SAN FRANCISCO — Troubling cases in which doctors were accused of botching operations while undergoing treatment for drugs or alcohol have led to criticism of rehab programs that allow thousands of American physicians to keep their addictions hidden from their patients.

Nearly all states have confidential rehab programs that let doctors continue practicing as long as they stick with the treatment regimen. Nationwide, as many as 8,000 doctors may be in such programs, by one estimate.

These arrangements largely escaped public scrutiny until last summer, when California’s medical board outraged physicians across the country by abolishing its 27-year-old program. A review concluded that the system failed to protect patients or help addicted doctors get better. Opponents say the medical establishment uses confidential treatment to protect dangerous physicians.

“Patients have no way to protect themselves from these doctors,” said Julie Fellmeth, who heads the University of San Diego’s Center for Public Interest Law and led the opposition to California’s so-called diversion program.

Most addiction specialists favor allowing doctors to continue practicing while in confidential treatment, as does the American Medical Association.

Supporters of such programs say that cases in which patients are harmed by doctors in treatment are extremely rare and would pale next to the havoc that could result if physicians had no such option. “If you don’t have confidential participation, you don’t get people into the program,” Sandra Bressler, the California Medical Association’s senior director for medical board affairs, said.

California’s program ends June 30. If no alternative program is adopted, the rules could revert back to the zero-tolerance policy in place before 1980, when doctors who were found by the medical board to have drug or alcohol problems were immediately stripped of their licenses.