Higher prevalence for excess vs higher prevalence by excess

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Looking on the internet deeply has found these results:

higher prevalence for excess is the most popular phrase on the web. 

higher prevalence by excess

10 results on the web

higher prevalence for excess

11 results on the web

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Some examples and use cases from the internet:

Some examples and use cases from the internet:
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  • Women who were married (95%CI=46.54; 61.33) or separated/widowed (95%CI =46.63; 73.37) had higher prevalence for excess weight than single women ...

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