The cake for nurse Carole's 21st birthday provided a touch of normality otherwise missing at the main hospital still operating in the beleagured Christian stronghold of East Beirut.

Laughter and hugs rewarded the intrepid visitor who had driven the cake - and some friends - through the notorious museum crossing, a nearby sniper's paradise dividing the city's Christian and Moslem halves.

But soon it was back to business at the Hotel Deiu Hospital caring for the wounded and coping with the damage caused by the latest round of fighting.

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Since the Syrian and Christian big guns began their artillary duel a week ago, hits have forced the operating theater, intensive care unit and laundry to shut down. But the Hotel Dieu was weathered many another crisis since fighting began here in April 1975 and a dynamite-laden car was blown up in front of the main entrance.

Coping this time meant rigging a makeshift operating theater underground and shifting patients from an exposed old outlying building and upper floors to the relative safety of the basement and ground-floor corridors, where they are behind thicker walls and protected from broken window glass.

Despite the right-wing radio's claims of massive casualties caused by the shelling, not all the 70 emergency beds were filled. Normally the Hotel Dieu can handle 265 patients.

"Only a few of the normal 250,000 residents are left in East Beirut," a staff member said, "and they're in shelters out of harm's way."

Most of the patients were civilians with a sprinling of militiamen whose uniformed comrades came visiting as often as not cradling their Soviet-designed AK47 assault rifles.

Staff, which in normal times runs to more than 100 doctors alone, was down to a surgeon, a handful of residents and interns, about 15 nurses and Mother Superior Marie Leonard.

"The civil war was child's play compared to this," explained surgeon Henri Ingea, "because then we could go home and come back to work. This time we're living here around the clock."

The biggest problem, a staff member said, was what to do with the eight corpses in the morgue. As in the rest of East Beirut - and West Beirut, too - there is no city electricity and the hospital's own generator is not powerful enough to provide current for the morgue. Telephones are almost all dead throughout East Beirut.

Despite sizable quantities of drugs, some antibiotics were in short supply and water was rationed "by the eye-dropper," a staff member said.

What passes for small talk concentrated on the relative calm overnight - compared to the night before - although the steady thump of heavy weaponry was audible and a shroud of smoke rose from nearby fuel storage tanks hit two days ago by shellfire.

"What we've shown in our years of practice," said Saunders, who is in this country for about a month visiting hospices, "is that we are in fact extremely cost effective. The cost of a patient for a week in St. Christopher's Hospice (in London) is 55.5 percent of the cost of a week in a teaching hospital in our area, 65 percent of the cost of a nonteaching general hospital. And anyway," she added, "half our patients are at home."

Hospice care can be provided on either an in-patient or out-patient basis. The New Haven program is entirely home-care based at this time, with an in-patient unit scheduled to open next September. Teams of nurses, backed up by physicians, visit the patient and patient's family as often as necessary to provide what every medical and psychological support is needed to make the family group comfortable.

While Califano, Kennedy and Dole endorsed the basic concept of hospice care, all three, and particularly Califano and Dole, stressed the need for a cautious examination of hospice care before the federal government jumps into paying for it on a general basis.

Many services provided by hospices, such as bereavement counseling and other forms of psychological support, are not funded by Medicare or Medicaid, said Califano, but the proposed experimental projects will cover such care.

"Then there is the issue of family control," he said. "The hospice movement is young, small, innovative, still-evolving. All of us are sensitive to the need to endure quaity; to protect the movement, as it grows, from exploitation, fraud, quackery and profiteering. Yet we are sensitive also to the danger that rigid standards, applied too tightly from within or without, could stifle innovation, smother creativity and choke growth."

The HEW secretary said a task force in his office has been studying the hospice concept since June and come up with four basic questions:

"How can we build an adequate base of knowledge and experience to assess the economics of hospice care?

"How can we guarantee that federal assistance for hospice care, if it should develop, will not weaken private and voluntary support?

"How can we foster quality and prevent abuses without over-regulation?

"How can we encourage the concept of hospice, yet discourage the building of unneeded new facilities that drive up costs?"

A nurse shooed a wounded old man away from a window, apparently fearful that he might be further injured by glass in case of a hit or near hit.

It was a rare sign of tension.

Not even Ingea seemed disappointed by the failure of other colleagues to come and help him out.