PRINCETON, N.J.—Sixteen-year-old Megan Crowley lay facedown on an operating table last June as her surgeon tried to straighten her spine, badly contorted by a genetic disease that nearly killed her as a little girl.

The doctor had warned Megan that she stood a 5% chance of dying from the risky surgery, but she eagerly chose it anyway. Her 15-year-old brother Patrick, stricken with the same rare disease, refused the procedure and awaited news of her at home.

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