The idea of chemotherapy terrified Pushpa Damle. She was scared of the side effects. She was scared of feeling weak. She was scared she couldn’t do it.

Pushpa had already undergone a successful lung cancer surgery, but doctors at MD Anderson in Sugar Land told her that chemotherapy could ensure that her non-small cell lung cancer didn’t return.

“I asked myself, ‘Do you want to give life a shot?’” she says.

In the...