As 1986 begins, the United States offers the world's most advanced medical care, but has yet to solve the problem of persons who can't pay for it.

More and more, Dr. Dollar is taking charge of American medicine. The growing drive to hold down health costs is increasingly determining how much care we may get, where we get it and even who gives it.

This drive played a major role in reshaping American medical care in 1985 and is expected to become even more so in 1986, as federal budget-cutters seek new targets.

Health care remains a large target. The nation's medical bill exceeded $400 billion in 1985 -- it reached an estimated $418 billion -- and accounted for $1 in every $10 of the gross national product.

Among the methods of cost-cutting, or at least keeping costs from rising wildly: The government is paying hospitals a flat sum, depending on type of illness, for almost all Medicare patients. Taking a cue from these diagnosis related groups (DRGs), many health care plans are negotiating similar flat or lowered rates. More and more insurors, health plans and employers require preadmission approval of nonemergency hospital stays before they will pay for them. Prepaid health care plans -- organizations selling you almost all your care for one fixed fee each a month -- are proliferating. There are now more than 350 such HMOs (or health maintenance organizations) with 20 million members, compared with 50 in 1973 when the Nixon administration got behind them. You don't have many medical bills when you belong to such a plan, but you don't go to the hospital or see a specialist at the plan's expense unless your primary care doctor says so -- which is how the plan keeps its costs down. And he or she has to be one of the plan's doctors. More companies are making employes pay part of the cost of their health coverage, or otherwise encouraging workers to choose lower-cost plans. Chrysler Corp., for example, pays the full cost of eye and foot care only if the employe uses a provider with whom Chrysler has a cut-price contract. Big unions, eager to get pay boosts rather than benefit increases, are cooperating. Hoping to cut 10 percent from its medical bill, the Teamsters' Central State Welfare Fund has negotiated a "preferred provider" deal with a hospital group. A teamster gets full coverage only at a hospital that charges the fund lower rates. All over the country, doctors whose numbers are growing and hospitals whose wards are often partly empty are competing to make similar deals, even at reduced rates.

These and other efforts are moderating health spending. The nation's health bill rose by an estimated 8 percent in 1985, the lowest increase in 21 years, this after 1984's 9 percent increase became the first under two digits in 20 years. The administration and Congress are now considering a freeze rather than any increase in Medicare payments to hospitals, as well as new limits on doctors' fees.

The effect on patient care? The administration says it is just cutting fat by eliminating unnecessary care. But many doctors say care is suffering. The final answer is not in yet, but it is clear that hospitals are shunting more poor, non-paying patients to public or charity hospitals.

Low-income persons and those who don't belong to some group are having a harder time buying adequate health coverage. Most HMOs and other insurors are not interested in these often higher risk persons.

And the House has voted to eliminate the federal tax exemption of nonprofit Blue Cross-Blue Shield plans, often the only ones that offer unprofitable individual or small-group coverage. If the harder-pressed Blues have to start dropping this coverage, things may become even harder for the non- or under-insured.