In my pipeline, I started using BWA-MEM with the hg19 reference, should I stay consistent for the same reference with GATK? or it seems to me Broad Institute people recommend using b37, as they said hg18, b36, etc were lifted over from b37 - confused here. thanks
This GRCh37-derived alignment set includes chromosomal plus unlocalized and unplaced contigs, the rCRS mitochondrial sequence (AC:NC_012920), Human herpesvirus 4 type 1 (AC:NC_007605) and decoy sequence derived from HuRef, Human Bac and Fosmid clones and NA12878.
So, it's derived from GRCh37, just as UCSC hg19 is, but contains a different mitochondrial sequence, a herpesvirus, and some other unplaced contigs and sequences. The most practical difference is that the contigs are named 17 instead of chr17, using human chromosome 17 as an example.
And finally, yes, once you have generated an alignment to a specific reference genome you need to use the same reference genome in all of your downstream analyses. There is no "switching" for any good reason that I can think of. It's like asking if you should use a French dictionary to decode and English text.
My practical advice would be to perform your BWA-MEM alignment using b37.