Population density variations across countries

Hello, I am facing a problem for an independent variable for subnational population density in a view to make cross-national analysis across countries. My problem is that I have in my dataset some very densely populated metropolitan areas categorized as a region and great variability in my population density variable.

I have considered using a log-transformation of pop density or normalizing the variable by country by combining with indicators of national population concentration.

Do you have other ideas on how I could deal with the high variability of regional pop density in order to make better cross-national comparisons?

Thank you.
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