“We understand that people are frustrated by how long the process takes,” said Shelby Hallmark, director of workers’ compensation programs at the Department of Labor. He added that a substantial number of workers or their survivors may still not be aware of the program and have not yet filed claims, “but over all, this program is working well.”

Image Despite colon cancer and spots on his lungs, Russell Earley has been denied compensation. Credit... Fred R. Conrad/The New York Times

Some sick workers in western New York, however, say too many claims are being denied without proper cause.

“For God’s sake, if somebody deserves it and has as much proof as we have, there’s no reason at all that they shouldn’t be compensated,” said Edwin Walker, 74, who worked at Bethlehem Steel in Lackawanna from 1951 to 1954. He repaired furnaces and cooling beds where uranium ingots were shaped into rods. Now he has bladder cancer. While pursuing his claim for compensation, he has become an unofficial spokesman for more than 300 Bethlehem retirees fighting for compensation and care.

“We were told that to get compensated we would have to prove that we were diagnosed with cancer and that we worked there at the time,” Mr. Walker said. “Those were the two criteria. That’s all they told us.”

It can be difficult for workers to understand how much proof the government needs. Russell Earley, 83, operated a crane at Bethlehem Steel from 1941 to 1983, when he had surgery for colon cancer. In 2006 doctors told him he had a suspicious spot on each lung. His compensation claim has been denied twice.

“They took 24 inches of intestines, sewed my rectum up and hung a colostomy bag on me,” he said. “And when they denied me, they said, ‘Sickness not bad enough.’ Can you imagine?”

Under the program, workers exposed to radiation can receive compensation two ways.

They can apply individually, using employment, medical and exposure records to link their work to the cancer they developed. Government doctors and scientists at the National Institute for Occupational Safety and Health then analyze the data to determine whether it is more likely than not that the disease was caused by the radiation. At the outset of the program in 2000, officials believed that only 10 percent of claims would be approved.