Models for predicting sleep latency and sleep duration

Study Objectives: Planning effective sleep-wake schedules for civilian and military settings depends on the ability to predict the extent to which restorative sleep is likely for a specified sleep period. Here, we developed and validated two mathematical models, one for predicting sleep latency and a second for predicting sleep duration, as decision aids to predict efficacious sleep periods. Methods: We extended the Unified Model of Performance (UMP), a well-validated mathematical model of neurobehavioral performance, to predict sleep latency and sleep duration, which vary nonlinearly as a function of the homeostatic sleep pressure and the circadian rhythm. To this end, we used the UMP to predict the time course of neurobehavioral performance under different conditions. We developed and validated the models using experimental data from 317 unique subjects from 24 different studies, which included sleep conditions spanning the entire circadian cycle. Results: The sleep-latency and sleep-duration models accounted for 42% and 84% of the variance in the data, respectively, and yielded acceptable average prediction errors for planning sleep schedules (4.0 min for sleep latency and 0.8 h for sleep duration). Importantly, we identified conditions under which small shifts in sleep onset timing result in disproportionately large differences in sleep duration-knowledge that may be applied to improve performance, safety, and sustainability in civilian and military operations. Conclusions: These models extend the capabilities of existing predictive fatigue-management tools, allowing users to anticipate the most opportune times to schedule sleep periods.