Initial Condition Decision to Ensure Reliable Circadian Phase Estimation with Shorter-Term Wearable Data

Various studies in the medical field highlight the importance of circadian medicine, which optimizes treatment timing based on patients circadian phases. While the circadian phase has been measured using dim light melatonin onset (DLMO), the gold standard marker, its high cost and time-intensive nature have led to the development of alternative estimation methods. Among these, the most promising method is using ordinary differential equation (ODE) models, which simulate the circadian rhythm by using a light exposure profile estimated from sleep data. These ODE models require an initial condition (IC) representing the initial state of the circadian rhythm, which is unknown in real-world settings. However, it is unclear how the uncertainty of IC affects the accuracy of circadian phase estimation. In this study, by using sleep data collected from 28 shift workers using ActiWatch (mean duration = 56 days, range = 34-75 days), we found that [≥]18 days of sleep data are required for the circadian phase to become independent of the subjective IC choice. The result showed that without an accurate IC, circadian phase estimation is dependent on subjective IC choice, meaning that circadian phase estimates in the first 17 days are not reliable. Indeed, these days were reduced to 13 - 15 days on average when previous studies IC estimation methods were used. To further shorten this length, we developed new IC estimation methods--period- and work history-based sleep methods--that incorporate daily variations in sleep history. Notably, the new methods reduced the number of days required for reliable circadian phase estimation to about seven days. Hence, our approach allows a larger portion of circadian phase estimates from given sleep data to be used as reliable information. The superiority of our methods paves the way for improved circadian phase estimation, ultimately enhancing the practicality of chronotherapy applications.