I want to investigate how people (lets say smokers and non-smokers) differ in various characteristics. So I want to perform a binary logistic regression with SPSS. However, my event rate is very low (number of events = 27 and number of non-event = 200). I want to include several predictors: 3 factors, which I gained from a PCA, 4 socio-demographic variables and 3 other variables (including categorial variables). I've read that if the sample size is too small, I can't perform a binary logistic regression.
- In my case, is it better to perform an exact logistic regression or a Firth's logistic regression due to the small sample size?
- If I would only consider the 3 components (without including the other 6 variables) in my binary logistic regression model , can I perform a binary logistic regression then? So Is the sample size here adequate? In that case, should I use the "enter" method or a stepwise method like "backward LR"? (In the theory model (backward LR), 2 out of 3 factors (p=0.030 (factor 1) and p=0.088 (factor 2) and p=0.000 (constant)) were included. In the overall model (enter), one factor was significant (p=0.33 (factor 1) and p= 0.94 (factor 2) and p=0.115 (factor 3) and p=0.000 (constant) . Which method should I prefer?