2.7. Statistical Analysis 
failure of the mixed models, depression
REGRESSION
All efficacy analyses were conducted according to randomized assignment (ITT principle). Both intervention groups were compared by visit using descriptive statistics, multivariable mixed models corrected for the stratification factors sex and site, and visits, allocated arms, and interactions between visits and allocated arms (or non-parametric Wilcoxon test in the case of failure of the mixed models) (post hoc analyses). Parameters for longitudinal analyses were estimated using either the non-linear mixed model (Gompertz) or the linear mixed model for repeated measurements (MMRM) corrected for individuals’ chronological age (log-transformed, when necessary) and stratification factors. Analyses were performed to compare the non-randomized breastfed reference group with the two randomized arms, providing the descriptive statistics and inferential analyses conducted (superiority, two-sided) using mixed models (linear and non-linear) corrected for the stratification factors, visits, allocated arms, and interactions between visits and allocated arms and weighted by the estimated inverse propensity score (PS) of being breastfed (1/PS for breastfed infants and 1/(1-PS) for formula-fed infants). The score was calculated with a logistic regression on breastfed/not breastfed explained using the baseline covariates maternal marital status, family income, maternal full-scale IQ estimate (WASI-II), number of siblings, highest level of education (mother, father, or any adult living with the child), father living with child, and maternal depression score (EPDS) at 6 weeks postpartum. When mixed models were not appropriate even after data log transformation (residues not following a normal distribution or failure to converge), a non-parametrical Wilcoxon test was applied disregarding the propensity score adjustment.Associations between the MRI outcomes and clinical outcomes were listed as exploratory endpoints and evaluated using Spearman correlation (adjusted for the false discovery rate with the Benjamini–Hochberg method applied on all 