Sample size and statistical analysis
The sample size calculation was performed using the statistical software Epidat 4.2. It was calculated to detect the smallest significant effects on the main variable. Assuming a large intervention effect using an F test with two tails (0.5), an alpha error of 0.05, 80% power, and accounting for a dropout rate of 10%, it was determined that two groups of 80 subjects each would be required. Additionally, after evaluating the data using the G*Power software (v. 3.1.9.7, Universität Kiel, Germany), we found an actual power of 0.96 in one of our main outcomes, specifically the SPPB score.To maintain the initial comparability between the groups, and to preserve the sample size while minimizing bias, an intention-to-treat analysis was employed. All data are presented as mean ± standard deviation (SD) or counts (percentages). The normality of continuous variables was assessed using the Kolmogorov–Smirnov test, the Levene test was used to check the homogeneity of variance and sphericity with the Mauchly test. A 2×2 mixed factorial analysis of variance (ANOVA) was used, with the group (intervention vs. control) as the between-subjects factor, and the time (pre-test vs. post-test) as the within-subject factor. Bonferroni post-hoc comparisons were applied. The effect size of each variable was tested using partial eta squared (η2p), with values of 0.01, 0.06, and 0.14 used to indicate small, medium, and large effects, respectively. After carefully examining potential confounding factors, we included sex, age, frailty phenotype, BMI and educational level as covariates in the analysis. Deltas, representing the changes from post-intervention values to post-intervention values, were calculated for the key parameters as post-intervention values minus pre-intervention values. These changes were then compared between groups using either an independent sample t-test or a Mann–Whitney U-test, depending on the normality distribution of the variables. Furthermore, an Quade’s analysis of covariance (Quade’s ANCOVA) was conducted, employing the same covariates as in the previous analysis. All statistical analyses were performed using IBM SPSS Statistics version 26 software (SPSS Inc., Chicago, IL, United States) and STATA 13.0 (StataCorp LLC, Texas, United States). The significance level was set at 