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Sleep is important for daily wellbeing and long-term health. Obstructive sleep apnea (OSA) is a common sleep disorder that deteriorates sleep quality and has various adverse health effects. OSA is caused by repetitive partial or complete obstruction of the upper airways during sleep, leading to hypopneas or obstructive apneas respectively, typically followed by oxygen desaturations and arousals. Despite several limitations, the severity of obstructive sleep apnea (OSA) is typically measured using the apnea-hypopnea index (AHI), which counts the number of obstructive apneas and hypopneas per hour of sleep. Monitoring the AHI is useful during OSA treatment, as it provides an indication of whether respiratory events are adequately addressed, or, in case it increases, that therapy might require adjustments. Ideally, sleep itself should also be monitored during treatment, but this is not yet feasible. Positive airway pressure (PAP) is an often-used therapy for OSA. Typically, PAP devices also monitor the AHI by analysing the airflow signal, but do not assess sleep itself. Besides PAP therapy, alternative OSA treatments have been developed. An interesting alternative therapy targets specifically positional OSA, a phenotype where apnea and hypopnea events predominantly occur in supine posture. Positional therapy (PT) devices use a chest-worn accelerometer to assess posture and provide haptic feedback to avoid the supine position, reducing the burden of OSA. However, PT devices currently lack AHI measurement, as they typically are not able to measure airflow, and thus, miss a direct indication of decreased or interrupted breathing. This thesis focuses on the development of a method to assess sleep and estimate the AHI using chest-wall accelerometry. The first part of the thesis explores the development of novel techniques to extract cardiorespiratory metrics from a chest-worn accelerometer, focusing on reliability during overnight use by patients with sleep disorders. Chapters 1 and 2 introduce novel methods to estimate respiratory effort. In chapter 1, respiratory effort is estimated using an adapted version of principal component analysis, which leads to results with substantially lower error than state-of-the-art methods for estimating respiratory effort in healthy individuals. To further improve performance and robustness in larger, sleep-disordered breathing populations, chapter 2 introduces a novel regression method based on a convolutional neural network. This method shows a further reduction of error in estimating respiratory effort, even in the presence of sleep disorders. Chapter 3 presents a novel method for heartbeat localization and inter-beat interval estimation. The method utilizes maximum a posteriori estimation, and an optimal solution is approximated by means of a Markov decision process. The second part of the thesis investigates how methods, originally designed for estimating sleep stages and AHI from cardiorespiratory signals, obtained with electrocardiography (ECG) and respiratory belts, can also work with signals derived from a chest-worn accelerometer. In chapter 4, we investigate whether a neural network for cardiorespiratory sleep staging can be applied to the signals derived from a chest-worn accelerometer. We show that total sleep time, required for the computation of the AHI, can be computed accurately, and that estimated sleep stages show substantial agreement with those scored from polysomnography. In chapter 5, we adapt a neural network for AHI estimation from cardiorespiratory metrics to the specific characteristics of chest-wall accelerometry by means of transfer learning. The estimated AHI and corresponding severity classification reach a high correlation and show substantial agreement with that scored from polysomnography. In summary, the work presented in this thesis significantly advances the performance and robustness of estimation of cardiorespiratory metrics from chest-wall accelerometry, which allow for the accurate estimation of sleep stages and AHI. This work has several applications, for example enabling the use of chest-wall accelerometry for monitoring of residual AHI during therapy for positional OSA. Furthermore, implementation in diagnostic devices such as those for extended Holter monitoring could expand the yield of those investigations to include sleep apnea screening.