- Sample Size Calculation

Given the exploratory nature of the study, no formal sample size calculation was
performed. A total of 370 patients is expected to be enrolled.

- Data Analysis (as outlined in the approved protocol)

Data will be analyzed using t-tests (or Mann-Whitney tests, depending on the data type).
The correlation between obtained results and clinical outcomes will be tested using
Spearman's rank correlation coefficient to identify potential biomarkers.

For microbiota analysis, intra-sample diversity (alpha diversity) will be assessed using
Faith's phylogenetic diversity metrics, observed OTUs, and the Shannon index.
Inter-sample diversity (beta diversity) will be evaluated using weighted and unweighted
UniFrac distances, which will serve as input for principal coordinates analysis (PCoA).
PCoA plots, heatmaps, and bar plots will be created using the Made4 and Vegan packages in
R. Statistical analysis will be conducted using the Vegan and Stats packages. The
separation of data in PCoA will be tested using a permutation test with pseudo-F ratios
(Adonis function in Vegan). Fisher's exact test will be used to assess the significance
of differences between clusters obtained through hierarchical clustering analysis. The
Wilcoxon test (for paired or unpaired data) will be employed to compare alpha and beta
diversity, as well as the relative abundance of microbial groups (or functional groups)
between subject groups and over time. Discriminatory features (taxa or genes) will be
identified using Random Forests (Breiman, 2001). Microbiota sequences from healthy
subjects, matched for age, sex, and BMI, will be retrieved from publicly accessible
databases for comparative purposes. p-values will be adjusted for multiple comparisons
using the Benjamini-Hochberg method. A false discovery rate <0.05 will be considered
statistically significant.

Correlations between variables will be assessed using Kendall's correlation test with the
cor.test function from the Stats package in R.

For microbiota analysis, intra-sample diversity (alpha diversity) will be assessed using
Faith's phylogenetic diversity metrics, observed OTUs, and the Shannon index.
Inter-sample diversity (beta diversity) will be evaluated using weighted and unweighted
UniFrac distances, which will serve as input for principal coordinates analysis (PCoA).
PCoA plots, heatmaps, and bar plots will be created using the Made4 and Vegan packages in
R. Statistical analysis will be conducted using the Vegan and Stats packages. The
separation of data in PCoA will be tested using a permutation test with pseudo-F ratios
(Adonis function in Vegan). Fisher's exact test will be used to assess the significance
of differences between clusters obtained through hierarchical clustering analysis. The
Wilcoxon test (for paired or unpaired data) will be employed to compare alpha and beta
diversity, as well as the relative abundance of microbial groups (or functional groups)
between subject groups and over time. Discriminatory features (taxa or genes) will be
identified using Random Forests (Breiman, 2001). Microbiota sequences from healthy
subjects, matched for age, sex, and BMI, will be retrieved from publicly accessible
databases for comparative purposes. p-values will be adjusted for multiple comparisons
using the Benjamini-Hochberg method. A false discovery rate <0.05 will be considered
statistically significant.

Correlations between variables will be assessed using Kendall's correlation test with the
cor.test function from the Stats package in R.