Background and objective: Sleep Apnea Syndrome (SAS) is a multimorbid chronic disease with individual and societal deleterious consequences. Polysomnography (PSG) is the multi-parametric reference diagnostic tool that allows a manual quantification of the apnea-hypopnea index (AHI) to assess SAS severity. The burden of SAS is affecting nearly one billion people worldwide explaining that SAS remains largely under-diagnosed and undertreated. The development of an easy to use and automatic solution for early detection and screening of SAS is highly desirable. Methods: We proposed an Accelerometry-Derived Respiratory index (ADR) solution based on a dual accelerometry system for airflow estimation included in a machine learning process. It calculated the AHI thanks to a RUSBoosted Tree model and used physiological and explanatory specifically developed features. The performances of this method were evaluated against a configuration using gold-standard PSG signals on a database of 28 subjects. Results: The AHI estimation accuracy, specificity and sensitivity of the ADR index were 89%, 100% and 80% respectively. The added value of the specifically developed features was also demonstrated. Conclusion: Overnight physiological monitoring with the proposed ADR solution using a machine learning approach provided a clinically relevant estimate of AHI for SAS screening. The physiological component of the solution has a real interest for improving performance and facilitating physician's adhesion to an automatic AHI estimation.