Obstructive sleep apnoea (OSA) is a significant public health problem, with comorbidities including excessive daytime sleepiness, increased risk of motor vehicle accidents, cardiovascular disease, cognitive impairment, and decreased quality of life. OSA is characterised by intermittent periods of pharyngeal obstruction resulting in the absence (apnoea) or reduction (hypopnoea) of airflow during sleep. OSA severity is currently reported by the apnoea-hypopnoea index (AHI): the frequency of apnoeas and hypopnoeas per hour of sleep. However, the AHI is a poor predictor of an individual's day to day performance, symptomology and long-term health outcomes. This is likely due to a limitation with the event-based AHI, which inadequately describes the underlying neuro-mechanical airway resistance that leads to pharyngeal obstruction, and as such, does not capture the severity of airflow obstruction. Therefore, the overarching goal of this thesis is to develop non-invasive methods to objectively characterise the severity of airflow obstruction on a breath-by-breath basis. Previous literature has identified characteristics within the airflow signal that may indicate airflow obstruction. However, analysis of these features on a breath-by-breath basis requires accurate demarcation of "breath timing" (i.e. inspiratory and expiratory phases). As such, the first aim of this thesis was to develop methods that accurately demarcate breaths. We segmented breaths into inspiratory (TI, shortest period achieving 95% inspiratory volume), expiratory (TE, shortest period achieving 95% expiratory volume), and an inter-breath transition period (TTrans, the period between TE and subsequent TI). In a cohort of 37 patients with an epiglottic pressure catheter, we observed that compensatory increases in the inspiratory period (1.57±0.27 vs 1.74±0.27 seconds, mean±SD, P≤0.001) from reference breaths to partial airway obstruction (identified by increasing epiglottic pressure swings without increasing airflow) were primarily explained by reductions in the inter-breath transition period (0.82±0.28 vs 0.59±0.21 seconds, mean±SD, P≤0.001) and not by reduction of the expiratory airflow period (1.68±0.32 vs 1.60±0.25 seconds, mean±SD, P≤0.05). In addition to developing a method for demarcating breaths, we also identify TTrans as a novel feature associated with increased airway obstruction. Using our newly developed breath timing method in conjunction with the other known markers of flow limitation, we then aimed to characterise the flow shape of individual breaths to develop a transparent machine learning strategy for the non-invasive quantification of the severity of airflow iii obstruction. We defined gold-standard obstruction severity as the ratio of oronasal pneumotach (flow) and ventilatory drive (calibrated intra-oesophageal diaphragm EMG, drive), presented as a continuous breath-by-breath variable, flow:drivemeasured. Multivariable linear regression used noninvasive flow-shape features (inspiratory/expiratory timing, flatness, scooping, flutter...