Logistic Regression


Omega Contributor
I am looking at a medical outcome (binary) and known risk factors. There are 10 established risk factors that I will test in my sample of 300 patients.

However, all of the patients have one of the predictors (X1), so I know interpreting the intercept of the empty model provides the probability of this predictor (X1), 27% have outcome of interest.

Now when I examine the other 9 known predictors, 2 are significant in my sample (X2, X3). So I know patients can have between 1-3 significant predictors. Is there any other way I can present the intercept besides the probability of the outcome or do I always just report my odds ratios for the other two significant predictors as the odds of Y are 10 times greater for X1 patients when they have X2 and you control for X3? And vice versa.

Also, it seems like I would never know if there was an interaction between X1 and any of the other variable because I do not have data for the reference group for X1. I feel I can move forward, but wanted to see if anybody has any insights or suggestions!


Ambassador to the humans
Are you saying X1 is constant? There is no variation in the values in X1? It doesn't make sense to include it in the model.


Omega Contributor
Correct, I don't include it in the model. I called it X1 to give it a name, I thought the 1-3 risk factors line could be misleading as well.


Omega Contributor
For disclosure, there is another variable we will call X4, which no patients have.

So: percentage of patients with it...

X1 (not in model): 100%
X2: 4%
X3: 34%
X4: 0%

And some obvious combinations, so patient has X1-3, etc.


Omega Contributor
I have not written this, but all risk factors are binary, so I am just looking at:

In X1=1 and X4 = 0 patients, when controlling for X3, patients with X2=1 have 10 times greater odds of Y=1 than patients with X2=0.

This initially looks confusing, but is my scenario, with X1 and X4 not in the model
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