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I’m using the IHW package. What would be a useful IHW covariate (option "covariates" in ihw.default) for multiple regression?
I’ve searched “Introduction to IHW” as well as Bourgon, Gentleman, and Huber (2010) and Ignatiadis et al. (2016) but not found an answer.
With kindest regards,
Tyson
Dear Tyson, the choice is covariate is very application or data-type specific, and in some sense it encodes domain knowledge. Therefore it is not possible to answer your question in its current generic form. Perhaps you can expand.
Please also note that IHW and similar methods are most useful in the context of thousands or more hypothesis tests (and hardly so with only a handful). Best wishes Wolfgang
Thank you, Professor Huber.
I fit a regression model, obtain a regression coefficient estimate with its standard error, and perform a two-tailed test. Ignatiadis et al. (2016) suggests using the "Sign of the effect" for two-tailed tests. Would I then create a binary (e.g., 0/1) covariate for IHW? I guess I'm also a little unclear on how the sign alone would be an effective covariate.
With kindest regards,
Tyson
Indeed, for the two-sided t-test (and similar), the sign of the test statistic is independent of the p-value under the null hypothesis, and is therefore a legitimate candidate for hypothesis stratification in the sense of IHW (Table 1, doi:10.1038/nmeth.3885).
Scenarios where this would be useful are e.g. ones in which alternatives in one direction are a lot more frequent than in the other.
Note that we are talking about multiple testing here, where multiple is meant to imply numbers in the thousands. (Just to make sure we are on the same page, since you use the singular above.)
Hope this helps,
Wolfgang