Cancer is basically a problem of the immune system. We have a lot of cancer cells in our bodies and our bodies manage to kill them quite efficiently. Something went wrong in your body and a cell or two survived.
I'm in no way a doctor (I have experience with cancer, but as a, hm, 'user', or better, observer) but IMHO the thrill of working in the startup and doing stuff that you really like can substantially help your immune system to fight the hostile lifeform in your body. "Positive" hormones stimulate the immune system.
On the other side, having not enough sleep, eating shit, having a lot of excess weight (having a little is considered good) would actually harm your immune system.
That said, if I were you, I'd take the startup job, but would take extra care of myself, not working 6x16+1x10 hours, eating right (not necessarily fancy or organic, just basically good food), exercising enough and having enough fresh air and rest.
One doctor once said to me that I can cure any illness by just sleeping 10+ hours a day. He was joking, but every good joke is just partially a joke.
Yeah, and buy COBRA. Just in case. Most likely you will just waste a couple grand on it, but this is your life on the line. Small companies use complete idiots as insurance brokers (large ones do too, but they learned how to hide this) these idiots may screw up you forms/submissions/cards/accounts/whatever even multiple times in a row. You'd better be covered while you sort this out.
Yeah, and buy COBRA. Just in case. Most likely you will just waste a couple grand on it, but this is your life on the line. Small companies use complete idiots as insurance brokers (large ones do too, but they learned how to hide this) these idiots may screw up you forms/submissions/cards/accounts/whatever even multiple times in a row. You'd better be covered while you sort this out.