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Objective: wearable sensor technology has progressed significantly in the last decade, but its clinical usability for the assessment of obstructive sleep apnea (OSA) is limited by the lack of large and representative datasets simultaneously acquired with polysomnography (PSG). The objective of this study was to explore the use of cardiorespiratory signals common in standard PSGs which can be easily measured with wearable sensors, to estimate the severity of OSA. Methods: an artificial neural network was developed for detecting sleep disordered breathing events using electrocardiogram (ECG) and respiratory effort. The network was combined with a previously developed cardiorespiratory sleep staging algorithm and evaluated in terms of sleep staging classification performance, apnea-hypopnea index (AHI) estimation, and OSA severity estimation against PSG on a cohort of 653 participants with a wide range of OSA severity. Results: four-class sleep staging achieved a κ of 0.69 versus PSG, distinguishing wake, combined N1-N2, N3 and REM. AHI estimation achieved an intraclass correlation coefficient of 0.91, and high diagnostic performance for different OSA severity thresholds. Conclusions: this study highlights the potential of using cardiorespiratory signals to estimate OSA severity, even without the need for airflow or oxygen saturation (SpO2), traditionally used for assessing OSA. Significance: while further research is required to translate these findings to practical and unobtrusive sensors, this study demonstrates how existing, large datasets can serve as a foundation for wearable systems for OSA monitoring. Ultimately, this approach could enable long-term assessment of sleep disordered breathing, facilitating new avenues for clinical research in this field.