The Combination of Topological Data Analysis and Mathematical Modeling Improves Sleep Stage Prediction From...

Wearable devices have become commonplace tools for tracking behavioral and physiological parameters in real-world settings. Nonetheless, the practical utility of these data for clinical and research applications, such as sleep analysis, is hindered by their noisy, large-scale, and multidimensional characteristics. Here, we develop a neural network algorithm that predicts sleep stages by tracking topological features (TFs) of wearable data and model-driven clock proxies (CPs) reflecting the circadian propensity for sleep. To evaluate its accuracy, we apply it to motion and heart rate data from the Apple Watch worn by young subjects undergoing polysomnography (PSG) and compare the predicted sleep stages with the corresponding ground truth PSG records. The neural network that includes TFs and CPs along with raw wearable data as inputs shows improved performance in classifying Wake/REM/NREM sleep. For example, it shows significant improvements in identifying REM and NREM sleep (AUROC/AUPRC improvements >13% and REM/NREM accuracy improvement of 12%) compared with the neural network using only raw data inputs. We find that this improvement is mainly attributed to the heart rate TFs. To further validate our algorithm on a different population, we test it on elderly subjects from the Multi-ethnic Study of Atherosclerosis cohort. This confirms that TFs and CPs contribute to the improvements in Wake/REM/NREM classification. We next compare the performance of our algorithm with previous state-of-the-art wearable-based sleep scoring algorithms and find that our algorithm outperforms them within and across different populations. This study demonstrates the benefits of combining topological data analysis and mathematical modeling to extract hidden inputs of neural networks from puzzling wearable data.