Does the order of variables matter in ANCOM-BC

Hi, when I am using "--p-formula" in ANCOM-BC, I was wondering if the order of the variables matter? For example, if my variable of interest is sex and I want to add body-site and treatment as covariates, is there any difference between:

  1. --p-formula "Sex+Body-site+Treatment"
  2. --p-formula "Sex+Treatment+Body-site"
  3. --p-formula "Treatment+Body-site+Sex"
  4. --p-formula "Body-site+Treatment+Sex"
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It's such a good question!

This page discibes the formula inputs as 'fixed-effects' which implies independant, but that's ANCOM-BC2
ANCOM-BC2 Tutorial

The page for ANCOM-BC does not mention fixed effects at all... ANCOM-BC Tutorial

I think the function stats::model.matrix() ignores order. Can't find stuff on that either!

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I tried running this with data from PD-mice

In this example, donor and genotype are fully blocked and perfectly balanced:

$ cut -f 4,6 metadata.tsv | sort | uniq -c
      1 categorical     categorical
      1 genotype        donor
     12 susceptible     hc_1
     12 susceptible     pd_1
     12 wild type       hc_1
     12 wild type       pd_1
qiime composition ancombc \
  --i-table table_2k_abund.qza \
  --m-metadata-file metadata.tsv \
  --p-formula 'donor + genotype' \
  --o-differentials ancombc_donor_first.qza

qiime composition ancombc \
  --i-table table_2k_abund.qza \
  --m-metadata-file metadata.tsv \
  --p-formula 'genotype + donor' \
  --o-differentials ancombc_genotype_first.qza

# Then qiime composition da-barplot to make these:

ancombc_genotype_first.qzv (222.0 KB)
ancombc_donor_first.qzv (222.0 KB)

On first inspection, these look the same...

Remember that

  • this study is fully blocked (no confounding factors) and
  • all cohorts are balanced (n = 12 for subgroups)
  • which is cleaner than most real studies! :melting_face:

What I don't have is a citation that says formula order doesn't matter.

Remember that different packages run different tests, so formula order can absolutely matter!

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