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"Only 13 percent of women consider cardiovascular desease, or CVD, their greatest health risk, but not even cancer claims as many women's lives as CVD"

Is this a good sentence gramatically? I kind of feel the meaning of it, but I don't think this is a good sentence. What about the second half of the sentence:

"but not even cancer claims as many women's lives as CVD"

Is this grammatically right? Can anybody paraphase the whole sentence into a easier ( and more simple) to understand one?

Thank you for your help
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I think you need to keep it as one sentence as the point is that women do not recognise the risk of CVD.

Only 13% of women consider CVD to be the greatest risk to their health, but women are actually more likely to die from this than from cancer.
Comments  
"Only 13 percent of women consider cardiovascular desease, or CVD, as their greatest health risk. Not even cancer claims as many women's lives as CVD does."

To me, this works better Emotion: wink
 nona the brit's reply was promoted to an answer.