1. ## Logistic Regression

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!

2. ## Re: Logistic Regression

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.

3. ## Re: Logistic Regression

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.

4. ## Re: Logistic Regression

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.

5. ## Re: Logistic Regression

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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