Two studies for analyzing healthcare time-series with the ordinary differential equation model and the variants of the Gaussian processes

Abstract

Healthcare outcomes are commonly tracked across time owing to technological advances in wearable devices. This advance then makes it possible to predict health risks and to practice personalized medicine. For this type of healthcare data, it is important to reflect huge variation among subjects where the subject becomes an experimental unit. In this paper, we propose personalized analyses for two healthcare data, sleep-wake patterns, and heart rates. First, for sleep-wake patterns of shift workers measured with wearables, analysis is conducted by developing a computational package that simulates homeostatic sleep pressure –physiological need for sleep– and the circadian rhythm. This reveals that shift workers who align sleep-wake patterns with their circadian rhythm have lower daytime sleepiness, even if they sleep less. The alignment, quantified by the new sleep parameter, circadian sleep sufficiency, can be increased by dynamically adjusting daily sleep durations according to varying bedtimes. Our computational package provides flexible and personalized real-time sleep-wake patterns for individuals to reduce their daytime sleepiness. Second, for heart rate data of the cardiac surgery recovery unit, we extend a deep mixed effect model via a mixture of deep mixed effects models. It has been demonstrated that sharing information across subjects via a mixed effect model can improve the prediction of individual responses. However, sharing information across all patients can dilute signals when there are several different patterns present in the data. Our mixture of deep mixed effect models captures a highly nonlinear trend shared among segments of patients while clustering patients with similar trends into groups. Our approach shows great performance in simulation studies as well as real heart rate data analysis, emphasizing the importance of modeling group-specific trends when making accurate predictions from healthcare time-series data.