## Logistic regression with random effects

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# Logistic regression with random effects

[ Edited ]

Hello all,

I have a complicated dataset which I try to model. I will try to explain it simplyfied...

Every patient is going through a procedure with some continuous parameter set to 50. If a sucees is obtained, the problem is re-created, and another attempt is done with a setting of 40. If another success is obtained, the problem is re-created and a third attempt is done using a setting of 30. In this case this patient will have 3 observations, with 3 different settings, and all will be sucess. If another patient has success with 50 and 40, but failure with 30, it will have 3 observations with 2 successes and 1 failure. Another example, a patient fail with 50, and then we try 60. It will only has 2 observations. In general, there are 5 possible settings for every patient, yielding either 2 or 3 observations (let's ignore the story behind, it's not in my hands anyway).

The data looks like this:

ID, Setting, Sucess

An example of some vectors are: (1, 50,1), (1,40,1),(1,30,0) - this is a patient with success at 50 and 40, but failure at 30.

My main goal is to estimate the probability of success as a function of the setting variable. I wanted to use a logistic regression with random effect (someone suggested bayesian logistic, any idea why ?)

I tried:

proc genmod data = Example descending;
class ID;
model Success = setting / d=bin link = logit;
repeated subject=ID / type=cs;
run;

I am not sure if the results are correct or not, and I think GLIMMIX must be more appropriate (I have around 20 patients with almost 50 observations). How can I obtain a probability of success for a given setting ? Is it possible to get the setting for which I will get 80% success ? Can I ask SAS to draw a sigmoid plot form which I can read probabilities ?