Conditional Spectral Analysis of Replicated Multiple Time Series With Application to Nocturnal Physiology

• Published in: Journal of the American Statistical Association Vol. 112; no. 520; pp. 1405 - 1416
• Main Authors: Krafty, Robert T., Rosen, Ori, Stoffer, David S., Buysse, Daniel J., Hall, Martica H.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 02.10.2017; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Algorithms; Applications and Case Studies; Arousal; automation; Bayesian analysis; Biological activity; Circadian rhythm; Coherence; Computer simulation; elderly; Geometric constraints; geometry; Heart rate variability; Markov analysis; Markov chain; Markov chains; Mathematical analysis; Matrix methods; MCMC; medicine; Monte Carlo method; Monte Carlo simulation; Multivariate time series; Older people; Physiology; Power; Power spectra; Regression analysis; Sleep; Smoothing spline; Spectral analysis; Spectrum analysis; Statistical methods; Statistics; Tensor-product ANOVA; Tensors; Time series; time series analysis; Whittle likelihood; Multivariate Time Series; Whittle Likelihood; Smoothing Spline; Tensor-Product ANOVA; Bayesian Analysis; Sleep; Coherence; MCMC; Spectral Analysis; Heart Rate Variability
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2017.1281811

This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine, where researchers are able to noninvasively record physiological time series signals during sleep. The frequency patterns of these signals, which can be quantified through the power spectrum, contain interpretable information about biological processes. An important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics; these connections are key to understanding biological pathways through which sleep affects, and can be treated to improve, health. Such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive-definite matrix-valued function. This article proposes a new approach to such analyses based on a tensor-product spline model of Cholesky components of outcome-dependent power spectra. The approach flexibly models power spectra as nonparametric functions of frequency and outcome while preserving geometric constraints. Formulated in a fully Bayesian framework, a Whittle likelihood-based Markov chain Monte Carlo (MCMC) algorithm is developed for automated model fitting and for conducting inference on associations between outcomes and spectral measures. The method is used to analyze data from a study of sleep in older adults and uncovers new insights into how stress and arousal are connected to the amount of time one spends in bed. Supplementary materials for this article are available online.