Statistical analysis
REGRESSION
Data wrangling and statistical analyses for this purpose were performed using R version 4.0.3. and the packages: tidyverse, readxl, performance, tableone, gtools, MASS, bootStepAIC, lmtest, rpart and car. When relevant, data and all linear model residuals were tested for normality using stats::shapiro.test. A Friedman Test was used to analyze pharmacokinetics data and differences between responders and non-responders were analyzed using Mann–Whitney and Kruskal–Wallis’s rank sum tests. Baseline vs follow-up metabolite changes were analyzed using Wilcoxon tests.To identify factors associated with positively responding to KBs supplementation, we evaluated the relevance of different combinations of independent predictors according with the explanatory capacity of each model Akaike’s Information Criterion (AIC), the consistency of their coefficient signs, and the consistency of their statistical relevance. This procedure was performed via a bootstrap AIC consistency diagnosis in which 100 independent samples drawn at random from the dataset using Finally, we used supervised machine-learning regression trees to identify potentially useful cutoffs for relevant predictors using 