Observations for logistic regression

I am a analysing data for a study that looks at risk factors for postpartum depression in a special population. I am using SAS studio for the analysis.
I am running logestic regression for each variable (risk factor) and all risk factors are binary variables.
Some of the risk factor variables have very few postives (for example I am looking at postpartum UTI as a possible risk factor and only 18 people out of 68 with the depression has it).
My questions is, is there a rule for the minimum number of positive observations for a variable to be considered for inclusion in the final regression model?
I have a small sample size (total: 300, depression: 68).

Thank you


Fortran must die
There are various rules of thumb and various authors disagree about them. Commonly they focus on the least common level of the dependent variable. However, some say if you have a dummy predictor with (I think) 90 percent or more of the values at one level it will attenuate the slope.

If I can find any of the rules of thumb in my notes I will list them. They are buried in my notes.


Less is more. Stay pure. Stay poor.
I believe, Frank Harrel Jr. list 10-20 observations in the less outcome group for each predictor in "Regression Modeling Strategies". But many things come into play. Common sense works most of the time. Ideally you have lots of data and split it. in the training set you build the model and then you use that model in the test set. Though you familiarity with the study context should dictate if you need to control for something or not.