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.
I tested if I get the value for the intercept using the logistic regression. I did.
proc logistic data=temp descending;