# Viability of multivariable Cox regression results when one combination of variables has no events

I'm trying to figure out, if the results of a multivariable Cox regression analysis are viable when there are no outcome-events in one of the combination of categories of variables. Online, I could not find a concise answer so far.

Included are:

• Variable X with two categories X1 and X2;
• Variable Y with 4 categories Y1, Y2, Y3, Y4
• several other variables (all categorical).

For univariable Analysis there's events for every variable and category. But looking at the combination of categories, there are no events for Y1 in the X2 category and for Y2 in the X1 category. All other combination of variables have at least one event.

When there happen to be no events in a univariable regression (i.e. filtering for X and doing univariable regression of Y), I expect an error saying the coefficients are not converging and degenerate estimates, but I'm getting no error in this multivariable regression. How does this (not) affect the multivariable regression? I feel like I'm missing something about how the influences of the variables are actually measured in multivariable analysis for this to no give an error, so please enlighten me.

Are the results of the whole regression model still viable, given the lack of events in one/two combinations of categories?

• With no events the hazard is 0 and that may not cause any problems. The cases that cause problems are the ones where relative risks are infinite.
– DWin
Commented Nov 25, 2020 at 0:59

You could have the convergence problem you expected if you were examining an interaction between your categorical predictors X and Y.

If you don't specify an interaction, however, you are implicitly assuming that the association of X with outcome doesn't depend on the value of Y, and vice-versa. So, without an interaction term, the coefficient estimates for either of X and Y don't depend on having events corresponding to all combinations of their values.