Estimation of apnea-hypopnea index uncertainty in the presence of long wake bouts and overdispersion

<i>Objective.</i>In the analysis of obstructive sleep apnea (OSA), the main clinical index is the apnea-hypopnea index (AHI), or the average rate of respiratory events during sleep. This rate fluctuates during sleep, due to a variety of factors, such as sleep phases, body position, and other physiological mechanisms. Two people with the same AHI may manifest OSA may manifest OSA in drastically different ways. Therefore, a computed degree of statistical uncertainty alongside the average AHI would be a useful addition to a comprehensive sleep report-. In the current literature, the AHI uncertainty was modeled as a Poisson process and empirically estimated using bootstrap sampling of inter-event times (or intervals). However, we observed that long wake bouts, stochastic outliers in the intervals' distribution, and events' dispersion directly influence the bootstrap sampling, with either empirical over-estimation or theoretical under-estimation. In some cases, the result is a spurious empirical estimate of both AHI and its uncertainty. In others, a broad AHI uncertainty can be the correct description of the underlying process, and a Poisson model would be ill-fitted.<i>Approach.</i>We propose here three methods that improve the estimation of AHI uncertainty based on bootstrap sampling, making it more robust to the presence of spurious intervals caused by long wake bouts and events' overdispersion. We examine the violation of Poisson assumptions as the main cause of discrepancy between theoretical and empirical estimates, and propose the Negative Binomial distribution as an alternative model.<i>Main results.</i>Compared to the original Poisson-based method, we proved that the Negative Binomial can be a better theoretical model of uncertainty. Furthermore, our proposed methodology improved the estimation error of both AHI (up to 91% of the recordings) and the discrepancy with theoretical confidence intervals, in both Poisson and Negative Binomial models.<i>Significance.</i>This work provides notable improvements in the theoretical models of AHI uncertainty and in the robustness of empirical estimates.