Background: Continuous positive airway pressure (CPAP), the reference treatment for obstructive sleep apnoea (OSA), is used by millions of individuals worldwide with remote telemonitoring providing daily information on CPAP usage and efficacy, a currently underused resource. Here, we aimed to implement state-of-the-art data science methods to describe heterogeneity and diversity of time-series of residual apnoea-hypopnoea indexes (rAHI) from CPAP telemonitoring. Methods: We analysed a CPAP telemonitoring database to model and cluster rAHI trajectories. Our primary objective was to use Hidden Markov models (HMMs) as a probabilistic model-based approach to extract features from rAHI time-series. Secondary goals were to identify clusters of rAHI trajectories and their relation to CPAP treatment outcomes, adherence and leaks. Findings: From telemonitoring records of 2,860 CPAP-treated patients (age: 66·31 ± 12·92 years, 69·9% male), HMM modelling revealed three states differing in variability within a given state and probability of shifting from one state to another. Six clusters of rAHI trajectories were identified ranging from well controlled CPAP-treated patients (Cluster 0: 669 (23%); mean rAHI 0·58 ± 0·59 events/hour) to the most unstable (Cluster 5: 470 (16%); mean rAHI 9·62 ± 5·62 events/hour). CPAP adherence was 30 minutes higher in cluster 0 compared to clusters 4 and 5 (p-value <0·01). Leaks were significantly more frequent in cluster 5. Interpretation: This new approach based on HMM might constitute the backbone for deployment of digital health solutions improving the interpretation of telemonitoring data from CPAP-treated patients. Funding Information: JLP, SB, and RT are supported by the French National Research Agency in the framework of the Investissements d’avenir” program (ANR-15-IDEX-02) and the “e-health and integrated care and trajectories medicine and MIAI artificial intelligence” Chairs of excellence from the Grenoble Alpes University Foundation (ANR-19-P3IA-0003). AM is supported by Probayes and MIAI in the framework of a “Convention Industrielle de Formation par la Recherche” (CIFRE) PhD. The PhD is also supported by the French National Research Agency (grant 2020/0007). Declaration of Interests: JLP reports grants from Air Liquide Foundation, grants and personal fees from Agiradom, grants and personal fees from AstraZeneca, grants from Fisher and Paykel, grants from Mutualia, grants and personal fees from Philips, grants and personal fees from Resmed, grants from Vitalaire, grants from Boehringer Ingelheim, grants from Jazz Pharmaceuticals, grants from Night Balance, grants from Sefam, outside the submitted work; JCB is employee of AGiR-a-dom, a French home-care provider; RT reports other from AGiR-a-dom, grants from Resmed, outside the submitted work; AM, RLH and MCS report other from AGiR-a-dom, and SB have no conflict of interest directly related to this work. Ethics Approval Statement: We analysed a CPAP telemonitoring database [registered and ethically approved by the French C.C.T.I.R.S: N°15.925bis and ethics regulations MR003 N° 1996650v0] to model and cluster patients’ rAHI trajectories.