their data because the risk of deriving a risk higher than 100%. Thanks.