In Massachusetts, more than 18,000 doctors care for nearly 700,000 Blue Cross Blue Shield members under an alternative way of paying for medical treatment that is meant to control costs and reward physician groups that keep patients healthier. These physicians may be changing how they treat their other patients as well, a new study suggests.

Researchers wanted to find out whether there is “spill over’’ in practices that care for Blue Cross members as part of the insurer’s “alternative quality contract’’ to patients in the practices who are insured by Medicare. They found there was an impact on controlling costs of treating Medicare patients, but not for improving quality.

The Blue Cross contract gives doctors fixed budgets for patient care rather than paying them for each visit and procedure, and provides financial incentives for improving health.

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The study compared Medicare patients in these practices to those in practices that do not participate in the Blue Cross contract. Researchers from Harvard Medical School found that spending on Medicare patients in practices with the alternative quality contract fell 3.4 percent.

The findings suggest that doctors might be able to quickly adopt global payment arrangements with multiple insurers, researchers said. But they also warn of “a free-riding problem to commercial insurers engaged in’’ in global payments, “since competing insurers with similar provider networks could offer lower premiums without incurring the costs of managing’’ these contracts.

See the full results here.