An Investigation of the Relationship between the Apnoea Hypopnoea Index and Apnoea Hypopnoea Duration per Hour

A number of automated apnoea hypopnoea index (AHI) prediction algorithms first divide the signal(s) of interest into epochs, make a prediction for each epoch, determine the number of epoch predictions per hour and map this to an AHI value. An underlying assumption of this approach is a smooth relationship between the apnoea plus hypopnoea duration and the AHI value. In this study we investigate this relationship to establish if this assumption impacts the final system. We compare two models: one which divides the duration by recording time, and the second which divides the duration by sleep time. Data for study was obtained from 200 scored overnight polysomnogram recordings. Our results show that the relationship is a power-law distribution with an exponent of 0.9 and a multiplicative noise term. Analysis of the variance of the noise term revealed that algorithms that scale the apnoea duration by the recording time will have an inherent 37% error in the AHI estimate, while algorithms that scale by sleep time will have an inherent 25% error in the AHI estimate. Receiver operator curve (ROC) analysis of the duration-based models at the clinically important values of AHI 5 and 15 revealed an area under the ROC of greater than 0.96. We conclude that epoch-based models for AHI estimation do have an inherent error in their estimates, with models that divide the duration by sleep time providing a better estimate. Both models can correctly identify normal and apnoeic patients at the clinically important values with high sensitivity and specificity.