After joining the center last June 2015, Ms. Malveaux began seeing a psychiatrist and went on medication for depression. A social worker coached her grandson, Jermaine Malveaux, on how to care for someone with dementia. Three days a week, an InnovAge van picks up Ms. Malveaux at home and takes her to the center to share lunch with other older adults and try her luck at bingo and ceramics.

“I make friends easily,” she said with a smile. “And the guys flirt with me.”

The InnovAge center, like other PACE facilities, is inspired by Britain’s much-lauded Day Hospitals, outpatient health care facilities that arose in the 1950s that became a hub of daily life for many older people. In the United States, the earliest incarnation of PACE was started in San Francisco in 1971 by a group of Asian and Italian immigrant families seeking alternatives to the American nursing home.

Federal health officials allowed the group, called On Lok — Cantonese for “peaceful, happy abode” — to test what was then a novel and prophetic approach to health care financing. Instead of physicians billing Medicare each time they treated a patient, the government would pay a fixed amount to the center for each member. On Lok would assume the financial risk, similar to an insurance company. In 1990, Medicare officially sanctioned the model.

In exchange for a capped monthly payment from Medicare and Medicaid, PACE staff members arrange and pay for all of a patient’s doctors’ visits, medications, rehabilitation and hospitalizations. At the same time, they are supposed to pay attention to the patient’s daily needs — meals, bathing, housekeeping and transportation to day centers, where older people can ward off isolation and cognitive decline by socializing. (Studies have found that the intensive caretaking reduces costly hospital stays.)

Comparing the cost effectiveness of PACE against nursing homes is difficult, partly because state Medicaid agencies pay a variety of rates. But all the states are required to keep their rates below what they would pay for nursing home care. In Colorado, for example, that amounts to 7 percent less per patient.

On average, Medicare and Medicaid pay PACE providers $76,728 a person a year, about $5,500 less than the average cost of a nursing home. And the money going to PACE covers all of the person’s health and social needs, unlike nursing home care, which doesn’t include hospitalizations and other expensive medical care.