Let me start out by answering the question: I don’t know if cancer is a family thing. The only genetic evidence that I know of is the breast cancer tendency that some families have. Beyond that I know of no discovered gene that predicts cancer, but I am not a medical person. That said families do seem to have cancer or not have cancer. Just like some have tendencies to alcoholism and some do not. But I talk to people who have cancer who have no one in their family with the disease.
In my family, my grandmother died of bone cancer. My uncle and brother died of liver cancer, and my parents both died of leukemia. I have survived multiple myeloma and have been cancer free for over two years. That’s definitely a family full of cancer.
Should you be worried if you are in one of those families? I don’t know the answer, but I would be very sensitive to what’s going on in your body. Get things checked if you detect anything out of the ordinary. The early detection thing that the medical community talks about is very real.
Some women who have the breast cancer tendency in their family react by having mastectomies before cancer comes to lessen the chances of contracting the disease. Each of us has to do what we feel is best in our situations. But the bottom line here is if something comes up, get it checked out.
That is not to say you should be paranoid either. If you are worrying about cancer and this is upsetting your peace with God, you have lost perspective about life. Get your concerns checked out. Talk to doctors and friends who have had similar conditions.
Scripture tells us to be anxious about nothing. If you are worrying, then examine your relationship with God. Call on Him and confess your anxiety, but follow up with a visit to someone who can honestly answer your questions. Your worries may be about nothing, and then again you may be getting prompted by the Holy Spirit to have something checked out.
Cancer Faith and You 
This is a question that probably most of us think about, since most of us have someone in the family line that had cancer. For instance, my father and one of my older brothers died of cancer. But I wonder if that’s just focusing on the fear. After all, in my family line is also my grandfather who lived to 89 and died peacefully in his sleep; my aunt is now 91 and still going strong. I like your biblical admonition: be anxious for nothing. Phil 4:8-13 also tells us to think on the good things in life!
Pat,
Thanks for the comment and your observation. Many times we look at our family histories and get filled with fear when what the Lord wants of us is to be anxious about nothing. I don’t know why we don’t choose that simple truth each time we face fears like cancer.
Marv