1. feature_table.txt (.csv): input (based on prv_cut and lib_cut) count table. Taxa with nonzero counts in less than 10% of all samples were removed.

2. res_global.txt (.csv): global test result for the variable specified in group, each column is:
– W, test statistics.
– p_val, p-values, which are obtained from two-sided Chi-square test using W.
– q_val, adjusted p-values. Adjusted p-values are obtained by applying p_adj_method to p_val.
– diff_abn, A logical vector. TRUE if the taxon has q_val less than alpha

3. res_pair.txt (.csv): pairwise directional test result for the variable specified in group:
– lfc: log fold changes.
– se: standard errors (SEs).
– W: test statistics.
– p: p-values.
– q: adjusted p-values.
– diff: TRUE if the taxon is significant (has q less than alpha)

In the pairwise directional test, the mixed directional false discover rate (mdFDR) was taken into account. The mdFDR is the combination of false discovery rate due to multiple testing, multiple pairwise comparisons, and directional tests within each pairwise comparison. 

The overall false discovery rate is controlled by the mdFDR methodology adopted from Guo, Sarkar, and Peddada (2010) and Grandhi, Guo, and Peddada (2016). 

The family wise error (FWER) was controlled with "holm" and the number of bootstrap samples was default at 100. 

# added optional confounder adjustment 2023-11-17
    if the comparison is done with confounder adjustment, the comparision title will have postfix as group+group1+group2, 
    with group as the comparison group and group1 and group2 as confounding factors
    The description of the fix_formula is described by ancombc2 as:
    fix_formula: the character string expresses how the microbial absolute abundances 
    for each taxon depend on the fixed effects in metadata. When specifying the 
    fix_formula, make sure to include the group variable in the formula if it is not NULL.	
    here first fix_formula groups are seperated by + and the first one is the comparison group

References:

Guo W, Sarkar SK, Peddada SD. Controlling false discoveries in multidimensional directional decisions, with applications to gene expression data on ordered categories. Biometrics. 2010 Jun;66(2):485-92. doi: 10.1111/j.1541-0420.2009.01292.x. Epub 2009 Jul 23. PMID: 19645703; PMCID: PMC2895927.

Grandhi A, Guo W, Peddada SD. A multiple testing procedure for multi-dimensional pairwise comparisons with application to gene expression studies. BMC Bioinformatics. 2016 Feb 25;17:104. doi: 10.1186/s12859-016-0937-5. PMID: 26917217; PMCID: PMC4768411.