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Weighting the p-values is a well-established strategy that improves the power of multiple testing procedures while dealing with heterogeneous data.
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[author] Roeder, KathrynK., Bacanu, Silvi-AlinS.-A., Wasserman, LarryL. and Devlin, BB. (2006). Using linkage genome scans to improve power of association in genome scans. The American Journal of Human Genetics 78 243–252
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2017
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[author] Lei, LihuaL. and Fithian, WilliamW. (2018). AdaPT: an interactive procedure for multiple testing with side information. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 649–679
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[author] Barber, Rina FoygelR. F., Candès, Emmanuel JE. J. et al. (2015). Controlling the false discovery rate via knockoffs. The Annals of Statistics 43 2055–2085
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