In wadpac/GGIR: Raw Accelerometer Data Analysis

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In chapters 8, 9, and 10 we discussed the classification of sleep and in chapter 11 we discussed the classification of daytime physical behavioural classes. These are typically reported as time spent per behavioural class. An complementary way of describing the data is by looking at the fragmentation of these behaviours of time.

Defining fragments

In GGIR, a fragment for daytime is a defined as a sequence of epochs that belong to one of the four categories:

Inactivity
Light Physical Activity (LIPA)
Moderate or Vigorous Physical Acitivty (MVPA)
Physical activity (can be either LIPA or MVPA)

Each of these categories represents the combination of bouted and unbouted time in the respective categories. Inactivity and physical activity add up to a full day (outside SPT), as well as inactivity, LIPA and MVPA.

A fragment of SPT is defined as a sequence of epochs that belong to one of the four categories:

Estimated sleep
Estimated wakefulness
Inactivity
Physical activity (can be either LIPA or MVPA)

With parameter frag.metrics = "all" we can instruct GGIR part 5 to derive behavioural fragmentation metrics. You may want to consider combining this with parameter part5_agg2_60seconds=TRUE as that will aggregate the time series to 1 minute resolution as is common in behavioural fragmentation literature. GGIR part 6 performs fragmentation analysis when part6CR is set to TRUE. For this it uses the time series output generated in part 5 as discussed in the previous chapter.

GGIR derives fragmentation metrics in two ways:

In part 5 fragmentation is quantified per waking hours of the day and reported per day and as recording average of the daily estimates.
In part 6 fragmentation is quantified based on all data in the recording within the window as specifed by parameter part6Window.

Calculation per day allows us to explore and possibly account for behavioural differences between days of the week. However, a day level estimate could be considered less robust than the recording level estimates as generated in part 6.

The in internal function g.fragmentation for fragmentation metric calculation is used in both part 5 and 6 ensuring that the calculation are otherwise consistent.

Fragmentation metrics

Note that from the fragmentation metrics discussed below only fragmentation metrics TP and NFrag are calculated for the SPT fragments.

Coefficient of Variance (CoV) is calculated according to Blikman et al. 2014, which entails dividing the standard deviation by the mean lognormal transformed fragment length (minutes).
Transition probability (TP) from Inactivity (IN) to Physical activity (IN2PA), from Physical activity to inactivity (PA2IN), and from IN to LIPA or MVPA are all calculated according to Danilevicz et al. 2024.
Gini index is calculated with function Gini from the ineq R package, and with ineq argument corr set to TRUE.
Power law exponent metrics: Alpha, x0.5, and W0.5 are calculated according to Chastin et al. 2010. Note that compared with R package ActFrag as described in Junrui Di et al. 2017 we we use the theoretical minimum fragment duration instead of the observed minimum fragment duration.
Number of fragment per minutes (NFragPM) is calculated identical to metric fragmentation index in Chastin et al. 2012, but it is renamed here to be a more specific reflection of the calculation. The term fragmentation index appears too generic given that all fragmentation metrics inform us about fragmentation. Please note that this is close to the metrics for transition probability, because total number divided by total sum in duration equals 1 divided by average duration. Although the exact math is slightly different.

Conditions for calculation

Metrics Gini and CoV are only calculated if there are at least 10 fragments (e.g. 5 inactive and 5 active). If this condition is not met the metric value will be set to missing.
Metrics related to power law exponent alpha are also only calculated when there are at least 10 fragments, but with the additional condition that the standard deviation in fragment duration is not zero. If these conditions are not met the metric value will be set to missing.
Other metrics related to binary fragmentation (mean_dur_PA and mean_dur_IN), are calculated when there are at least 2 fragments (1 inactive, 1 active). If this condition is not met the value will is set to zero.
Metrics related to TP are calculated if: There is at least 1 inactivity fragment AND (1 LIPA OR 1 MVPA fragment). If this condition is not met the TP metric value is set to zero.

To keep an overview of which recording days met the criteria for non-zero standard deviation and at least ten fragments, GGIR part 5 stores variable Nvaliddays_AL10F at person level (i.e., number of valid days with at least 10 fragments), and SD_dur (i.e., standard deviation of fragment durations) at day level as well as aggregated per person.