Statistical analysis
Statistical data were reported as mean ± standard deviation (SD) for continuous variables and frequency and percentage for categorical variables. Quantitative variables were studied using analytical method in order to test if data were normally distributed (Kolmogorov–Smirnov/Shapiro–Wilk test). Chi square test was used to compare frequency between categorical variables. Fisher test was applied when expected frequency was < 5. For comparisons between groups (VLCKD and HBD) t-test for independent samples or the Mann–Whitney test were used if they did not respect normality; to evaluate the pre-post treatment within the group, t-test was used for paired samples or the Wilcoxon test if they did not respect the normality. Due to the exploratory nature of the study, no correction for multiple comparisons was applied. Given the high dropout rate, especially in the control group, a sensitivity analysis was performed to evaluate the presence of attrition bias.The level of significance was set at p < 0.05. Statistical analyses were performed using the Statistical Package for Social Sciences (SPSS) software (version 28, IBM, Armonk, New York, NY, USA).