That film was The Conqueror, a Howard Hughes venture shot just a grenade-propelled-stone's-throw away from a wildly active U.S. nuclear bomb test site.
Frances Farmer, another star of Among the Living, also died of cancer, but I'm guessing that was the least of her worries.
The Conqueror (1956, Howard Hughes)
An article in People Magazine (11/10/1980) goes into more atomic detail about the filming of The Conqueror, including the moving of 60 tons of radioactive dirt by Howard Hughes back to the studio for use for retakes — on top of the 13 weeks of location shooting in the hot zone.
Anyway, Howard Hughes said he felt real, real bad about it later.