Could it be something else? There's interesting research suggesting that dogs can detect cancer and other diseases. The most likely explanation is not some psychic ability but instead that the dogs' super-sensitive noses can detect faint biochemical traces given off by the body's reaction to the disease.
While studies show that canine disease detection is better than chance, it is still not as accurate as formal medical tests in many cases. A 2004 British Medical Journal study found that dogs could detect bladder cancer in patients at a rate 25 percent better than chance, but at a lower rate than standard tests.
Dosa offers a similar mechanism as a potential explanation for Oscar's powers, though it's not clear what specific chemicals released just before death would trigger a reaction. In addition, there are countless confounding odors in a hospital setting that might mask any animal-detected "death scent," including flowers, food, cleaning sanitizers, drugs and perfumes.
The story of Oscar the death-detecting cat is an interesting, lighthearted story, but falls short of being scientifically unexplainable. However that interpretation is more comforting than another explanation: that the lovable Oscar is really a feline serial killer, bringing death wherever he goes.