Cigna Corp. on Wednesday announced that it has entered into an agreement with Thousand Oaks biotech Amgen Inc. that will directly tie the price the insurance company will pay for a pricey new cholesterol drug to its effectiveness on individual patients.

The contract will provide Cigna of Bloomfield, Conn. discounts based on the effectiveness of Amgen’s Repatha, which is part of a new class of cholesterol-lowering medications that can cut “bad” cholesterol by more than 60 percent.

Under the agreement, if a patient meets or exceeds the anticipated reduction in cholesterol, the full price would be paid. However, the price decreases in proportion to missed cholesterol targets. Cigna has not disclosed specifics on the deal.

Last year, Amgen released Repatha, which costs approximately $14,000 annually for treatment. Sales for Repatha have had a slow start as many insurers and doctors have been hesitant to approve and prescribe the pricey new med.

As a result of the lack of price regulations on prescription drugs in the United States as well as the emphasis on reasonably priced health care by the Affordable Care Act, insurers are starting to demand more contracts like these to control costs.

Cigna also announced a similar contract with Sanofi and Regeneron Pharmaceuticals Inc. for their competing cholesterol drug Praluent, which costs approximately $14,600.

Amgen shares on Wednesday closed down $3.06, or a little less than 2 percent, to $154.18 on the Nasdaq.