**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;

intercept_derived=log((-1*per)/(per-1));

run;

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;

run;