‘Non-parametric’ actigraphy statistics

Copied from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4559593/ (no paywall)

The rest–activity rhythm in humans is commonly studied using actigraphy, a technology which measures gross motor movement. Adjusting a cosine function to actigraphic data provides parameters that are used in circadian rhythmicity studies. The parameters that describe rhythm characteristics include: amplitude, mesor, acrophase, and period. However, as the rest–activity rhythm does not behave exactly as a cosine function, other variables have been studied and new methodologies have been developed. Since these variables are not associated with parameters of a known function, they are called nonparametric.

In 1990, nonparametric variables were primarily proposed by Witting et al., who had studied the effect of age and Alzheimer׳s disease on rest–activity rhythm. These variables quantify the main characteristics of the rest–activity circadian rhythm, such as intradaily variability (IV), which quantifies the rhythm fragmentation; interdaily stability (IS), which quantifies the synchronization to the 24-h light–dark cycle; the average activity during the least active 5-h period, or nocturnal activity (L5); and the average activity during the most active 10-h period, or daily activity (M10).

Rhythmic fragmentation and synchronization are measured, respectively, by IV and IS. Intradaily variability quantifies the frequency and extent of transitions between periods of rest and activity on an hourly basis . High IV values indicate the occurrence of daytime naps and/or nocturnal activity episodes. Interdaily stability quantifies rhythm׳s synchronization to zeitgeber׳s 24-h day–night (or light–dark) cycle.

Studies have shown that IV is an excellent variable for analysis, as it serves as a marker of sleep–wake cycle disturbances. Assessment of interdaily variability in an elderly population shows a more fragmented rest–activity rhythm (high IV values). Researchers have also observed higher values of IV in patients with Alzheimer׳s disease when compared to controls. Aging and Alzheimer׳s disease are factors that contribute to the degeneration of the suprachiasmatic nucleus, which may explain rhythm fragmentation. Furthermore, it was demonstrated that high IV (high rhythm fragmentation) is associated with decreased sleep quality, decreased cognitive functions and decreased circadian rhythm amplitude.

On the other hand, high IS values indicate good synchronization of zeitgeber׳s 24 h cycle, and good operation of the circadian timing system׳s (CTS) components, which are connected to photic and nonphotic synchronizations. This synchronization can be influenced by age, neurological disorders, and lifestyle. In terms of aging, the synchronization to zeitgeber׳s cycle increases the CTS maturity level. The rhythm stability measured by IS has a direct relationship with quality of life measures. Studies have shown that IS is directly related to rhythm amplitude and light exposure, Mini Mental State Examination, and sleep quality. A well synchronized rhythm is associated with less fragmentation, less nocturnal activity, and better cognitive, behavioral, and emotional functioning.

Interdaily Stability

From ‘nparACT’ package for R: A free software tool for the non-parametric analysis of actigraphy data

Publication available (no paywall) at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890079/

Interdaily Stability describes the coupling of the circadian rhythm to external zeitgebers, that is environmental cues such as light that entrain an organism’s internal biological clock to the earth’s 24 h cycle. IS varies between 0 (Gaussian noise) and 1 with values closer to 1 indicating stronger coupling to a zeitgeber with a period length of 24 h.

Formula is as follows:

I S = n ∑ h = 1 p ( X ¯ h - X ¯ ) 2 p ∑ i = 1 n ( X i - X ¯ ) 2

Intradaily Variability

From ‘nparACT’ package for R: A free software tool for the non-parametric analysis of actigraphy data

Publication available (no paywall) at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890079/

In contrast to Interdaily Stability, Intradaily Variability quantifies the fragmentation of a rest-activity pattern. IV converges to zero for a perfect sine wave and approaches two for Gaussian noise. It may even be higher than two if a definite ultradian component with a period length of two hours is present in the rest-activity cycle.

Formula is as follows:

I V = n ∑ i = 2 n ( X i − X i − 1 ) 2 ( n − 1 ) ∑ i = 1 n ( X i − X ¯ ) 2

Relative Amplitude

From ‘nparACT’ package for R: A free software tool for the non-parametric analysis of actigraphy data

Publication available (no paywall) at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890079/

RA is a non-parametric parameter, which can be calculated from the M10 and L5 values, that is the ten hours with maximal (M10) and the five hours with minimal (L5) activity. Usually, M10 covers 10 h during the day and may be influenced by e.g. daytime napping. L5, on the other hand, should reflect movements during the night as well as arousals and awakenings.

Formula is as follows:

R A = ( M 10 − L 5 ) ( M 10 + L 5 )

Interpretation of the RA statistic therefore must consider the distribution of the dataset and what the relationship between m10 and L5 are in each sample. As an example:

Low activity during the day, low activity during the night:

          if m10 = 10
               and L5 = 5
                     then (10-5)/(10+5)
                               = 0.33

High activity during the day, low activity at night:

          if m10 = 20
               and L5 = 5
                     then (20-5)/(20+5)
                                = 0.60
                                             conversely…

Low activity during the day, high activity during the night:

          if m10 = 10
               and L5 = 8
                     then (10-8)/(10+8)
                                = 0.11

High activity during the day, high activity during the night:

          if m10 = 20
               and L5 = 8
                     then (20-8)/(20+8)
                                = 0.42

L5

See: ‘nparACT’ package for R: A free software tool for the non-parametric analysis of actigraphy data

Publication available (no paywall) at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890079/

The L5 statistic is the average activity during the least-active 5 hours of each day.

The L5 statistic is calculated on a minute-wise level across days.

m10

See: ‘nparACT’ package for R: A free software tool for the non-parametric analysis of actigraphy data

Publication available (no paywall) at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890079/

The m10 statistic is the average activity during the most-active 10 hours of each day.

Like L5, the m10 statistic is calculated on a minute-wise level across days.