How to derive the logit intercept value from %

I use this a lot to convert a logit coefficient (from a logistic regression model) to a probability.

p=exp(X) / (1+ exp(X))

This time I wanted to convert a probability (from the control group) into a logit.

I put X on the left side.

X= log( -p / (p-1)

This means that if I know the probability of a successful outcome occurance of the comparison group, I can get the logit intercept for the logistic regression model where only the treatment status was a predictor.  (I can use this to create a graph).


I tested this using a dataset.  Based on a data, I know the probability of a failure was 0.6214286.

data x;
per= 0.6214286;

I tested if I get the value for the intercept using the logistic regression.  I did.

proc logistic data=temp descending;
model Y1_to_Y2_persistence=treat_original;

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