[TheMrZZ]

To add some proofs to my answer, I actually coded a Z3 program to prove it! The 3-variables version takes too long to resolve, but I got results for the 2-variables version (tumor size + gender):

Results can be found in this GSheet: https://docs.google.com/spreadsheets/d/1tsBhElTgXjVTeas8quar...

Code is here: https://gist.github.com/TheMrZZ/c33927ca2cc917997a67d7f84b82...

I'm currently running the 3-variables version, hopefully I'll get results this afternoon.

We can clearly see the same problems that arise in the 1-variable Simpson's paradox (widely different population sizes).