This is the time of year when people repair to the Caribbean to escape the phone, the rain and the gloom.

But people with medical concerns, either chronic diseases or past narrow escapes, and families with children, may have legitimate worries about getting help in an emergency.Going to a relatively small island anywhere means leaving the safety of the urban infrastructure.

Assunta Uffer-Marcolongo, president of a volunteer organization, International Association for Medical Assistance to Travelers, says that anyone with serious health concerns should buy a travel insurance policy that includes emergency air evacuation, but insurers warn that the patient should be sure that evacuation is authorized in advance by the company.

Experts assessing hospitals in the Caribbean say that generally the bigger, more developed islands have more advanced facilities.

Dr. George Alleyne, assistant director of the Pan American Health Union, cited Jamaica, Barbados, Trinidad and Tobago among English-speaking countries and Martinique and Guadeloupe in the French islands as having more diverse facilities.

When U.S. Peace Corps people in the Caribbean need hospital treatment, they are sent to Queen Elizabeth Hospital in Bridgetown, Barbados, or to the University of the West Indies Hospital or St. Joseph's Medical Center in Kingston, Jamaica.

Dr. Joseph Peterson, executive director of World Access, which owns the medical assistance and insurance company Access America, said that there was not a great problem finding a good doctor most places in the Caribbean; the problem is hospital care.

He cited six hospitals, not all of them large, as among those providing satisfactory hospital care: Aruba, Oduber Hospital; Bridgetown, Barbados, Queen Elizabeth Hospital; Curacao, St. Elisabeth's Hospital; Kingston, Jamaica, University of the West Indies Hospital; Martinique, Le Maynard Hospital, and San Juan, P.R., Ashford Presbyterian Hospital.

Peterson, a member of the emergency medicine faculty at George Washington University Medical Center in Washington, added counsel to people with heart disease, or even to someone who may suffer a heart attack without warning while traveling.

"It's a new era in the treatment of heart patients with the advent of thrombolytic drugs, which dissolve the clot," he said.

"It is really effective in reducing the size of the clot and in improving the survival rate. But it requires sophisticated care and it cannot be done every place."

He suggested people with heart disease consult their doctors before taking off for the Caribbean.

The International Association for Medical Assistance to Travelers publishes a roster of physicians who meet certain standards, who speak English or another second language and who agree to charge specified fees.

The organization's list for the Caribbean increased by "a couple of doctors" in 1990, but Miss Uffer-Marcolongo hopes to make a trip there this year to sign up more.

"Most of the physicians have been trained in the United States, Canada and Europe, and they are good," she said.

"The problem is that the facilities are not up to U.S. standards, and this can frighten visitors. Progress is slow because these countries do not have the finances."

Even an up-to-date list is not necessarily the solution. International Claim Service in Richardson, Tex., which provides emergency medical advice and assistance to employees and travelers overseas, maintains a list of almost 50 hospitals in the Caribbean, Bermuda and the Bahamas.

But Jerry Edwards, the president, said that when an emergency call comes in, the closest clinic may not be best because the French-speaking doctor may be away, or a phone call may elicit unsatisfactory answers. An evacuation to Miami may be a better solution.

The 1990 IAMAT directory lists physicians, hospitals and clinics worldwide, including these places in the Caribbean and the Bahamas:

Freeport, the Bahamas; Bridgetown and Christ Church, Barbados; Anguilla, British West Indies; Grand Cayman; San Pedro de Macoris, Santiago and Santo Domingo, Dominican Republic; Guadeloupe, Martinique, St. Barthelemy and St. Martin, French West Indies; St. George's, Grenada; Port-au-Prince, Haiti; Kingston, May Pen, Ochos Rios, Port Antonio and St. Ann's Bay, Jamaica; Aruba and Curacao, the Netherlands Antilles; Mayaguez, Ponce, Santurce, Vega Alta and Vega Baja, P.R.; Vieux Fort, St. Lucia; Port of Spain, Trinidad, and St. Thomas and St. Croix, U.S. Virgin Islands.

Most physicians and clinics agree to accept $45 for an office visit, $55 for a house call and $65 for a house call at night or on Sunday or a local holiday.

The agreed-upon fees do not apply to doctors called in for consultation or laboratory procedures, surgical procedures, hospitalization or other expenses.

The 72-page directory, plus informational leaflets and a membership card, is available from IAMAT, 417 Center Street, Lewiston, N.Y. 14092.

There is no fee, but Miss Uffer-Marcolongo said that contributions were welcome. Asked if she would like to specify a minimum, she said she believed that such information should not be sold, but be available free. The association has 80,000 members who contribute, she said.

Readers often ask for accredited hospitals in the Caribbean, which ignores the reality that most islands are independent nations.

U.S. hospitals receive accreditation, which is voluntary, from the Joint Commission on Accreditation of Healthcare Organizations. When a hospital seeks accreditation, it must pay for inspections involving 2,400 standards; accreditation, if it is granted, is good for three years.

Puerto Rico at this writing has 32 accredited hospitals. Government hospitals in St. Thomas and St. Croix in the Virgin Islands had hoped to receive accreditation in 1990, but Hurricane Hugo in 1989 damaged them.

The joint committee maintains a customer service office, reachable at 708-916-5600; it will answer questions about accredited hospitals in a particular area. Marita Gomez of the joint committee said that although a non-U.S. hospital could not be accredited, it could ask for an inspection to establish that it was providing care matching the standards of an accredited hospital. She knew of no hospitals in the Caribbean that had done this.

The good news for island visitors with health concerns is improved telephone links with the United States. More reliable connections since the hurricane mean that a visitor can conveniently talk to a doctor at home, or an island doctor can consult with a patient's doctor.

According to Lynn Newman, a spokeswoman for AT&T, in July 1990 a new fiber optic cable was run from West Palm Beach, Fla., to San Juan; Santo Domingo, the Dominican Republic; Kingston, Jamaica, and on to Barranquilla, Colombia. The sound quality of telephone calls to and from these areas has been greatly improved.

Ms. Newman said that in 1990 connections to many Leeward and Windward Islands shifted to a digital microwave service, an upgraded form of radio transmission: Tortola, the British Virgin Islands; Saba, the Netherlands Antilles; St. Kitts; Antigua; Montserrat; Guadeloupe, the French West Indies; Dominica; Martinique, the French West Indies; St. Lucia; St. Vincent; Barbados; Grenada and Trinidad.

On the subject of medicine in the Caribbean, Cuba is an emerging topic.

"Fielding's Caribbean 1991" by Margaret Zellers (William Morrow & Co., $14.95 in paperback) includes a chapter on Cuba, which she had not covered for several years, since travel to Cuba by United States citizens is restricted. Ms. Zellers maintains that medical standards there are high.

"In the 1960s and 70s," she writes, "many doctors were trained in the Soviet Union and Eastern bloc countries. These days, there are highly regarded medical schools in Cuba with students from many other countries."

Students from European countries attend Cuban medical schools now. The Cuba section of the 1991 edition of the "Caribbean Islands Handbook" (Prentice Hall Press, $16.95) says that in Havana or Varadero, clinics charge small fees in dollars and visitors needing medical care are steered there.

Two parting words. If you have a chronic health problem that may act up, insurance that provides for evacuation by plane or air ambulance is readily available.

Second, be sure to take along medical records as well as a note with your physician's phone number or paging-service number. Everything should be legible and readily understandable in case you are not alert enough to explain.