## 2 Materials and Methods  
The design and main results of the TELEREH-HF study have been published elsewhere [16; 17]. The TELEREH-HF trial was a randomized (1:1), multi-center (5 centers in Poland), prospective, open-label, parallel-group, controlled study (Clinical Trials.gov NCT 02523560) that compared HCTR plus usual care (UC) with UC alone in 850 clinically stable HF patients (New York Heart Association (NYHA) class I, II, or III) with left ventricular ejection fraction ( LVEF) \(\leq\) 40% after a hospitalization due to worsening HF within 6 monthsprior to randomization. The detailed TELEREH-HF inclusion and exclusion criteria were previously published elsewhere [16; 17]. This analysis regarding adherence to exercise training focuses on patients randomized to the HCTR arm. The HCTR intervention was multidisciplinary and consisted of telecare, personalized home-based telecrabilitation, and remote monitoring of cardiovascular implantable electronic devices. The HCTR group patients underwent a 9-week HCTR program consisting of an initial stage (1 week) in hospital and a basic stage (8 weeks) of HCTR performed at home, five times weekly. The HCTR was initiated during an in-hospital stay (five educational training sessions), and later on, the patients had to continue the remotely supervised exercise training at home (forty training sessions) over eight additional weeks combined with a multi-parameter telemonitoring. Exercise training was planned according to the published recommendations for HF patients [15; 18]. Patients underwent 3 training modalities: endurance aerobic training based on Nordic walking, respiratory muscle training, and light resistance and strength training (Supplementary Materials Table S1). A medical team (physicians, physiotherapists, nurses, and psychologists) was responsible for conducting the training sessions and interactive collaboration with patients. The equipment for telemonitoring consisted of a remote device for tele-ECG-monitoring and supervising exercise training (the telecrabilitation set), a mobile phone, and the IT platform in a monitoring center. An EHO mini device is adjusted to register fragments of ECG (electrocardiographic) recording from three precordial leads and to transmit the data via a mobile phone network to the monitoring center. This device has training sessions preprogrammed individually for each patient (defined exercise duration, breaks, timing of ECG recording). The moments of automatic ECG registration are preset and coordinated with the exercise training [16; 17]. The HCTR group patients, before each training session (performed at home), were contacted via mobile phone by the nurse from the monitoring center and answered a series of questions regarding present symptoms and confirmed if they were taking any prescribed medications. Then patients transmitted their resting ECG, blood pressure, and body mass data to the monitoring center. If no contraindications to exercise training were found, patients received consent to start their training session. The ECGs were automatically recorded during the training session and transmitted to the monitoring center. After each training session, all data were evaluated in the monitoring center, and the physiotherapist contacted the patients to assess the patients' subjective perceived exertion on the Borg scale. Based on the data sent by patients, consultants were able to make further decisions. A detailed description of the equipment and the intervention, including telesupervised exercise training, has been published elsewhere [16; 17]. The study was guided by good clinical practice, in accordance with the Declaration of Helsinki and the regulations applicable in Poland. The trial protocol was approved by the local ethics committee (IK-NP-0021-85/1402/13). Each patient provided written informed consent [16; 17].