The federal government, trying to put a tourniquet on its Medicare bills, wants to carve the world of ailments into 467 pieces and stick a price tag on each.

An appendectomy would be No. 167, unless there are complications. Then it would become a No. 165. A vasectomy would be a No. 351. Kidney transplant? That would be covered under No. 302.

For those whose aches defy such handy description, there's always No. 467. That's "other factors influencing health status," the medical equivalent of "miscellaneous."

If it all sounds a little cold and calculating, be advised that hospitals have been using the treatment-by-number system for years as a sort of shorthand to help them process data about their patients. Researchers at Yale University put together the first set of categories more than a decade ago, and the 467-ailment model is the latest refinement of a system that started out with 333.

What brings the numbers to the fore these days is a proposal to change the way hospitals are paid for treating patients under Medicare, the government's health insurance program for the elderly and disabled. The Reagan administration, hoping to rein in the government's galloping Medicare bill, wants to use the numbers to set up a system of fixed prices for various hospital treatments.

The so-called "prospective payment plan" would be a marked change from the current system, under which hospitals are paid essentially whatever they spend on the treatment of a Medicare patient.

The administration argues that this "retrospective" system offers no incentive for hospitals to hold down their costs and is one of the reasons the cost of federal hospital care has been rising at an annual rate of 19 percent for three years and is expected to reach $44 billion in fiscal 1984.

So it has launched, at Congress' invitation, what amounts to the strongest attack on hospital costs since the Carter administration's ill-fated hospital cost-containment bill. That effort failed under heavy lobbying by hospitals, which solemnly promised to police their own costs.

The voluntary approach worked pretty well, until the mandatory cost-control legislation died on Capitol Hill. Costs rose again.

Now, figuring that a tonsillectomy is a tonsillectomy (or a No. 59 is a No. 59) wherever it's done, the administration proposes to figure out a national average cost for each of the 467 treatment categories, adjust the figure for local wage rates and pay hospitals that amount for Medicare patients.

If the average cost of a tonsillectomy, adjusted for wage rates in Wichita, came to $1,500, that's what a Wichita hospital would be paid, even if it cost the hospital $2,000 or $1,000.

The hospital that charged $1,000 would get to pocket the difference--sort of an efficiency bonus. The hospital that charged $2,000 would have to swallow the loss. In a report to Congress in December, former health and human services secretary Richard S. Schweiker said the proposal "promotes efficiency in a simple effective way."

"At present, payments for hip replacements can vary from $2,100 to $8,400, with no difference in quality," Schweiker told the House Ways and Means Committee last week. House members, like the senators who heard Schweiker a day earlier, generally nodded in agreement.

The American Hospital Association agrees, too, up to a point.

The association, which represents all the nation's hospitals, is willing to go along with the idea of prospective payments, rather than payments based on their actual costs. It agrees that the diagnostic numbers should be used to figure out the payments.

But it doesn't agree with the idea of a national average, preferring a payment based on an individual hospital's average cost, and it says hospitals ought to be allowed to bill the Medicare patient for any charges over what the government will pay.

"As a realistic matter, hospitals are not going to try to bill patients who don't have the money to pay," said Edmund Rice, the association's legislative policy director, but he points out that Medicare, unlike Medicaid, is not limited to the poor.

Others have expressed concern that hospitals, limited to fixed prices for their Medicare patients, would make up their losses by charging higher prices to other patients.

"That's been the traditional method. That's been true," Rice conceded. "But what's been happening is that commercial insurers have vigorously resisted paying any extra in their rates to cover Medicare shortfalls. As a practical matter, the opportunity to shift costs is evaporating rapidly."

It's enough to give a hospital administrator a case of No. 436. That's alcohol dependence.