Measuring Variability in Rest-Activity Rhythms from Actigraphy with Application to Characterizing Symptoms of Depression
Open accessAbstract
The twenty-four hour sleep-wake pattern known as the rest-activity rhythm (RAR) is associated with many aspects of health and well-being. Researchers have utilized a number of interpretable, person-specific RAR measures that can be estimated from actigraphy. Actigraphs are wearable devices that dynamically record acceleration and provide indirect measures of physical activity over time. One class of useful RAR measures are those that quantify variability around a mean circadian pattern. However, current parametric and nonparametric RAR measures used by applied researchers can only quantify variability from a limited or undefined number of rhythmic sources. The primary goal of this article is to consider a new measure of RAR variability: the log-power spectrum of stochastic error around a circadian mean. This functional measure quantifies the relative contributions of variability about a circadian mean from all possibly frequencies, including weekly, daily, and high-frequency sources of variation. It can be estimated through a two-stage procedure that smooths the log-periodogram of residuals after estimating a circadian mean. The development of this measure was motivated by a study of depression in older adults and revealed that slow, rhythmic variations in activity from a circadian pattern are correlated with depression symptoms.
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People with clinically significant depressive symptoms have lower interdaily stability (IS) and higher intradaily variability (IV) of circadian activity rhythm.
“Few studies using nonparametric rhythm measures demonstrated that participants with more severe depressive symptoms had lower interdaily stability (IS) and higher intradaily variability (IV) of circadian activity rhythm [31,34], reduced relative amplitude (RA) between the highest and the lowest activity levels [28,35], and reduced RA of skin temperature [36].”
From Digital Biomarkers for Depression Screening With Wearable Devices: Cross-sectional Study With Machine Learning Modeling (2021) · cites this paper as [31]
A lower steps-based weekday IS was robustly associated with a greater severity of depressive symptoms independent of confounders.
“we found that a lower steps-based weekday IS—a nonparametric measure of rhythm regularity—was robustly associated with a greater severity of depressive symptoms independent of confounders”
From Digital Biomarkers for Depression Screening With Wearable Devices: Cross-sectional Study With Machine Learning Modeling (2021) · cites this paper as [31]
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Cites
Hamilton, M. (1960) · Journal of Neurology, Neurosurgery & Psychiatry · doi:10.1136/jnnp.23.1.56 · Cited by 32,817 · see citing works
‘Small Changes' to Diet and Physical Activity Behaviors for Weight Management
Hills, A. P., Byrne, N. M., Lindstrom, R. C., & Hill, J. O. (2013) · Obesity Facts · doi:10.1159/000345030 · Cited by 9,526 · see citing works
Physical Activity in the United States Measured by Accelerometer
TROIANO, R. P., BERRIGAN, D., DODD, K. W., MÂSSE, L. C., TILERT, T., & MCDOWELL, M. (2008) · Medicine & Science in Sports & Exercise · doi:10.1249/mss.0b013e31815a51b3 · Cited by 7,638 · see citing works
Wood, S. N. (2010) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2010.00749.x · Cited by 7,538 · see citing works
Least-squares frequency analysis of unequally spaced data
Lomb, N. (1976) · Astrophysics and Space Science · doi:10.1007/bf00648343 · Cited by 5,724 · see citing works
(2001) · doi:10.1017/cbo9780511546396 · Cited by 4,482 · see citing works
Nonlinear Regression Analysis and Its Applications
Bates, D. M., & Watts, D. G. (1988) · Wiley series in probability and statistics · doi:10.1002/9780470316757 · Cited by 4,017 · see citing works
The Role of Actigraphy in the Study of Sleep and Circadian Rhythms
Ancoli-Israel, S., Cole, R., Alessi, C., Chambers, M., Moorcroft, W., & Pollak, C. P. (2003) · Sleep · doi:10.1093/sleep/26.3.342 · Cited by 2,751 · see citing works
Time Series Analysis and Its Applications
Shumway, R. H., & Stoffer, D. S. (2010) · Springer texts in statistics · doi:10.1007/978-1-4419-7865-3 · Cited by 2,015 · see citing works
Severity classification on the Hamilton depression rating scale
Zimmerman, M., Martinez, J. H., Young, D., Chelminski, I., & Dalrymple, K. (2013) · Journal of Affective Disorders · doi:10.1016/j.jad.2013.04.028 · Cited by 1,199 · see citing works
Gu, C. (2013) · Springer series in statistics · doi:10.1007/978-1-4614-5369-7 · Cited by 891 · see citing works
Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves
Rice, J. A., & Silverman, B. W. (1991) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1991.tb01821.x · Cited by 877 · see citing works
Estimation and information in stationary time series
Whittle, P. J. L. (1953) · Arkiv för matematik · doi:10.1007/bf02590998 · Cited by 566 · see citing works
Circadian rest—activity rhythm disturbances in alzheimer's disease
Someren, E. J. W. V., Hagebeuk, E. E. O., Lijzenga, C., Scheltens, P., Rooij, S. E. J. A. D., Jonker, C., Pot, A. M., Mirmiran, M., & Swaab, D. F. (1996) · Biological Psychiatry · doi:10.1016/0006-3223(95)00370-3 · Cited by 453 · see citing works
Nonlinear Regression Analysis and Its Applications.
Kass, R. E., Bates, D. M., Watts, D. G., Seber, G. A. F., & Wild, C. J. (1990) · Journal of the American Statistical Association · doi:10.2307/2289810 · Cited by 397 · see citing works
Principal Components Analysis of Sampled Functions
Besse, P. C., & Ramsay, J. O. (1986) · Psychometrika · doi:10.1007/bf02293986 · Cited by 257 · see citing works
Automatic Smoothing of the Log Periodogram
Wahba, G. (1980) · Journal of the American Statistical Association · doi:10.1080/01621459.1980.10477441 · Cited by 236 · see citing works
Marler, M., Gehrman, P., Martin, J. L., & Ancoli‐Israel, S. (2005) · Statistics in Medicine · doi:10.1002/sim.2466 · Cited by 209 · see citing works
Dahlhaus, R. (2012) · Handbook of statistics · doi:10.1016/b978-0-444-53858-1.00013-2 · Cited by 208 · see citing works
Nonparametric methods in actigraphy: An update
Gonçalves, B. S. B., Cavalcanti, P., Tavares, G. R., Campos, T. F., & Araújo, J. F. (2014) · Sleep Science · doi:10.1016/j.slsci.2014.09.013 · Cited by 195 · see citing works
Wavelet thresholding techniques for power spectrum estimation
Moulin, P. (1994) · IEEE Transactions on Signal Processing · doi:10.1109/78.330372 · Cited by 160 · see citing works
Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis
Goldsmith, J., Zipunnikov, V., & Schrack, J. A. (2015) · Biometrics · doi:10.1111/biom.12278 · Cited by 140 · see citing works
Nonparametric Spectral Density Estimation Using Penalized Whittle Likelihood
Pawitan, Y., & O’Sullivan, F. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476785 · Cited by 123 · see citing works
Israel, B., Buysse, D. J., Krafty, R. T., Begley, A., Miewald, J., & Hall, M. (2012) · Sleep · doi:10.5665/sleep.2088 · Cited by 114 · see citing works
Self-citationWang, J., Xian, H., Licis, A., Deych, E., Ding, J., McLeland, J., Toedebusch, C. D., Li, T., Duntley, S. P., & Shannon, W. D. (2011) · Journal of Circadian Rhythms · doi:10.1186/1740-3391-9-11 · Cited by 72 · see citing works
Xiao, L., Huang, L., Schrack, J. A., Ferrucci, L., Zipunnikov, V., & Crainiceanu, C. M. (2015) · Biostatistics · doi:10.1093/biostatistics/kxu045 · Cited by 71 · see citing works
Morris, J. S., Arroyo, C., Coull, B. A., RYAN, L. M., Herrick, R. C., & Gortmaker, S. L. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000465 · Cited by 63 · see citing works
Localized Functional Principal Component Analysis
Chen, K., & Lei, J. (2015) · Journal of the American Statistical Association · doi:10.1080/01621459.2015.1016225 · Cited by 61 · see citing works
Smagula, S. F. (2016) · Current Opinion in Psychiatry · doi:10.1097/yco.0000000000000283 · Cited by 47 · see citing works
Self-citationSPECTRAL ANALYSIS OF ASYMPTOTICALLY STATIONARY TIME SERIES
Parzen, E. (1961) · Defense Technical Information Center (DTIC) · Cited by 46 · see citing works
Penalized multivariate Whittle likelihood for power spectrum estimation
Krafty, R. T., & Collinge, W. O. (2013) · Biometrika · doi:10.1093/biomet/ass088 · Cited by 33 · see citing works
Self-citationNonparametric spectral analysis with applications to seizure characterization using EEG time seriesPreprint
Li, Q., & Wang, Y. (2008) · Cited by 21 · see citing works
Nonparametric spectral analysis with applications to seizure characterization using EEG time series
Qin, L., & Wang, Y. (2008) · The Annals of Applied Statistics · doi:10.1214/08-aoas185 · Cited by 18 · see citing works
Nonparametric spectral analysis of heart rate variability through penalized sum of squares
Krafty, R. T., Zhao, M., Buysse, D. J., Thayer, J. F., & Hall, M. H. (2013) · Statistics in Medicine · doi:10.1002/sim.6038 · Cited by 12 · see citing works
Self-citation
Flagged first, then by citations
1 of the 35 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- [4]Cacioppo JT, Tassinary LG, Bernston G: Handbook of Psycholphysiology, 3 edn. Cambridge University Press, Cambridge (2007)
Cited by
Sorted by citations
Rykov, Y., Thach, T.-Q., Bojic, I., Christopoulos, G., & Car, J. (2021) · JMIR mHealth and uHealth · doi:10.2196/24872 · Cited by 151 · see citing works
Dopamine D1 and D2 receptors are distinctly associated with rest-activity rhythms and drug reward
Zhang, R., Manza, P., Tomasi, D. G., Kim, S. W., Kojori, E. S., Demiral, Ş. B., Kroll, D. S., Feldman, D. E., McPherson, K. L., Biesecker, C. L., et al. (2021) · Journal of Clinical Investigation · doi:10.1172/jci149722 · Cited by 32 · see citing works
Graves, J., Qiao, Y., Moored, K., Boudreau, R. M., Venditti, E. M., Krafty, R. T., Shiroma, E. J., Harezlak, J., & Glynn, N. W. (2021) · Sensors · doi:10.3390/s21051718 · Cited by 21 · see citing works
Self-citationLarge cognitive fluctuations surrounding sleep in daily living
Huber, R., & Ghosh, A. (2021) · iScience · doi:10.1016/j.isci.2021.102159 · Cited by 18 · see citing works
Suibkitwanchai, K., Sykulski, A. M., Algorta, G. P., Waller, D., & Walshe, C. (2020) · PLoS ONE · doi:10.1371/journal.pone.0239368 · Cited by 13 · see citing works
Sarwar, A., Agu, E., Polcari, J. J., Ciroli, J., Nephew, B. C., & King, J. A. (2022) · Smart Health · doi:10.1016/j.smhl.2022.100344 · Cited by 12 · see citing works
Actigraphic correlates of neuropsychiatric symptoms in adults with focal epilepsy
Abboud, M. A., Kamen, J. L., Bass, J. S., Lin, L., Gavvala, J. R., Rao, S., Smagula, S. F., & Krishnan, V. (2023) · Epilepsia · doi:10.1111/epi.17611 · Cited by 10 · see citing works
Self-citationGao, C., & Scullin, M. K. (2024) · Psychosomatic Medicine · doi:10.1097/psy.0000000000001301 · Cited by 9 · see citing works
Yeom, J. W., Kim, H., Pack, S. P., Lee, H., Cheong, T., & Cho, C. (2025) · JMIR Mental Health · doi:10.2196/67478 · Cited by 7 · see citing works
Smagula, S. F., Zhang, G., Krafty, R. T., Ramos, A. R., Sotres‐Alvarez, D., Rodakowski, J. L., Gallo, L. C., Lamar, M., Gujral, S., Fischer, D. R., et al. (2024) · Sleep Health · doi:10.1016/j.sleh.2024.02.002 · Cited by 5 · see citing works
Self-citationVieluf, S., Cantley, S., Krishnan, V., & Loddenkemper, T. (2024) · Brain Communications · doi:10.1093/braincomms/fcae034 · Cited by 5 · see citing works
Cakmak, A. S., Thigpen, N., Honke, G., Alday, E. A. P., Rad, A. B., Adaimi, R., Chang, C.-J., Li, Q., Gupta, P., Neylan, T. C., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.07406 · Cited by 4 · see citing works
Aging and activity patterns: actigraphy evidence from NHANES studies
Luo, W., Scharf, M. T., & Androulakis, I. P. (2025) · Frontiers in Systems Biology · doi:10.3389/fsysb.2025.1632110 · Cited by 3 · see citing works
Hartman, A. G., McKendry, S., Akcakaya, M., Soehner, A. M., Bodison, S. C., DeAlmeida, D. R., & Bendixen, R. M. (2023) · Sleep Medicine · doi:10.1016/j.sleep.2023.03.024 · Cited by 3 · see citing works
Deep phenotyping of insomnia: a multimodal assessment protocol
Lee, Y., Kim, S., Kim, S., Pack, S. P., Lee, H., & Cho, C. (2025) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2025.1696593 · Cited by 2 · see citing works
Rest‐activity rhythm phenotypes in adults with epilepsy and intellectual disability
Adhyapak, N., Cardenas, G. E., Abboud, M. A., & Krishnan, V. (2025) · Epilepsia Open · doi:10.1002/epi4.70063 · Cited by 1 · see citing works
Biphasic sleep is a feature of sleep disturbance in SYNGAP1-RD
Doucoure, A., Patel, H., Abboud, M. A., Sperry, A. D., Wanigatunga, S., Crocetti, D., Volk, H. E., Spira, A. P., Mostofsky, S. H., Krishnan, V., et al. (2026) · Sleep Medicine · doi:10.1016/j.sleep.2026.108908 · Cited by 1 · see citing works
Stallen, A. V., deyne, M. D., Labie, C., & Baets, L. D. (2026) · Clocks & Sleep · doi:10.3390/clockssleep8020032 · Cited by 1 · see citing works
Stability and Volatility of Human Rest-Activity Rhythms: Insights from Very Long Actograms (VLAs)Preprint
Adhyapak, N., Abboud, M. A., Rao, P. S. K., Kar, A., Mignot, E. J.-M., delucca, G., Smagula, S. F., & Krishnan, V. (2024) · medRxiv · doi:10.1101/2024.01.22.24301243 · Cited by 1 · see citing works
Self-citationCharacterization of Chronotypes Using the Symbolic Aggregate apprXimation (SAX) on Actigraphy DataPreprint
Luo, W., & Androulakis, I. P. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.09.03.611014
Bayesian Covariate-Dependent Circadian Modeling of Rest-Activity Rhythms
Hadj-Amar, B., Krishnan, V., & Vannucci, M. (2025) · Data Science in Science · doi:10.1080/26941899.2025.2474943
Rest–Activity Rhythm Characteristics and Cognitive Function in Cognitively Healthy Older Adults
Zhang, M., Hoth, K. F., Whitaker, K. M., Linkenmeyer, C., & Moon, C. (2025) · Journal of Aging and Physical Activity · doi:10.1123/japa.2024-0234
actiRhythm: Circadian Rest-Activity Rhythm Analysis
Azadda, R. D., CEAL Team, & Rasmus, S. (2026) · doi:10.32614/cran.package.actirhythm
Song, A., Xu, K., Wang, K.-Y., Kong, L., Sison, S. D. M., Shi, S., Paluch, A., & Kim, D. H. (2026) · Innovation in Aging · doi:10.1093/geroni/igag092
Zhang, W., Zhao, J., Guo, C., Hu, S., Zhang, X., Liu, X., Shen, H., Zhang, X., Cao, F., & Cui, N. (2026) · Journal of Affective Disorders · doi:10.1016/j.jad.2026.122437
- Authors
- Krafty, R. T., Fu, H., Graves, J. L., Bruce, S. A., Hall, M. H., & Smagula, S. F.
- Affiliations
- University of Pittsburgh (US)
- George Mason University (US)
- Corresponding author
- Krafty, Robert T.
- Venue
- Statistics in Biosciences
- Published
- 2019-01-05
- Volume
- 11
- Issue
- 2
- Pages
- 314-333
- ISSN
- 1867-1764 (ISSN-L)
- 1867-1772
- PMC
- PMC6884363
- OpenAlex
- W2907641598
- Cited by
- 23
- References
- 35
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 5 · 2023: 2 · 2022: 1 · 2021: 4 · 2020: 2
- FWCI
- 0.97
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Statistics in Biosciences (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Institute of General Medical Sciences (R01GM113243)
- National Heart, Lung, and Blood Institute (R01HL1104607)
- National Institute of Mental Health (K01MH112683)
- Topics
- Life Sciences › Neuroscience › Endocrine and Autonomic Systems › Circadian rhythm and melatonin
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Sleep and related disorders
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- rest-activity rhythm, actigraphy, circadian rhythm, measures of variability, depressive symptoms, older adults, sleep-wake patterns
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