Are fertility drugs safe? The industry says yes; critics worry they’re overprescribed.

Logan Andreotta had been told she was an ideal candidate for in vitro fertilization. Though unable to get pregnant, the Bowling Green, Ky., woman was just 24 and in terrific health. But three days after she began taking fertility drugs, her ovaries went haywire and swelled with 50 eggs — four years’ worth in a single go.

“I felt like my insides were going to bust out of my stomach,” Andreotta recalled.

This was ovarian hyperstimulation syndrome — OHSS for short — a potentially fatal complication the U.S. fertility industry describes as extremely rare. But the incidence of OHSS and the broader long-term safety of hormone-boosting fertility drugs remain open to debate, even as the clinics have blossomed into a multibillion-dollar industry serving hundreds of thousands of women a year.

Industry critics worry that unregulated providers are overprescribing the drugs, glossing over potential hazards and failing to properly report problems when they arise. One recently published study, for example, blamed “increasingly aggressive treatment protocols” for incidents of OHSS, while another argued that most cases are completely “avoidable.”

Some researchers have theorized...