I have a data set that looks like this:

GENDER    SMOKER    SURVIVED    DIED
male      yes       341         23
male      no        231         11
female    yes       378         19
female    no        476         15

The question I would like to answer is: "Holding gender constant, is there strong evidence to believe there are more deaths among smokers rather than non-smokers?" What test/method is the most appropriate for this and how do you interpret its results? I was thinking I could run 2 chi-square tests, one for each gender, to check if the proportions of survived vs. died for the 2 groups smokers vs. non-smokers are statistically different from one another. Is there a better way of doing this?