These are the sorts of studies many seriously ill patients have been craving — a guarantee that if they enter a study they will get a promising new drug. And the studies move fast; it does not take years to see a big effect if there is one at all.

In Mrs. Hurwitz’s case, the mutation in her rare cancer is in a gene, BRAF, found in about 50 percent of melanomas but rare in other cancers. She is among dozens of patients with the same mutation, but different cancers, in the new study that gives everyone the melanoma drug that attacks the mutation.

Basket studies became possible only recently, when gene sequencing became so good and its price so low that doctors could routinely look for 50, 60 or more known cancer-causing mutations in tumors. At the same time, more and more drugs were being developed to attack those mutations. So even if, as often happens, only a small percentage of patients with a particular tumor type have a particular mutation, it was possible to find a few dozen patients or more for a clinical trial by grouping everyone with that mutation together.

In a way, this is a leading edge of precision medicine that aims to target the drug to the patient. Unlike previous efforts that looked for small differences between a new treatment and an older one, with basket studies, researchers are gambling on finding huge effects.

“This is really a new breed of study,” said Dr. David Hyman, a cancer specialist at Memorial Sloan Kettering who directs the study Mrs. Hurwitz is in and two similar ones.

And they are seeing some unprecedented responses, along with some failures. The responses, though, can be so striking that control groups might be unwarranted or infeasible, Dr. Pazdur said.

“Conventional therapy might give a response rate of 10 or 20 percent,” Dr. Pazdur said. “The newer drug has a response rate of 50 or 60 percent. Does it make sense to do a randomized trial?” And even if a trial were planned, he said: “Who would go on that trial? Would you go on that trial?”