Eli Lilly and Co., maker of several blockbuster drugs for cancer, normally is pleased to see its name associated with the disease.

But that’s not likely this time.

A breast-cancer advocacy group based in San Francisco is planning to plaster a message on a billboard in Indianapolis, demanding that Lilly “stop milking cancer.”

Breast Cancer Action, which calls itself “the watchdog of the breast cancer movement,” is taking aim at an animal-growth hormone called Posilac, marketed by Lilly to increase milk production in dairy cows.

The group says the hormone has been linked to cancer and is passed on to humans through milk. It is demanding that Lilly, which makes cancer drugs, stop making and selling the hormone.

Lilly responded that Posilac is not a cancer risk and has been approved by the Food and Drug Administration. It acquired the product from Monsanto in 2008.

Yet the drug maker finds itself under increasing pressure over the issue. In recent years, several large retailers and food companies — including three of the nation’s largest grocery retailers, Wal-Mart Stores, Kroger and Costco — have pledged to stop selling dairy products from hormone-stimulated cows, citing growing customer demand for hormone-free dairy products.