The Reagan administration has approved a controversial regulation granting public access to statistics showing how well hospitals treat various illnesses.

Using this information, people could compare hospitals and decide which provide the best care, according to advocates of the regulation.

"We're happy it's final; it's long overdue," said Willis Goldbeck, director of the Washington Business Group on Health.

The regulation, to be published this week in the Federal Register, covers information on Medicare patients, and other classes of patients, gathered by the new Professional Review Organizations (PROs) set up by Congress to monitor how well hospitals treating Medicare patients perform.

The law directs PROs to determine whether hospitals permit unnecessary admissions, have high death rates, follow approved professional practices or keep patients too long, for example.

Under the regulation, the PROs, which consist of doctors and other health professionals, would be required to make available information they gather to anyone who wants to see it.

In the past, such "hospital-identified" data has been restricted.

The information available to the public for any hospital would include statistics gathered by the PROs on admission rates, lengths of stay, medical procedures used, the prevalence of hospital-acquired infections and death rates for different departments and illnesses. No information identifying a doctor or patient by name would be released to the public, however.

The Department of Health and Human Services, in drafting the final rule, said it rejected proposals -- advocated by Dr. Sidney M. Wolfe of Public Citizen Health Research Group and others -- that information about the performance of doctors identified by name be made public.

The American Medical Association had strongly opposed the idea of identifying doctors.

Although the final regulation forbids that, an AMA source said the medical group is concerned that the issue may resurface.

The final regulation also authorizes the PROs to "disclose their interpretations and generalizations about the quality of health care in particular institutions to the public."

As the regulation was being developed, the hospital industry argued that releasing information about death rates and similar statistics could mislead the public, because some hospitals in a community habitually treat older or sicker people than others.

The final regulation requires the review organization to include data the hospital may wish to add to put its performance statistics in perspective.