*2.7. Statistical Analysis*

Analyses were performed in the per-protocol (PP) data set, which included all participants who completed the 6-week study period and underwent tests #1 and #2. The sample size was calculated for an expected mean difference between groups in serum levels of MDA of 1.34 nmol/mL with a standard deviation of 1.6 nmol/L according to data of Krotkiewsky et al. [23], so that for a significance level of 5% and statistical power of 80% assuming a drop-out rate of 10% since the primary analysis was performed in the PP data set, 20 evaluable participants for each treatment group were required. Categorical variables were expressed as frequencies and percentages, and continuous variables as mean and standard error (SE). Mean differences and 95% confidence intervals (CI) were calculated for changes between data at 6 weeks as compared with baseline. The chi-square (χ2) test

or the Fisher's exact probability test was used for the comparison of categorical variables between the probiotic and placebo groups. Quantitative variables were assessed using the analysis of variance (ANOVA) for repeated measures with three factors: time (baseline and final), test (test #1 and test #2) as within-subject factors and intervention (probiotic and placebo) as between-subject factor, with Bonferroni's correction for pairwise comparisons.

In the case of microbiome analysis, alpha diversity was conducted using the vegan package, and statistical significance analyzed with the ANOVA test. The DESeq2 package from R (R Core Team, 2012) was used to generate a generalized linear model with fixed effects with negative binomial family, and the Wald test was used to compare operational taxonomic unit (OTU) counts between groups.

Statistical significance was set at *p* < 0.05. The SPSS software version 21.0 (IMB Corp., Armonk, NY, USA) was used for statistical analysis.
