If all the different niiXX outcomes are correlated to each other (which we might expect if these are possibly just different effects of a common pathology), then they will tend to have similar results. If the me/cfs_status association with NII-RF has that 0,1 significance pattern, then we can expect others with similar relationships to also have that pattern.To be reasonably likely to get the results from this study where only one association was significant in univariate but nearly all had significance in multivariate, you’d need 0,1 to generally dominate
For example, we can imagine testing mecfs association with leukocyte count in four regions of the brain, but the regions are only 1 mm away from each other. Whatever p-value one region has, the others probably will [edit: have very similar p-values] due to them being markers of the same underlying process.
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