Regression Models for the Estimation of Orcadian Rhythms in the Presence of Effects Due to Masking

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Abstract
The estimation of human circadian rhythms from experimental data is complicated by the presence of “masking” effects associated with the sleep-wake cycle. The observed rhythm may include a component due to masking, as well as the endogenous component linked to a circadian pacemaker. In situations where the relationship between the sleep-wake cycle and the circadian rhythm is not constant, it may be possible to obtain individual estimates of these two components, but methods commonly used for the estimation of circadian rhythms, such as the cosinor analysis, spectral analysis, average waveforms and complex demodulation, have not generally been adapted to identify the modulations that arise from masking. The estimates relate to the observed rhythms, and the amplitudes and acrophases do not necessarily refer to the endogenous rhythm. In this paper methods are discussed for the separation of circadian and masking effects using regression models that incorporate a sinusoidal circadian variation together with functions of time since sleep and time during sleep. The basic model can be extended to include a time-varying circadian rhythm and estimates are available for the amplitude and phase at a given time, together with their joint confidence intervals and tests for changes in amplitude and acrophase between any two selected times. Modifications of these procedures are discussed to allow for non-sinusoidal circadian rhythms, non-additivity of the circadian and time-since-sleep effects and the breakdown of the usual assumptions concerning the residual errors. This approach enables systematic masking effects associated with the sleep-wake cycle to be separated from the circadian rhythm, and it has applications to the analysis of data from experiments where the sleep-wake cycle is not synchronized with the circadian rhythm, for example after time-zone transitions or during irregular schedules of work and rest.