You may have heard about doctors who practice “direct primary care” or “concierge medicine." They offer what’s known as private medicine, where patients pay a fee up front (usually an annual or monthly retainer) for the privilege of having the physician at their beck and call, which may include sharing his or her cell-phone number.

About 6,500 physicians in the U.S. currently offer the service, up from fewer than 150 in 2005, according to the American Academy of Private Physicians. They're expected to grow by about 25 percent a year.

Retainer fees vary, but you can expect to pay about $1,200 to $1,500 per year.  Since these physicians have fewer patients, they often offer same-day appointments, longer office visits, and frequent email and phone communication.  

A few studies have found that patients who sign up for this type of care report more satisfaction and fewer visits to emergency rooms and specialists, but there’s not enough research to prove they receive better care, stay healthier, or recover faster from injury or disease.

And the retainers won’t pay for all of the care you need. You’ll have to buy additional insurance because the retainers don’t cover drugs, most treatments, and hospitalization costs. If you're under age 65, that means at least a high-deductible plan purchased either from your employer or through a state or federal marketplace. If you are 65 or older, you should still enroll in Medicare, and consider extra coverage, such as Medigap or Medicare Advantage.

That extra insurance can cost a few hundreds dollars per month.

In addition, concierge medicine raises some thorny ethical issues, according to Consumer Reports' chief medical adviser,  Marvin M. Lipman, M.D. For example,  whether it’s appropriate that a concierge doctor who treats Medicare recipients essentially gets paid twice: the premium he or she collects from the patient, plus payment from Medicare, which is funded by taxpayers.

Lipman also worries that if too many doctors move toward the concierge or direct-primary care doctors, fewer doctors may accept patients with Medicare, Medicaid, or other forms of insurance.

While the Affordable Care Act has increased the number of people with health insurance, "If concierge medicine continues to expand, people who struggled for years without health insurance might find themselves grappling with a whole new problem: adequate insurance, but no one to accept it."