## 3 Statistical Analysis  
The Shapiro-Wilk test will be used to check for the normal distribution of continuous data. Normally distributed variables will be presented in mean \(\pm\) standard deviation (SD), and skewed distribution will be reported as a median and inter-quartile range. [PERSON]'s test will be used for the comparison of homogeneity of variance.  
The principal analysis compares the primary outcome between the two trial groups at months 3, 6, and 9. First, the difference between the groups in the mean change from baseline to month 3 in the peak VO\({}_{2}\) will be analyzed using [PERSON]'s test. Second, the peak VO\({}_{2}\) at 3 months will be assessed using an analysis of the covariance model, taking into account baseline VO\({}_{2}\).  
The principal secondary analysis is a comparison of the comprehensive assessment of the efficiency of HCR rated by workload duration during the CPET, 6-MWT distance, psychological parameters evaluating the quality of life, NT-pro NBP, parameters of the LV diastolic function (E/A, E/e', myocardial strain rate--strain rate), right ventricular systolic pressure, the gradient in the left ventricle, and laboratory parameters (e.g., creatinine, morphology) between months 0 and 3. A random-effects pattern will be used to account for repeated measures within participants. Progress of heart failure will be gauged based on changes in mean values. There is no plan for the correction of multiple comparisons of secondary outcomes. These results will be presented as point estimates with unadjusted 95% confidence intervals without \(p\) values.  
The sample size calculation was performed with the assumption of a significance level of \(p\) = 0.05, two-sided testing, and the expected mean increases in peak VO\({}_{2}\) (over 3 months) in the intervention group by 10% (1.9 mL \(\pm\) 2.6 mL/kg/min) and in the control group by 0.5% (0.10 \(\pm\) 1.9 mL/kg/min). Two-sample Satterthwaite \(t\)-test for mean differences with the above assumptions and a sample of 54 people in total (27 patients in the intervention and control groups) gives the power of 81.2% to achieve a statistically significant result. Considering the possibility of a 10% loss of participants during the trial, the total number of participants was increased to 60 people.  
We will also be analyzing the between-groups differences in the other variables. We will use appropriate parametric and nonparametric statistics to compare the other outcomes. Categorical variables will be summed up as absolute frequencies and percentages. Relation between them will be carried out by [PERSON]'s \(\chi\)2 test with continuity correction or [PERSON]'s exact test if the expected cell count is less than 5.  
Multivariate analysis: multiple binomial or ordinal logistic regression analyses will be applied to examine associations between individual factors (e.g., sex, age, etc.) and secondary endpoints (e.g., hospitalizations due to heart failure aggravation, NYHA class, etc.). Adjusted for confounders, odds ratios (OR) with an adequate 95% confidence interval (CI) will be counted. Patterns will be assessed by calculating the area under the receiver-operating characteristic curve (ROC, C-statistic).  
The probability of free events survival by randomized arm will be graphically displayed by the method of Kaplan-Meier, with a comparison of cumulative events by the log-rank test. Multivariate analysis will be performed using Cox proportional hazards regression modeling.  
All statistical assumptions will be two-tailed, and the type I error rate will be 5%. Statistical analyses will be carried out using SAS software release 9.4. (SAS Institute Inc., Cary, NC, USA).