# Rare event logistic regression

I have a situation in which that there are 4 cases with a condition per 1000 people surveyed (binary). I am interested in performing a logistic regression to determine the risk factors (binary). Is it possible to perform such an analysis with SPSS?

If the total sample size is such that you have at least 15 times as many cases (not people) as there are candidate variables you should be OK. Note that SPSS does not make it easy to relax the linearity assumption of predictors.

• My total sample size is 8 cases from 2000 people surveyed. I'm unsure of how to proceed beyond the basic logistic regression. – swirly_imm Sep 25 '13 at 15:50
• With only 8 cases you cannot even estimate the intercept in a model with no predictors. The only thing you could possibly estimate would be the proportion of $Y=1$ along with a 0.95 Wilson confidence interval. – Frank Harrell Sep 25 '13 at 21:19
• Since this is the case, can I at least use Chi-square and relative risk for the analysis of this sample? – swirly_imm Sep 26 '13 at 2:19
• Not at all. You do not have the sample size needed to analyze a single variable and will have a tough time estimating the overall probability of the event (your confidence interval will be tight for absolute probability but not tight on a relative, e.g., log odds, basis). – Frank Harrell Sep 26 '13 at 2:50
• Incorrect. You can only report a single proportion. Of course you can report anything but you do not have sufficient statistical information to make any comparisons. – Frank Harrell Sep 26 '13 at 11:12