*2.6. Statistical Analysis*

Hierarchical regression models were implemented in R to estimate the effects of dietary consumption of fructose on the volume of the hippocampus and its connectivity with the rest of the brain. The dependent variables for the volume of the hippocampus included the following regions of interest (ROIs): (i) Whole hippocampus, (ii) CA1, (iii) CA2/3, (iv) CA4, (v) DG/GC/ML, (vi) subiculum. Left and right values were tested separately for a total of 12 tests, which led to a per-test p-value of 0.004 to reach an overall alpha of *p* < 0.05 using Bonferroni correction. The dependent variables for the connectivity between the hippocampus and the rest of the brain included the following tracts: (i) uncinate, (ii) fornix, (iii) cingulum–prefrontal section, and (iv) cingulum–temporal section. Left and right values were tested separately and MD and FA were tested separately for a total of 16 tests, which led to a per-test p-value of 0.003 to reach an overall alpha of *p* < 0.05 using Bonferroni correction. Planned post-hocs included: testing the associations of dietary added sugar and glucose intake on brain metrics that showed evidence of being affected by fructose, and testing the effects of axial and radial diffusivity for any tests that showed significant effects in FA or MD. Associations of sugar consumption with total intracranial volume were also computed as a negative control.

Model 1 was the unadjusted model for percent calories from fructose. Model 2 included age and sex (and intracranial volume for analyses of the volume of the hippocampus). Model 3 included the child's BMI z-score. Model 4 included two categorical variables aimed at measuring socioeconomic status: the highest education level attained by the mother and the family income level. Model 5 included maternal measures that impact prenatal environment, i.e., gestational diabetes (binary) and pre-pregnancy BMI. As variables were added, an F-test was used to determine whether the newly added variables showed a significant improvement in R2. Semi-partial r values were calculated as an indication of effect size, where r < 0.1 is a small effect size, 0.1 < r < 0.3 is a medium effect size, and r > 0.3 is a large effect size.

Effects of Tanner stage and potential interactions with sex were tested as Models 2A and 2B respectively. If either or both were found to explain significantly more variance than Model 2, then models 3–5 included a covariate for Tanner stage and/or an interaction between the dietary measure and sex.
