# Sample size for unequal groups in logistic regression

I am conducting a study, in which I will be using Logistic Regression for analysis. I will be collecting data in an education setting (about cancer prevention), then I will follow subjects to collect data on who took action after their education (cancer prevention screening) among those who were educated. The two groups (DV) will be "screened" and "not screened." Among the surveys that are administered, I am sure the number of subjects in a group that were screened will be much higher than those who did not. Without unequal groups considerations, my sample size, using Green's formula, i.e. $N\geq 104+m$, is 114.

Do the number of subjects in each group have to be equal? How much of a difference is considered not equal? In the case when groups will be unequal, how should it be dealt with for sample size calculation or analysis?

• welcome to the website. Green's formula that you referred to must be some ad-hoc rule of thumb. I have not heard of it. Can you edit your post to give a reference? – StasK Feb 7 '12 at 0:28

It does not matter much that your groups are balanced. What is important is the smallest of (the number of zeroes, the number of ones), let's call this number $\nu$, is substantially greater than the number of explanatory variables. If $\nu=$ the number of explanatory variables, then the model is likely to be exactly identified, and the coefficient estimates will diverge to infinity. You would want to stay away from this situation.