How to remove batch effect from TCGA and GTEx data

Question

I want to play some differentially expressed genes for gliomas cancer. I collected cancer tissue profiles from the TCGA database and normal tissue profiles from the GTEx database. I straightforward use ComBat from R package "sva", and the result shows little differentially expressed genes (DEGs) were found. How can I remove batch effects correctly?
Thanks

haci · Answer

This has been asked and answered here and Biostars. My take home message from many similar posts is "not to bother with correcting batch effects when performing differential expression analysis but to include 'batch' as a covariate". The latter accounts for the batch effects.
EDIT: This does not really answer OP's question, as @swbarnes2 and @ATpoint pointed out, they have a completely confounded design and the linear regression model would not accept such a model matrix.

burger · Answer

There is a paper that did what you are asking: Unifying cancer and normal RNA sequencing data from different sources.

How to remove batch effect from TCGA and GTEx data

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