Women with this form of ovarian cancer were sharing news and tips online in a closed Yahoo group. Dr. Levine asked to become part of the group and began joining the discussions. There he discovered patients who had persuaded doctors to give them an immunotherapy drug, even though there was no reason to think it would work.

The women reported that their tumors shrank immediately.

The idea behind immunotherapy is to dismantle a molecular shield that some tumors use to avoid an attack by the body’s white blood cells.

The immune system sees these tumors as foreign — they are fueled by hundreds of genetic mutations, which drive their growth and are recognized by the body. But when white blood cells swarm in to attack the cancer cells, they bounce back, rebuffed.

Immunotherapy drugs pierce that protective shield, allowing the immune system to recognize and demolish tumor cells. But the new drugs do not work against many common cancers.

Those cancers are supported by fewer genetic mutations, and experts believe that the tumor cells just do not look threatening enough to the body to spur a response. So the immune system leaves them alone.

Lung cancer, a genetic type of colorectal cancer and melanoma have huge numbers of mutations, and immunotherapy drugs often are successful in treating them. Cancers of the prostate, pancreas, breast, ovaries — and most other tumors — carry few mutations.

“These are the cancers that rarely respond,” Dr. Pardoll said.

The idea that the drugs might work against something like hypercalcemic ovarian cancer, which is fueled by just one genetic mutation, just made no sense.