# Interaction effects in a Cox model

In regression models, usually a (descriptive) indicator of an interaction effect can be plotted via a plot with x-axis with the potential interaction variable (e.g., gender) and the outcome variable on the y-axis – if the outcome is continuous. Else, a 2×2 table should give a hint to interaction effects.

In Cox models, however, I'm a bit confused about whether I should check the time until event variable or the number of event variable itself to descriptively see whether an interaction effect occurs. I know the underlying formula specifies both, time until and number of events:

$$S(t|x)=\exp(−H(t|x))$$ with $$H(t|x).$$

But what is the "more important variable"? Consider e.g. a case where 100/100 male participants have an event, while only 75/100 female participants have an event. However, all of the male participants have the event later than the female participants. Would there be a significant difference and in which direction (assuming power is high enough)? When looking at the formula, it seems that it's time, but it's somehow confusing to understand.

So my questions would be:

1. if I want to descriptively look at an interaction effect, should I plot the moderator (e.g., gender) and time until event, a 2×2 table with moderator and number of events, or both?
2. What would be the result of a Cox regression with the example I gave above?