Sleep 6.5 Understanding Sleep Regularity Metrics

Review major metrics of sleep regularity, their calculation methods, strengths, and how to select the right one for research or clinical use.

Video Breakdown:

00:00 Introduction to Sleep Regularity Metrics

01:24 Understanding Standard Deviation in Sleep Studies

04:44 Exploring Interdaily Stability

07:34 The Concept of Social Jet Lag

12:10 Sleep Regularity Index and Its Importance

20:51 Choosing the Right Sleep Regularity Metric

So now what are the regularity metrics that are available for us to utilize, in the studies that we do? And how would you quantify this? So if you can imagine, you have this individual who has this raster plot, clearly has low sleep regularity. How would you create a quantitative measure to quantify this?
And there's a multiple number of ways to do it, you can, for instance, calculate the variability in the sleep onset or the sleep offset, what time you wake up. Or you could incorporate sleep midpoint, which is the midpoint between the sleep onset and the time you wake up.
Or you could do actually standard deviation or variability in sleep duration from day after day. How about these wake periods? Obviously the fact that you have broken up or fragmented sleep should play a factor in irregularity too. So how do you incorporate that and then there is the weekend versus the weekday effect as well.
People tend to sleep longer and later in weekends, compared to the weekdays. So how do you incorporate that in your regularity metric? So the first one that is probably the oldest one around, and probably the easiest to interpret is standard deviation. And in this case, this shows an example of the standard deviation of mid sleep.
And the idea is that you identify the mean average of the sleep across all the sleep period that you have. You calculate the deviation at from each night, from this mean. So this creates this standard deviation. So it makes sense that this, just means literally the statistical dispersion around the mean across multiple days.
Now you can use standard deviation to multiple daily values. You can apply this not only to mid sleep, but you could do standard deviation of sleep onset. Also standard deviation of offset, and you could do the standard deviation for the duration of the night, so you could use that as a marker as well.
So naturally, a low standard deviation value means more regularity, and in order to do this in your study, you could just simply, use diaries, although it's probably easier just to use actigraphy so that your study participants don't have to, go through the labor of filling this out on a daily basis.
The issues or the properties with standard deviation is that it is insensitive to date order, You could mix this up entirely and you would get the same standard deviation value, and it's insensitive to naps or fragmentation, right? So if you have breaks where you're waking up in the middle of the night here, this value is not going to take that into consideration.
I'm gonna talk a little bit about this later. So, why is standard deviation itself important? This is, as I mentioned, it is probably the oldest sleep regularity measure out there.
And as a result, there's decent amount of literature evaluating the importance of this measure in a number of clinical outcomes. This, uh, comes from that NSF consensus statement. They, drew out a figure here, and this took from the data from the MESA study again. And they focused on two clinical outcomes, metabolic syndrome, cardiovascular disease, and within each of these clinical outcomes, they focused on sleep onset standard deviation, and sleep duration standard deviation.
And so they did this for both. Simultaneously they also evaluated the proportional risk estimates for each additional hour of standard deviation for both metrics, and what they found out was that for each one hour of sleep onset standard deviation would increase your risk of metabolic syndrome by 23%.
For cardiovascular disease events, for each additional hour of sleep onset standard deviation, you increase your risk of cardiovascular disease events by 18%. So not insignificant. This is, you know, pretty important stuff. The other, measure that's out there is called interdaily stability. The idea behind this is it quantifies the overall variability and time signal after averaging across days rather than quantifying how rapidly sleep patterns change between consecutive days.
So, actually this came from the actigraphy world. They take actigraph or activity counts. And what you can do is after, obtaining data, after many days, you obtain a mean activity level, which is demonstrated here on the bottom, and then for each day you calculate the deviation of the values from this mean value.
So it assesses the stability of this 24 hour rest activity rhythm on each day compared to this average 24 hour pattern. And it has a scale of scoring from zero to one, one meaning that has the highest regularity. Now, because you are getting such continuous granular data, you cannot just use a diary. In order to do this measurement, you have to use actigraphy.
And in the literature it appears that most of the time they use 30 second or one minute epochs. The property of this is that again, it is insensitive to day order, so you could shift around and mix around these days and you still get the same, results. But the difference, compared to the standard deviation is that since you're getting such granular data, you're applying it to the whole day and can incorporate thus naps and fragmentation. So it will incorporate that in the calculation. And for whatever reason, interdaily stability in the literature has been linked to rhythmicity because in order for the interdaily stability to have a substantial number, it needs alternating states.
So, if you have high interdaily stability suggesting that you have an element of rhythmicity in there as well. As it turns out, I was looking through the literature, there doesn't seem to be as many studies that incorporate interdaily stability as a proxy for sleep regularity, but there's a study that was published in 2021, it had three groups, healthy controls, insomnia, and Post-Traumatic Stress Disorder patients. They measured the interdaily stability. Since interdaily stability, the higher means that you're more stable and you can see that healthy controls had more sleep regularity compared to the insomnia patients and the PTSD patients. And this was statistically significant compared to the other two conditions. The third measure is the social jet lag index. This one I think is much easier to understand and interpret. It's basically finding the average, oftentimes the mid sleep time during the weekdays and comparing the mid sleep time during the free days, which is often the weekend times, and then what you're doing is you're just taking the difference between these two mid times. The social jet lag index is basically a mismatch and sleep timing between socially constrained days, which could be school or work versus your free days.
And again, low value indicates high regularity. And how you do this can be done through a number of ways. You can incorporate just questionnaires. A number of studies have used questionnaires just to derive the social jet lag index. Some have used diaries, others have used actigraphy.
The property of this is that this is at a weekly timescale compares to the others, which is at a daily timescale. Like the other two, this is insensitive to day order. So you can mix things up, you can mix up the workdays. Obviously you can't mix between the workdays and the free days themselves, but within the workdays, if you mix it up, or within the free days, you can mix it up, you still get the same results.
And, it does not incorporate naps or fragmentation. A good study that, shows the relevance of social jet lag index was published in sleep in 2023. This incorporated large longitudinal survey in Czech Republic. More than 5,000 individuals who filled that a Munich chronotype questionnaire, but they also got blood lipid panel testing done.
And what this found, this study found that as you age, your social jet lag tends to decrease. They also found that those individuals who are night owls tend to have higher social jet lag index compared to the larks. And I think this makes sense. Those people who tend to stay up late have to wake up early in the morning
to go to work or sleep, that's not going according to their natural rhythm, but, that as a result of that, they accumulate sleep, debt, which needs to be, recovered during the weekend. The importance of this social jet lag index, was seen in this blood cholesterol level.
Those who had high social jet lag index, tended to have higher total cholesterol levels and LDL levels, and this was true in both men and women, and it was statistically significant. But again, social jet lag is something of a mixed bag, in my opinion, because a high social jet lag index may actually be a good thing because that indicates that you're correcting your sleep debt during the weekend.
So if you're worried about sleep duration, if you're saying that you know, you're not getting the sleep during the weekdays, then the weekends become a time for you to catch up and that would be represented with a high social, jet lag index. However, a high SJI also indicates that your sleep is more irregular and as we've seen, that is bad too.
So, it's a little bit of mixed bag, but you know, I think you'll have to interpret it the way you want to by incorporating other measures. This is the way that, Dr. Fischer, sort of organizes this, is that, the way you could get sleep irregularity is based on the data that's processed. A single time point is used for standard deviation and social jet lag index.
You could use a diary, maybe a questionnaire to get to this, but if you're incorporating a whole day where you're incorporating naps and fragmentation, you need actigraphy types of data. And so interdaily stability would require actigraphy. The thing is, these three measures that I've mentioned, don't really take into consideration the order of the events, as I've mentioned. But as you know, circadian rhythms have an inherent inertia, so it's unlikely to change dramatically from one day to the next. So I think it's reasonable then to assume that significant differences in sleep and behavior from one day to the next would be more likely to be discord with your natural rhythms.
And for this reason, several regularity metrics were designed to assess consecutive changes in sleep patterns. So one day to the next, and this one is the sleep regularity index that I talked a lot about. This is the one that spurred a lot of interest in sleep regularity. This is the one that was incorporated in a lot of the large epidemiological studies such as the MESA and UK Biobank and associated with many of the clinical outcome measures. Sleep irregularity index, it's simply just the probability of being in the same state sleep and wake at any two points 24 hours apart. So, what you do is you just take your sleep wake classification for one day, let's say Thursday, and then compare it to the following day Friday. And then you use this method to calculate
the difference between the two. And then you do the next same thing for the following two days, with the overlap, obviously with Friday. And then you keep on doing this, and ultimately you get an average, which then generates a result called the Sleep Regularity Index. And this regulatory index is this complex formula which enables you to get a scale from zero to a hundred.
High meaning that it has high regularity. Because this data requires such granular almost every 30 seconds to every minute type of data for sleep/wake classification, it requires the use of actigraphy. You cannot use questionnaires for this, and this actigraphy should have sleep/wake classification in order for us to enter this into the formula.
The property for this SRI is that it's sensitive to the day order. As I mentioned, it incorporates the whole day. So it does incorporate naps and fragmentation. The results, the value is a little less intuitive than, let's just say the social jet lag index, but, it is being increasingly used in large, cohorts and thankfully there have been large population level studies to get an idea of what the population level pattern
of the SRI score is. And so, this was data obtained from the UK Biobank. They took 61,000 individuals again wearing the actigraph for one week, and they were able to identify that the median is around a score of around 82 or so. And then it seems to be heavy tailed on the left,
and so not too many people with very low scores. I guess a predominant number are in the 70 to 90 range and so the breakdown is shown here. And the final measure of sleep regularity is the composite phase deviation developed by Fischer. This is a combination of Irregularity and mistiming.
So this one incorporates sleep timing, in addition to sleep irregularity. And what Dr. Fischer did was she identified a person's chronotype is actually a not so straightforward, a calculation to figure out a person's chronotype. And then, had figure out from day to day how far apart were you from this chronotype, like your natural predisposition, and then use that as a sort of a value, which is the delta CT for each night.
And then also calculated the difference in the mid sleep from day to day. So you had both the deviation from your inherit rhythm, but also deviation from night after night. And then, so you get these two vectors which is represented here. Y here from the day-to-day difference and the change from the chronotype, and you can create this vector length, and if you have multiple days, you start to get this pattern and then you calculate basically the average magnitude to get the CPD value.
A low value indicates increased regularity. The way you do this can be because it's a single time scale as opposed to the granular actigraphy like minute to minute data, you can do diaries and questionnaires, but, you know, I think it's probably easier to incorporate in actigraphy. The property of this is that it's sensitive to day order.
It's insensitive to naps and fragmentation because it's a single a day value. It needs chronotype estimation, which makes it a little more complex. So this is just a study that was done by Dr. Fischer when she was at Harvard. She measured, US college students, about 220, they wore the MotionLogger for 30 days. They filled out daily questionnaires and diaries, so the actigraphy determines the time of sleep. The students on a daily basis had to describe their wellbeing and also describe when their first social event was. What Dr. Fischer did was calculate the composite phase deviation for sleep, but also the composite phase deviation for the first social event. So I think what's interesting is that a lot of these irregularity measures can also, be applied not only to sleep, but to, let's just say, the first diet, first social event, when you first exercise. So it actually has a lot of diverse use cases.
And interestingly, when she broke down this graph between the, the composite phase deviation of sleep, with a composite deviation of the first social activity, she found these four clusters and she found the cluster four, the students with both irregular sleep and irregular first event, which meaning like first class, first time they're meeting or whatever.
This cluster had worse wellbeing, there were more apt to be sad and more stressed out, compared to those who had one or the other. So the combination of irregularity, both sleep and event scheduling were important. And so this is the way we sort of break it down. If you are looking at single time points, you look at standard deviation or compound phase deviation.
This requires just the diary if you want the whole day, which requires granular information. You use the interdaily stability or the Sleep regularity index. These top values do not care about the day order, so that's why it has more of a global sort of relationship. These bottom ones care about the subsequent ordering, so the consecutive ordering.
And so if you are looking at that, then you want to look at the bottom two. Now the question is how many days is needed in order to get a good estimate of these values? This was again done by Fischer in 2021 while she was at Harvard. She created a simulated data set with a known true regularity over a full month. Then randomly sampled shorter windows, like let's say every two like for two, three or seven days. Then calculated the regularity metric of this, and then compared that result compared to the what is the known true gold standard. And what was found out was for standard deviation and inter daily stability, you need about 10 days of data to get a good enough estimate while sleep irregularity was surprisingly quite stable. So you only need, you know, as little as three days, but ideally seven days of data to get a good estimate as sleep regularity index. And maybe this is why the SRI, was so useful in these, large epidemiological studies. Because, if you recall, the UK Biobank only used one week of Actigraphy data. And so for that reason, SRI was a good measure for that. The other thing that she found out though is that in terms of the 95% confidence interval, for whatever reason, SRI and CPD had larger, confidence intervals. And what she required is that while it was
stable for within an individual, it tend to be a lot more variable across individuals. So I would guess that at least there's a greater interpersonal variability that you need to consider. So if you are gonna incorporate SRI, seven dates are gonna be sufficient, but you will probably need a larger sample size to account for the interpersonal variability.
And this is just a nice summary of how to choose what marker you're gonna use. If you have a type of data that has some limited data, like a lot of missing information, use the daily metrics like standard deviation or CPD. If it's not limited, but you're worried about fragmentation, you need whole signals like interdaily or SRI scores, or if you're not, then CPD and SRI scores.
And again, to consider the importance of study length. So the more days of is the standard deviation and interdaily stability. And you need to consider the sample size as well. So you can look this up in her publication to get this publication.
So this is the summary table that I put together here. Feel free to take a screenshot of this. These are the five metrics, the types of data that needs to be acquired to do this. The ones that are single measurements in a day are the standard deviation, social jet lag, and maybe CPD can just rely on diaries or questionnaires, but it's probably best to incorporate actigraphy in all of them.
Then you need to consider, the number of days and also the sample sizes in order to figure out which of these measures would be best for you.

Course episodes

Sleep 6.1 Intro to Sleep Regularity

Sleep 6.2 The Clinical Importance of Sleep Regularity

Sleep 6.3 Physiological Mechanisms of Sleep Regularity

Sleep 6.4 Exploring the Factors Influencing Sleep Regularity

Sleep 6.5 Understanding Sleep Regularity Metrics

Sleep 6.6 Future Innovations in Sleep Monitoring