Nonparametric Signal Extraction and Measurement Error in the Analysis of Electroencephalographic Activity During Sleep

Abstract

We introduce methods for signal and associated variability estimation based on hierarchical nonparametric smoothing with application to the Sleep Heart Health Study (SHHS). SHHS is the largest electroencephalographic (EEG) collection of sleep-related data, which contains, at each visit, two quasi-continuous EEG signals for each subject. The signal features extracted from EEG data are then used in second level analyses to investigate the relation between health, behavioral, or biometric outcomes and sleep. Using subject specific signals estimated with known variability in a second level regression becomes a nonstandard measurement error problem. We propose and implement methods that take into account cross-sectional and longitudinal measurement error. The research presented here forms the basis for EEG signal processing for the SHHS.

Figure 1

Proportion of sleep EEG δ-power for two subjects at the baseline and second visit estimated in 30-s intervals. The smooth line is the penalized spline estimator of the mean function using 100 knots and a thin-plate spline basis. The 95% pointwise CIs are shown as shaded areas.

Figure 2

Scatterplots of B = 10,000 bootstrap samples of 5 characteristics of the mean percent δ power function for the subject in the bottom/left panel of Figure 1.

Figure 3

Baseline versus visit 2 (roughly 5 years later) estimated mean sleep EEG δ-power for 2,993 subjects from SHHS. The line is the 45 degree line.

Figure 4

Three simulated datasets using the mean function (8) in Section 6 and the three different levels of noise. The solid line indicates the true mean function, whereas the circles are 300 noisy observations around the mean function.

Figure 5

Comparing the estimation error of functional features using the smoothing method described in Section 4 (solid line) with the naive approach (dashed line) that uses the observed data instead of the smooth data for feature extraction. In each panel, the amount of noise increases from left to right from 0.1 to 0.25 to 0.5. The letters C and N identify feature extraction based on smoothing and data, respectively, whereas the digits correspond to the amount of noise.

Figure 6

Distribution of estimation error of the location of the maximum. The solid line corresponds to the smoothing method described in Section 4. The dashed line corresponds to the naive approach that uses the observed data instead of the smooth data for feature extraction.

Figure 7

Effect of measurement error on the regression on maximum location of the δ-power spectrum and age using 500 subjects (no other covariates included).