After Mikhail Rubin learned his lethal blood disease had progressed, he decided that he wanted a stem-cell transplant through a clinical trial. But there was an obstacle: his age. Mr. Rubin, who is now 72, was too old to participate. Many cancer trials cap enrollment at age 65. People over 70 represent a growing share of the cancer-patient population but are vastly underrepresented in clinical trials, the study said.

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