Steve,
I suspect that:
For breast cancer, for example, about 82 percent of women in the U.K. and Denmark were alive five years after being diagnosed in 2007.
Might have been meant to say:
For breast cancer, for example, in 2007 about 82 percent of women in the U.K. and Denmark were alive five years after being diagnosed.
Just a thought, since the data was said to be up through 2007 ??