I have a dataset of brain images in which each pixel value corresponds to a measure of neuron activity. The images were taken in different conditions described by three regressors (two fixed-effects and their interaction).
I am going to analyse these data by performing a linear regression of each pixel values (each image is composed by about 3 millions of pixels and I have 12 images, so I have to perform about 3 millions of linear regressions taking into account 12 values of the dependent variable for each one) for the three regressors.
Then I am going to use a false-discovery-rate procedure (e.g. Benjamini–Yekutieli) for multiplicity correction to adjust the p-values found for each regressor and each pixel. I image that, for the multiplicity correction procedure, I should group the p-values based on the regressor they pertain to; is this correct?
The problem is that some of the pixel values in some images are not valid (i.e. not informative), therefore some of the linear regressions will be performed with all the 12 values of the dependent variable (full statistical power), while others will be performed with a reduced number (i.e. 11 or 10 or 9) of values of the dependent variable (reduced statistical power).
My question is: should I take into account the fact that the statistical power is not the same for all the tests when performing the multiplicity correction or can I just ignore this fact?
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