A battle has begun in the medical world, a battle over the numbers that tell how many patients die in hospitals.

It is a battle that patients who are interested in good care may be hearing about for years in this new era in which information about care has begun seeing the light.

It is a battle that may help tell patients when to ask, "Is this hospital safe for me?"

"Judging hospital quality, numbers aren't nearly enough." So argued the headline of a Dec. 20 American Hospital Association newspaper advertisement.

The provocative ad appeared a few days after the government released its first report on deaths of Medicare patients in 5,971 hospitals, one showing sharp variations in death rates -- in plain language, the chance of dying -- from hospital to hospital.

In the ad, Carol McCarthy, the hospital association's president, maintained that the government information "is of no help to health care consumers," since mortality rates higher than predicted {on the basis of national averages and other adjustments} "do not necessarily mean poor care. Rates can be higher or lower because the patients . . . differ from the patients treated in the 'average' hospital, because types of services provided differ . . . or simply because of chance."

No one can argue with this. The federal officials who issued and defended the report said much the same thing. So did officials of other medical and hospital groups who attacked it. So did consumerists who cheered it.

So did five Rand Corp. researchers who addressed the same subject in the New England Journal of Medicine four days after the hospital association ad appeared. The four said, yes, only a detailed look at the care of individual patients can tell whether a high-death-rate hospital truly had sicker-than-average patients or whether its doctors or others provided poor care.

The Rand doctors and statisticians therefore looked at the medical records of patients with heart attacks, strokes or pneumonia at six unnamed hospitals with death rates well above and six with rates well below expected figures.

In general, the hospitals with more deaths than expected indeed had sicker patients. This difference accounted for most -- but not all -- of the difference in death rates.

However, these hospitals also had more deaths that might not have occurred with better care, said Dr. Robert Dubois, study director.

Analysis showed that of 100 pneumonia patients who died at a high-death-rate hospital, five of the deaths might have been preventable. Of 100 who died at a low-death-rate hospital, only one might have been preventable.

To put it another way, even after some compensation was made for severity of illness, the death rates in the best-appearing of these hospitals were 10 to 15 percent

lower than might have been predicted. The death rates in the poorest hospitals were 5 to 10 percent higher.

This was only one study, and its authors called it preliminary, requiring confirmation. Yet one author, Dr. Robert Brook, said after the Dec. 17 federal report that in his opinion "maybe half, maybe 40 percent" of hospitals with strikingly high death rates give inferior care. ::

In the hospital group's ad, Carol McCarthy said, "Patterns of poor care that go uncorrected are simply not tolerated."

I am sure that she is among many hospital and medical officials who are working today to make this statement true. But the effort is far from finished.A March 1986 federal report on 289 hospitals with markedly high Medicare mortality rates showed many with two or four or even 10 times the expected rate based on national patterns.The Maryland Health Services Cost Review Commission reported six weeks ago that death rates after gastrointestinal surgery -- operations for liver, pancreas, gallbladder, stomach and other gastrointestinal illness -- varied widely in Maryland hospitals. They ranged from 12 "excess" deaths per 100 patients in the hospital with the poorest record -- 12 deaths more than might have been expected if the hospital had been average -- to four fewer deaths than expected at the hospital with the best record.In a pilot study, the New York State Bureau of Hospital Services reviewed the records of 1,300 patients who died at 18 New York City hospitals. It found that 43 patients, more than three in 100, died because of inadequate care, including emergency room errors, medical and nursing mistakes and missed diagnoses.

At the State University of New York Health Science Center at Brooklyn-University Hospital, a healthy man, 33, who donated a kidney and developed complications, died in the operating room because of an anesthesiologist's error. At Harlem Hospital, a woman, 49, in respiratory distress, died after a 15- to 20-minute delay in opening her throat so she could breathe. At Kings County Hospital, a pregnant woman, 30, died after failure to treat her for internal bleeding. New York state officials have accused Good Samaritan Hospital of West Islip, N.Y., of several deficiencies in the wake of 31 suspicious deaths and assault charges against nurse Richard Angelo, who admitted injecting patients with lethal drugs. State officials said the hospital's quality Many factors can contribute to high mortality rates.

control was so poor it had no way of detecting the poisonings.The Veterans Administration announcedlast year that it would close a third of its 51 heart surgery units after a study showed death rates varying from a low 1 percent at one hospital to an alarming 18 percent at another.The Public Citizen Health Research Group examined the death rates released Dec. 18 for two hospital chains: 26 Kaiser hospitals and 30 operated by investor-owned American Medical International. Seventeen (65 percent) of the Kaiser hospitals were in the lowest-mortality group for severe acute heart disease (mainly heart attacks); none was among highest-mortality hospitals. Six AMI hospitals (20 percent) were in the highest-mortality category, two (7 percent) in the lowest.

(AMI officials in Beverly Hills, Calif., declined to comment. AMI Doctors' Hospital in Lanham was in neither the highest nor lowest category. Its heart disease treatment rates were in the "predicted" or expected range.) ::

All the experts agree. It is impossible to point a finger at any one hospital on the basis of death rates alone. There may be good reasons why a hospital has some high death rates.

There may also be bad ones.

Some investigations have found that a few bad doctors are responsible for a hospital's bad overall record. Many observers have said that "it's more often the doctor than the hospital."

That's not the whole story, say researchers at the government's National Center for Health Services Research in Rockville. Joyce Kelly and Fred Hellinger there examined the fact that hospitals with a high volume of care generally have lower death rates than hospitals with low volume.

They did find a strong relationship between low mortality and two physician-connected factors: a high rate of certification of doctors by specialty boards and hospital affiliation with a medical school faculty. But they found no relationship between the volume of services by individual surgeons and low death rates.

This suggested, they said, that "other factors" must be involved, such as the quality of a hospital's nursing staff or the use of advanced technologies.

In short, too few nurses or overworked nurses or a poor laboratory or bad administration or the absence or misuse of advanced technologies can all help add up to bad care.

Next Week: Doctors' revealing letters to the New England Journal of Medicine.