The birth of Kenneth, Alexis, Natalie, Kelsey, Brandon, Nathanial, and Joel McCaughey in Iowa in November 1997—the world’s first surviving set of septuplets—was called a miracle by their parents (Kenny and Bobbi McCaughey), their doctors, and much of the world. The McCaughey septuplets are part of a national trend: The number of multiple births involving three or more babies has tripled since 1980 and quadrupled since 1971.

Like many babies of multiple births, the McCaughey septuplets were conceived when their mother, Bobbi McCaughey, 29, took the powerful fertility drug Pergonal. While fertility treatments such as McCaughey’s offer hope for millions of men and women who want to become parents, the drugs also raise ethical and health care concerns. Health care professionals are concerned that fertility specialists may not advise infertile couples of the risks they and their future babies...