Sleep Regularity Index (SRI) - Phillips (2017) Epoch-of-Day x Day Matrix

Computes the Sleep Regularity Index exactly as defined by Phillips et al. (2017) using the full epoch-of-day by day concordance matrix. This is the published form of the SRI. Unlike a single fixed 24-hour-lag comparison, every epoch is binned by its real clock time (epoch-of-day) and by calendar date, a binary sleep/wake matrix is built, and the index is the average agreement between the SAME clock time on CONSECUTIVE calendar days, rescaled to the interval [-100, 100].

Usage

sri.matrix(sleep_state, timestamps, epoch_length = 60)

Arguments

sleep_state: Sleep/wake state per epoch. Either a character vector of "S" (sleep) / "W" (wake), or a numeric/integer/logical vector where 1/TRUE = sleep and 0/FALSE = wake. NA marks unscored / non-wear epochs and is excluded from the concordance count. Must be the same length as timestamps.
timestamps: POSIXct vector of epoch start times, one per element of sleep_state. Need not start at midnight and need not be perfectly contiguous; alignment is by real clock time.
epoch_length: Epoch length in seconds (default 60). Must divide 86400 evenly; M = 86400 / epoch_length is the number of epochs per day.

Value

A list with components:

SRI: Numeric Sleep Regularity Index in [-100, 100] (rounded to 2 dp), or NA_real_ if it cannot be computed.
n_days: Integer number of distinct calendar days (N) spanned.
n_valid_pairs: Integer number of consecutive-day epoch pairs that were actually compared (both cells non-NA).
method: Character constant "phillips_matrix".

Details

Let M = 86400 / epoch_length be the number of epochs in a day and let N be the number of calendar days spanned by the recording. Each epoch is assigned an epoch-of-day index i (1..M) from its clock time (hour/minute/second) and a day index j (1..N) from its calendar date. These two indices populate a binary matrix s[i, j] where 1 = sleep and 0 = wake. The SRI is then

$$SRI = -100 + \frac{200}{M (N - 1)} \sum_{i=1}^{M} \sum_{j=1}^{N-1} \mathbf{1}\{ s_{i,j} = s_{i,j+1} \}$$

i.e. the proportion of clock-time epochs that hold the same state on two consecutive days, mapped linearly so that perfect regularity scores +100, chance-level (independent) scoring about 0, and perfect anti-regularity -100.

Robustness to gaps and partial wear: any consecutive-day pair (i, j) -> (i, j + 1) in which either cell is NA (missing epoch, non-wear, or a calendar day not represented in the data) is skipped and NOT counted. The sum is divided by the actual number of valid pairs rather than the theoretical M * (N - 1), so missing data reduce statistical power but do not bias the estimate.

Days are aligned by true clock time using as.POSIXlt() (hour, minute, second give the epoch-of-day; the calendar date gives the day index), so the result is correct even when a recording does not start at midnight.

A SRI of NA_real_ is returned (never an error) when there are fewer than two days, no valid consecutive-day pairs, or no usable input. The return structure is always the same list.

References

Phillips AJK, Clerx WM, O'Brien CS, Sano A, Barger LK, Picard RW, Lockley SW, Klerman EB, Czeisler CA (2017). “Irregular sleep/wake patterns are associated with poorer academic performance and delayed circadian and sleep/wake timing.” Scientific Reports, 7(1), 3216. doi:10.1038/s41598-017-03171-4 .

Examples

# A perfectly regular sleeper: same 8h sleep block every day -> SRI near 100
ts <- seq(as.POSIXct("2024-01-01 00:00:00", tz = "UTC"),
          by = 60, length.out = 1440 * 4)
tod <- as.POSIXlt(ts)$hour
state <- ifelse(tod < 8, "S", "W")   # asleep 00:00-08:00 every day
sri.matrix(state, ts, epoch_length = 60)$SRI
#> [1] 100