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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?
kjetil b halvorsen
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user49519
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    This has come up a few times lately. Gary King has done some work on this exact subject. Maybe it'll help? http://gking.harvard.edu/category/research-interests/methods/rare-events – shadowtalker Jul 04 '14 at 16:22
  • Thanks for answering. I still don't know if I can do a log. regression with 3 predictors for 27 events and which method is the best (see second part of the question). – user49519 Jul 04 '14 at 18:59
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    Might be some help in here: http://stats.stackexchange.com/questions/26016/sample-size-for-logistic-regression. If that still doesn't work, you could use a Bayesian model, which is typically more stable in small samples, or a regularized regression to improve the effective degrees of freedom (which is a special case of Bayesian regression anyway) – shadowtalker Jul 04 '14 at 19:14

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