As gout is largely a genetic disease, the criteria for an effective study would be gout incidence by race, rather than by country. As far as I am aware, there are no comprehensive analyses by country or by race,? but there are some that look at specific countries and at specific races.
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There are some statistics about gout deaths by country at nationmaster.com/graph/mor_gou-mortality-gout, but this is more likely to be an assessment of medical practices rather than incidence of gout.
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If anyone wants to investigate this further, please beware useless stats similar to cureresearch.com/g/gout/stats-country_printer.htm. All they have done is take an unverifiedd global gout incidence percentage and applied it to population estimates for various countries. What awaste of time and effort!