This is an empirical question. To develop a binary logistic regression model, what is the requirement of minimal number of responders (if the dependent variable is responders /nonresponders)?
First off, the dependent variable ought to be better represented as responders/(responders + nonresponders), otherwise you could get a ratio larger than one, which would not fit into logistic regression.
Once you get that going, I think I have seen a rule of thumb of 10 responders per independent variable estimated in the model. Should be a good starting place.
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