Measuring sleep regularity: theoretical properties and practical usage of existing metrics

Abstract

Study objectives: Sleep regularity predicts many health-related outcomes. Currently, however, there is no systematic approach to measuring sleep regularity. Traditionally, metrics have assessed deviations in sleep patterns from an individual's average; these traditional metrics include intra-individual standard deviation (StDev), interdaily stability (IS), and social jet lag (SJL). Two metrics were recently proposed that instead measure variability between consecutive days: composite phase deviation (CPD) and sleep regularity index (SRI). Using large-scale simulations, we investigated the theoretical properties of these five metrics.

Methods: Multiple sleep-wake patterns were systematically simulated, including variability in daily sleep timing and/or duration. Average estimates and 95% confidence intervals were calculated for six scenarios that affect the measurement of sleep regularity: "scrambling" the order of days; daily vs. weekly variation; naps; awakenings; "all-nighters"; and length of study.

Results: SJL measured weekly but not daily changes. Scrambling did not affect StDev or IS, but did affect CPD and SRI; these metrics, therefore, measure sleep regularity on multi-day and day-to-day timescales, respectively. StDev and CPD did not capture sleep fragmentation. IS and SRI behaved similarly in response to naps and awakenings but differed markedly for all-nighters. StDev and IS required over a week of sleep-wake data for unbiased estimates, whereas CPD and SRI required larger sample sizes to detect group differences.

Conclusions: Deciding which sleep regularity metric is most appropriate for a given study depends on a combination of the type of data gathered, the study length and sample size, and which aspects of sleep regularity are most pertinent to the research question.

Keywords: circadian disruption; circadian misalignment; inter-individual variability; intra-individual variability; sleep stability; sleep variability.

Figure 1.

Sleep regularity metrics. (A) Raster plot of a 28-day sleep–wake pattern with a weekly variation of 1 h later and 1 h longer sleep on weekends than weekdays. The gray box marks six days of the pattern used to illustrate the five sleep regularity metrics in panels B–F. (B) Social jet lag (SJL). (C) Standard deviation (StDev). (D) Interdaily stability (IS). (E1 and E2) Composite phase deviation (CPD). (F) Sleep regularity index (SRI). Note: Only clock times 0-8 are shown for space reasons.

Figure 2.

Scenarios of sleep regularity. (A) Scenario 0 illustrates a perfectly regular sleep–wake pattern over 28 days (zero variation). (B) Scenario 1 adds daily variation in midsleep, sleep duration, or both. (C) Scenario 1A uses sleep–wake patterns from Scenario 1, but with re-arranged (“scrambled”) order of days. (D) Scenario 2 adds weekly variation to sleep–wake patterns from Scenario 1. Scenarios 3 to 5 further add (E) daytime naps, (F) nocturnal awakenings, or (G) “all-nighters” (nights with no sleep) to Scenario 2. (H) Scenario 6 uses sleep–wake patterns of Scenario 2, varying the number of days (2–28) to simulate varying study lengths, illustrated by the gradual shading.

Figure 3.

Sources of variability: “scrambling,” daily variation, and weekly variation (Scenarios 1A + 2). Panels A–E show the five metrics for randomly re-ordered (“scrambled”) sleep–wake patterns in Scenario 1A. Note that the metrics SJL, StDev, and IS are identical for unscrambled and scrambled sleep patterns (i.e. zero-width 95% CIs, colored lines overlay). Panels F–J show the five metrics calculated for sleep–wake patterns of Scenario 2, with daily variation in midsleep OR sleep duration. Panels K–N show the metrics for the same patterns but with daily variations in midsleep AND sleep duration. Warmer colors in heat maps indicate “more irregular” values in all metrics. Note that SJL is not shown in the bottom row due to its non-response to daily variation (see panel A).

Figure 4.

Sources of variability: naps, awakenings, and “all-nighters” (Scenarios 3, 4, and 5). The far-left panel of each row shows example raster plots of 28-day sleep–wake patterns with (A) daytime naps, (F) nocturnal awakenings, and (K) nights with no sleep (“all-nighters”). Panels (B–E) StDev, CPD, IS, and SRI for sleep–wake patterns fragmented by daytime naps. For clearer illustration, only variations in midnap timing are shown, with metrics’ values averaged across variations in nap duration. Panels (G–J) IS and SRI for sleep–wake patterns fragmented by nocturnal awakenings (WASO, wake after sleep onset). Panels (L–O) StDev, CPD, IS, and SRI for sleep–wake patterns with all-nighters.

Figure 5.

Impact of study length on sleep regularity metrics (Scenario 6). The far-left panel of each row shows example raster plots of the same sleep–wake pattern, based on (A) 14 days or (F) 28 days of data. Panels (B–E) Average estimates and panels (G–J) width of 95% confidence intervals (CIs) for sleep–wake patterns based on 2–28 days of data.

Figure 6.

Correspondence between sleep regularity metrics: StDev vs. CPD and IS vs. SRI. The upper six panels show values of StDev and CPD plotted against each other. The lower six panels show values of IS and SRI plotted against each other. Results are shown for Scenario 2 (A, G), Scenario 3 (naps) (B, H), Scenario 4 (awakenings) (C, I), Scenario 5 (all-nighters) (D, J), and Scenario 6 (study length) (C–F, K–L). Note that StDev and CPD cannot be calculated for sleep–wake patterns with awakenings, so panel C is empty. The dotted lines all have a zero-intercept but the slope equals 1 in the lower six panels (G–L) and 0.7/0.5 in the upper six panels (panels A–E/panel F), corresponding to the factors by which values of StDev are generally smaller than those of CPD. The colored lines in each panel represent the different levels in a given variable, for example, number of naps in panel B. The arrows represent the effect of varying a second variable, for example, in panel B the spread in points of the same color (for each number of naps) is due to variation in midnap timing.

Figure 7.

Choosing the right sleep regularity metric. Selecting the appropriate metric depends on the type of data, study parameters (length, sample size), and which aspects of sleep regularity are considered key to the research question. Decision trees are provided with respect to the type of data and study parameters, indicating the preferred metrics in each case. In cases where four metrics are all viable choices, the preferred metrics are bolded. With regards to the research question, investigators may wish to include more than one metric to test competing mechanisms, for example, including one daily-value metric and one whole-signal metric to test whether the effect of irregular sleep on an outcome is driven by sleep fragmentation by comparing their predictive values. StDev = intra-individual standard deviation; IS = interdaily stability; CPD = composite phase deviation; SRI = sleep regularity index; SJL = social jet lag; WASO = wake after sleep onset.