Statistical analysis
Based on data from previous studies [All analyses were conducted in both the ITT and completer samples. A mixed-effects model was used to assess the effects of diet programs on the change in BMI, and an autoregressive correlation matrix was used to correct within-participant correlation for repeated measurements. In this model, participants were assumed to be random effects and intervention group, time and their 2-factor interactions, age, center, and sex were assumed to be estimable fixed effects that can be estimated. The PROC MIXED component of the SAS statistical software, version 9.4 (SAS Institute Inc.), was used to obtain point estimates and standard errors (SEs) of the treatment effects and to test for differences between treatments. Multiple imputations for missing data in the multivariable analyses were conducted using the Markov Chain Monte Carlo method. To determine the significant main effects and interactions between carbohydrates and calories, data were analyzed using factorial design ANOVA and two-way ANOVA using the general linear model procedures of SAS (Cary, NC). ANOVA results are presented in figure legends. When the interaction was not significant, the main effects were evaluated to assess the significance of the individual factors. Group differences in the study outcomes were evaluated using the general linear model for continuous variables and the chi-squared test for categorical variables. Data were presented as least-squares means with 95% confidence intervals (CIs) unless otherwise indicated. 