We calculated the following 40 parameters listed in Table 1 from the actigraphy data, whose details are described below.

The Cole-Kripke sleep/wake identification method was adopted to estimate wake-up and sleep-onset times from the actigraphy data (13). It has been reported that the agreement rate between the Cole-Kripke method and PSG was 88% (13, 14).

It is difficult to estimate sleep/awake timing using only the Cole-Kripke method because it uses 1-min activity counts data measured by means of actigraphy; therefore, we introduce a sleep/wake function r(i)

where x_i is a sleep/wake state at the time i estimated by means of the Cole-Kripke method: x_i = +1 and x_i = −1 denote sleep and awake, respectively. r(i) becomes large when the sleep state dominates and becomes small when the wake state dominates. The extreme points of r(i) may be times that the sleep/awake states change. Thus, its maximum and minimum points can be defined as the wake-up time and the sleeping time. If there are multiple maximum and minimum points within a day, we adopt the latest one as the wake-up time or the sleeping time.

Using the sleep/wake function r(i), the following measurements, which represent the sleep habits, are estimated: wake-up time (WU), sleep-onset time (SO), mid-sleep (MS), and sleep duration (SD). WU, SO and MS are expressed as the minutes elapsed from midnight. Their means and standard deviations were used in addition to these values for each weekday.

Sleep regularity index (SRI) (15) and sleep timing index (STI) (16) represent sleep rhythm. SRI is the agreement between sleep/wake states at any two-time points separated by 24 h. A large SRI means that the sleep rhythm is regular. SRI can be calculated based on the Cole-Kripke sleep/wake identification method. N and p are the numbers of measurement days and samples per day, respectively. s_k,j = 1 is satisfied if a person is determined to be in the sleep state at time j on the kth day, and s_k,j = 0 is satisfied if a person is determined to be in the awake state at time j on the kth day. SRI is defined as

where δ_i,j = 1 if i = j and δ_i,j = 0 otherwise.

STI expresses the mean sleep midpoint during the measurement days. When the time from 0:00 to 24:00 are associated with the angles θ = [0, 2π], a time point j is expressed as θ_j = 2πj/p. Using this relationship, STI is defined as

where i is the imaginary unit, and Θ is the argument of the sum of eiθj over the sleep states. Figure 1 shows a schematic diagram of STI, in which the triangles denote the times estimated as the sleep states, and eiθj is the composition of the vectors directing these triangles. Thus, the time corresponding to the argument of eiθj is STI.

Inter-daily stability (IS) and intra-daily variability (IV) are well-known parameters for activity rhythm evaluation based on the actigraphy data (17), which are defined as follows:

where A_i is the activity data at time i, A¯j is the average of the activity data at time j over different days, and A¯ is the average of all activity data. p is the number of activity data per day, and M is the total number of collected activity data. IS is the ratio of the variance of all the collected activity data to the variance of the average activity data at time j over different days. IS becomes large when the fluctuation of the diurnal activity data recorded at the same time of different days becomes large. IV is the ratio of the variance of the collected activity data to the sum of squares of the differences in activity data between a time point and the previous time point. IS and IV are measured for the synchronization of diurnal activity rhythm and the frequency of midday naps and nocturnal awakening, respectively (18).

IS and IV can be calculated from both the activity counts and illuminance in the actigraphy data, which are denoted as IS_act, IS_light, IV_act, IV_light, respectively.

Although IV represents intra-daily activity rhythm, M10 and L5 can be calculated from the actigraphy data to emphasize the rest-activity circadian rhythm. M10 and L5 are defined as the average activities during the most active 10-h period and during the least active 5-h period, respectively (17). M10 represents activity during the most active period within the day, which may be influenced by daytime napping. L5 represents movement activity during sleep.

Mid-sleep on free days (MSF) is a measurement of chronotype. Wake-up time on free days (WUF) and sleep-onset time on free days (SOF) are wake-up time and sleep onset time on the weekend, respectively. MSF is expressed as

Although sleep during the weekdays does not reflect the congenital biological clock much due to the effect of the social clock, weekend sleep significantly reflects the congenital biological clock. Chronotype is classified into three types based on MSF: morning type (MSF < 3:00), intermediate type (3:00 ≤ MSF ≤ 4:00), and evening type (MSF > 4:00) (19).

In addition, social jetlag (SJL) is the difference between the biological clock and the social clock, which is defined as

where MSW is the meantime of mid-sleep on the weekdays.

Although the Morningness Eveningness Questionnaire (MEQ) (20) or the Munich Chronotype Questionnaire (MCTQ) (21) is usually used for calculating MSF and SJL, we used the actigraphy data for calculating them instead of the questionnaires in this study.

In addition to the measurements derived from the actigraphy data, we collected answers to the following, modified for the Japanese population.

Sleep duration (SD) of each day can be calculated using the sleep/wake function r(i). By using the means of SD on the weekend (SD on a free day; SDF) (min), and SD on the weekday (SDW) (min), sleep rebound on the weekend (SRW) (min) (30) is defined as

A person may have chronic sleep deprivation during the weekdays when SRW ≥ 120 min (31). Based on this criterion, we judge that a person has WSD when SRW ≥ 120 min.

In this research, we adopt machine learning (ML) technologies to find the factors of WSD. A classifier that predicts whether a person has WSD is trained from the measurements described above or not, and feature importance is calculated based on the trained classifier. Feature importance is a well-known method for identifying which input features in a classifier contribute to output (32).

Although various classifier training methods have been used in ML, we adopted a support vector machine (SVM) in this work. SVM is a classical nonlinear classification technique that was originally developed for classifying data into two classes (33). SVM has been widely used for various applications such as spam mail filtering, bioinformatics, and object recognition (34–36). Thus, SVM is a reliable ML technique.

We used a permutation feature importance method to calculate feature importance, which is defined as the decrease in prediction performance when a single input feature is randomly shuffled (37, 38). E is the prediction performance of the trained classifier when the original feature set is input to the classifier, and E_j is the prediction performance of the classifier when a feature x_j is exchanged randomly into another feature. The feature importance of x_j is calculated as

We can judge that the feature x_j contributes to a prediction when Pimp(x_j) is large.

A cross-sectional survey was conducted in 324 employees at a drug wholesale company in Osaka, Japan, from January 26, 2004, to December 19, 2005.

All of the participants were male. It becomes difficult to focus on the relationship between work habits and activity rhythm when female employees are included in the survey. There are more factors affecting sleep and rhythm in females than in males, such as having small children or not, menstrual cycle, unmarried or married (39, 40). However, some studies have already reported that there were no significant differences in daytime activities between males and females (41, 42). Thus, it is expected that our analysis is applicable to females as well as males.

The workdays were from Monday to Friday, and the holidays were Saturday and Sunday, which are typical for Japanese companies and government offices. We used a wrist-type actigraph device (Actiwatch AW-Light, Mini-Mitter) for data recording, which measures the activity counts and illuminance within every one-minute bin. Illuminance is recorded by a photodiode equipped in the actigraph device. Its measurement range is 0.1 to 150,000 Lux with 0.1 Lux resolution, which is suitable for both interior and exterior illuminance measurement. The actigraph device worked for 2–3 months per one battery. Thus, data missing did not occur during data collection. In addition, we collected answers to the questionnaires and sleep diaries during the survey. The protocol of this study was approved by the Ethics Committee of the Shiga University of Medical Science (R2020-026).

Since all participants wore the actigraph device from around 5:00 pm on a Monday to around 8:00 am on the next Monday, the Monday (the first day) actigraphy data were not recorded in their entirety. The Monday data were excluded from the analysis except for wake-up and sleep-onset time estimation. On the other hand, sleep-onset time, mid-sleep, and sleep duration of Friday were not able to be calculated because sleep in the Friday night sleep is regarded as a weekend.

One hundred and six participants who removed the actigraph device for more than 30 min during the survey term were excluded from the analysis so that 218 participants were included in the analysis. The characteristics of the subjects are illustrated in Table 2, and a detailed description of the data used in this study is available in Kadotani et al. (3), Nakayama-Ashida et al. (43), and Gerstner et al. (44).

Our dataset consisted of 1-week actigraph data, which seems to be rather short for analysis. However, Tienoven et al. calculated SRM of healthy persons from their 1-week activity data (45). Fonseca et al. evaluated RM of stroke patients and healthy persons based on 1-week activity data (46). In addition, the sleep extension term required before performing PSG is also 1 week according to ICSD-3 (2). These indicate that 1-week activity data can be used for sleep rhythm evaluation.

An example of sleep/awake state estimation is shown in Figure 2. All participants were classified into the WSD group or the non-WSD group based on the SRW calculated from the actigraphy data. The numbers of persons with and without WSD were 89 and 129, respectively. Figure 3 shows the distribution of SRW in this data.

Before analysis, we validated the accuracy of the actigraphy data through a comparison between sleep durations derived from the actigraphy and the sleep diaries recorded by participants themselves. In addition, the answers of MEQ item 19, which asks self-awareness of chronotype were compared to verify whether the definition of WSD adopted in this study was supported by self-awareness of chronotype.

To specify the factors of WSD based on the feature importance, we needed to construct a classifier that predicts the presence of WSD. In general, the numbers of positive and negative examples for training should be balanced in binary classification problems to construct a good classifier (47). We randomly discarded non-WSD data so that the numbers of persons with WSD and non-WSD became even by means of random under-sampling because the number of persons without WSD was larger than that of persons with WSD.

As the input features of the WSD classifier, we used 40 features listed in Table 1, derived from the actigraphy data. The Gaussian kernel with a parameter γ was adopted in SVM, of which the parameter γ was tuned by means of 10-fold cross-validation. The WSD classifier training and permutation feature importance computation were repeated 100 times by changing the training and the test samples at random, in which the ratio of the number of training samples to that of test samples was fixed at 7:3. Finally, the mean of the computed permutation feature importance was calculated. In this study, we focus on features occupying the top 20% of the sum of importance, which does not necessarily mean only these factors are important (or statistically significant). We used the top 20% just for limiting the number of factors to discuss in detail, in which the cut-off value can be varied.

In addition, we examined whether the presence of WSD may relate to occupational categories or not. In this survey, employees were classified into the following categories: clerical, managers, professional and technical sales, service, transportation and communication, manufacturing, and others (43).

We compared each of the 40 input features and each of the collected answers to the questionnaires between the WSD and non-WSD groups by means of a statistical test.

We used the t-test for comparison between the WSD and non-WSD groups. The significance level was set to p < 0.05. To consider the multiple comparisons of the total of 40-measurements from the actigraphy data and 14-measurements from the questionnaires, the Bonferroni correction was adopted. That is, the significance levels were corrected as p < 0.05/40 = 0.00125 and p < 0.05/13 = 0.0038. In addition, we used the χ² test with significance p < 0.05 for examining the effect of occupational categories on WSD and MEQ item 19.

Computation in this study was performed in Python 3.6.4 with SciPy 1.3.0, NumPy 1.16.2, and scikit-learn 0.20.2.

There was a significant difference in MEQ item 19 between WSD and non-WSD groups (p = 0.12 × 10⁻⁷) although a significant difference in the total score of MEQ was not confirmed (p = 0.12).

Turco et al. (50) assessed the reliability of MEQ item 19 in comparison with the total score of MEQ, the time of subjective sleepiness, and real-life sleep timing variables. They found that significant differences in sleep-wake timing between the answers of MEQ item 19. In addition, such differences were still observed when sleep-wake habits were analyzed separately on work and free days. In addition, Arrona-Palacios and Díaz-Morales (51) confirmed Turco's study in the Mexican and Spanish populations. These findings suggest that MEQ item 19 is solely effective for subjective chronotype evaluation as well as objective chronotype evaluation.

Thus, it is concluded that the definition of WSD supported by MEQ item 19 was appropriate from the viewpoint of chronotype.

The weekday sleep conditions were different between the WSD and non-WSD groups, according to Table 2. Sleep duration during the weekdays of the WSD group was significantly shorter than that of the non-WSD group except for Wednesday (p < 0.05), which may be plausible from the viewpoint of the assumption that WSD compensates for sleep deprivation during the weekdays. SD_Thu and SO_Thu were important features for WSD based on the analysis result of permutation importance analysis, which indicated that Thursday was associated with WSD.

There were significant differences in MSF and SJL, the biological clock features (p < 0.05). MSF and SJL of the WSD group were later than those of the non-WSD group. That is, persons with WSD have eveningness tendencies. In addition, MSF and SJL were also important to WSD according to the permutation importance analysis. Since all of the participants worked at the same company, they might live and work following the same social clock. Thus, this result indicated that disagreement between the social clock and the individual biological clock might contribute to WSD, which is consistent with the previous study (5).

The inter-daily stability by the activity counts (IS_act) evaluates the synchronization of diurnal activity rhythm, and it was also an important feature for WSD according to the permutation importance analysis, although the significant difference of IS_act between the WSD and the non-WSD groups was not confirmed. Figure 5 shows the 24-h activity counts during the weekdays of two participants with and without WSD. Inter-daily synchronization of activity rhythm, including sleep conditions, might affect WSD.

On the other hand, intra-daily variability based on the activity counts (IV_act) was not significantly different between the WSD and non-WSD groups, and its feature importance was low. Since IV_act denotes the frequency of midday naps and nocturnal awakening, its low importance suggests that sleep disorders, such as narcolepsy or sleep apnea, might not contribute to WSD. In addition, IS and IV by illuminance (IS_light and IV_light) were not significantly different and of low importance, implying that illuminance might not affect WSD.

It was of note that Thursday was more important for WSD presence than other weekdays. This may be related to the participants' working conditions. All participants worked at the same drug wholesale company, which provides various medical supplies to hospitals and clinics. Since private clinics in Japan tend to close on Thursday evening (52), work habits on Thursdays are different from other workdays at the drug wholesale company. For example, employees might tend to do desk work rather than outside work or to go home earlier than other workdays. Such differences in work schedules might affect their social clock and disturb the synchronization of diurnal activity rhythm, which is consistent with the causes of WSD (5). Figure 8 clearly illustrates that the activity of a participant with WSD on Thursday was significantly different from those of other days while the activity of a participant without WSD synchronized even on Thursday. This difference might indicate increased desk time and reduced outside work on Thursday.

Thus, it is reasonable that Thursday was an important factor of WSD at the company. This analysis indicates that the work style differences on a specific day of the week may cause WSD.

In this survey, participants were classified into a salesperson group and a non-salesperson group, and the top five permutation feature importance derived from each group was the same, as shown in Figure 6. This result indicated that the factors of WSD were not related to specific occupational categories, which also suggests that our analysis may be applicable to data collected from other companies.

The limitations of this study include the collected data; all of the participants were male and Japanese. Hence, we could consider neither gender nor racial differences in this study. In addition, the participants worked at the same company; it was difficult to investigate the effects of other days of the week on WDS since we did not compare our data with persons working at companies that have different work habits on a specific day of the week. Accordingly, we need to collect data from employees working in various types of industries to confirm our results. In addition, we were not able to analyze the Monday activity data due to the constraint of the data collection, which might affect the analysis results.