In logistic regression and cox regression, a general recommendation is to include a maximum of one independent variable (IV) for every 10 events in order to avoid overfitting. I have seen some studies which recommend that it might be acceptable with a lower figure than 10, but that's not the point here, so for the sake of discussion, we can assume 10 events per IV as the rule.
Does this also apply to the other independent variables? Consider a situation where we have n = 1000, and a dependent variable with 40 events. This should allow us to include 4 IVs according to the rule above. But what if one of the IVs have very few events, say only 15 or so? To clarify, perhaps we have a binary IV on whether the subject has had a non-fatal overdose or not, which is not very common in our sample. Only 15 out of 1000 individuals in the sample has had an non-fatal overdose. Intuitively, it seems to me that the requirement of 40 events should apply to the IVs as well, but I may be wrong.
So what does the expertise say? Is an IV with very few events a problem that restricts the use of that IV in this way, or are we free to use the IVs regardless of number of events, as long as we stick to 10 events of the DV per IV included?