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Studies have shown that algorithms based on single-channel airflow records are effective in screening for sleep-disordered breathing diseases (SDB). In this study, we investigate the diagnostic effectiveness of a classifier trained on a set of features derived from single-channel airflow measurements. The features considered are based on recurrence quantification analysis (RQA) of the measurement time series and are optionally augmented with single measurements of neck circumference and body mass index. The airflow measurement utilized is the nasal pressure (NP). The study used an overnight recording from each of 77 patients undergoing PSG testing. Mixture discriminant analysis was used to obtain a classifier, which predicts whether or not a measurement segment contains an SDB event. Patients were diagnosed as having SDB disease if the recording contained measurement segments predicted to include an SDB event at a rate exceeding a threshold value. A patient can be diagnosed as having SDB disease if the rate of SDB events per hour of sleep, the respiratory disturbance index (RDI), is ≥15 or sometimes ≥5. Here we trained and evaluated the classifier under each assumption, obtaining areas under receiver operating curves using fivefold cross-validation of 0.96 and 0.93, respectively. We used a two-layer structure to select the optimal operating point and assess the resulting classifier to avoid unbiased estimates. The resulting estimates for diagnostic sensitivity/specificity were 71.5%/89.5% for disease classification when RDI ≥ 15 and 63.3%/100% for RDI ≥ 5. These results were found assuming that the costs of misclassifying healthy and diseased subjects are equal, but we provide a framework to vary these costs. The results suggest that a classifier based on RQA features derived from NP measurements could be used in an automated SDB screening device.