I'm having a difficult time choosing the correct statistical analysis to use.

My research question is below:

Does exposure to female hormone replacement therapies (i.e., estrogen replacement therapy, estrogen and progesterone replacement therapy) increase incidence of breast cancer?

I'm using the CDC's 2017-2018 NHANES data (link below):

https://wwwn.cdc.gov/nchs/nhanes/continuousnhanes/default.aspx?BeginYear=2017

As the research question poses, I'm trying to determine if there's correlation with EACH hormone replacement therapy on breast cancer incidence (i.e. testing each therapy separately). However, I would also like to incorporate age into the statistical analysis as well, since 1) age (in and of itself) is a determinant of cancer incidence and 2) older populations are more likely to be on one of the two hormone replacement therapies. However, I can't find a statistical analysis tool (e.g. Two-Way ANOVA, Chi-Square, etc.) which allows me to test the effects of two different independent variables (i.e. age being quantitative continuous and the given therapy being categorical nominal) on a categorical binary dependent variable (i.e. breast cancer diagnosis). Do you have a recommendation for which test I should use and why?

Please help and explain like I'm five! :)