Estimating dim light melatonin onset time in children using delta changes in melatonin

Abstract

We aimed to establish a method for estimating dim light melatonin onset (DLMO) using mathematical slopes calculated from melatonin concentrations at three sampling points before and after sleep in children. The saliva of 30 children (mean age ± SD: 10.2 ± 1.3 years old) was collected under dim-light conditions up to six times every hour starting at 17:30 (t17), namely, 18:30 (t18), 19:30 (t19), 20:30 (t20), 21:30 (t21), 22:30 (t22), and 23:30 (t23), in the evening, and at 6:00 (t30) the following morning. We calculated ${\mathit{SLOPE}}_{\mathit{on}}$ (mathematical slope between melatonin concentrations at t18 and t20, t21 or t22), ${\mathit{SLOPE}}_{\mathit{off}}$ (the slope between t20, t21 or t22, and t30), and $\mathrm{\Delta }SLOPE$, which is generated by subtracting ${\mathit{SLOPE}}_{\mathit{on}}$ from ${\mathit{SLOPE}}_{\mathit{off}}$. DLMO was estimated by multiple regression analysis with the leave-one-out cross-validation (LOOCV) method using ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$, and $\mathrm{\Delta }SLOPE$. The intraclass correlation coefficient (ICC) between the estimated and measured DLMOs was used as the index of estimation accuracy. DLMOs estimated using multiple regression equations with ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$ yielded significant ICCs for the measured DLMOs, with the largest ICC at t20 (ICC = 0.634). Additionally, the ICC between the estimated and measured DLMOs using the equation with $\mathrm{\Delta }SLOPE$ was significant, with a larger ICC at t20 (ICC = 0.726) than that of the equation with ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$. Our results showed that DLMO could be estimated with a certain level of accuracy from salivary melatonin levels at three time points before and after sleep in children.

Supplementary Information

The online version contains supplementary material available at 10.1007/s41105-023-00493-x.

Introduction

The central biological clock in humans is the suprachiasmatic nucleus (SCN) located in the anterior hypothalamus. As directly assessing SCN rhythms in humans is difficult, several physiological functions closely related to the SCN are used as markers of endogenous biological rhythms. Melatonin is a hormone produced by the pineal gland and its secretion pattern is regulated by direct innervation from the SCN, making it representative of circadian rhythms. The dim light melatonin onset (DLMO) time is widely used as the gold standard marker of circadian rhythm phases [1–3] because it is relatively accessible and requires a limited number of samplings (i.e., DLMO can be determined if measurements are only recorded during the early evening hours when melatonin secretion is expected). There are several methods for determining the DLMO [3, 4]. For example, in the fixed threshold method [1], which is commonly used in numerous studies, saliva or plasma samples are collected at regular intervals, ranging between 30 and 60 min. The samples are collected several hours before bedtime and the sample collection continues until bedtime, resulting in a total measurement duration of several hours. The time at which the melatonin concentration exceeds a threshold (3.0 pg/mL for saliva and 10.0 pg/mL for plasma) is determined as the DLMO. A repeatability and agreement study on the DLMO measurement method was conducted, demonstrating a certain degree of reliability in measuring DLMO [4].

However, there are some drawbacks to measuring DLMO. One of these is the “masking effect,” which is the effect of external or internal factors on changes in circadian markers [5]. To precisely evaluate DLMO, controls of ambient light and other factors (posture, diet, etc.) affecting melatonin secretion are required to avoid masking effects, such as the forced desynchrony protocol [6] and constant routines [7]. Additionally, melatonin concentrations in plasma or saliva are considerably low, requiring highly sensitive analyses, such as radioimmunoassays (RIAs) and enzyme-linked immunosorbent assays (ELISAs) [8], which are expensive and time consuming. Furthermore, to evaluate DLMOs, several blood or saliva samples need to be collected at 30–60 min intervals in the evening [9], as mentioned above, leading to an increased number of experiments and analyses. The development of a simplified DLMO assessment method would be beneficial for conducting measurements in participants who may not easily cooperate, such as children.

The timing of DLMO strongly reflects the temporal characteristics of melatonin secretion. In children, DLMO occurs on average one hour before the habitual sleep onset time and melatonin secretion ends close to the time of waking. Individuals with very early DLMOs demonstrate high melatonin secretion earlier in the evening and have already finished secretion by the time of waking. In contrast, individuals with late DLMOs have lower melatonin secretion even just before the onset of sleep, and a certain amount of melatonin secretion remains at the time of waking. Thus, melatonin concentrations before sleep and after waking are associated with DLMO and may be plausible predictors. Additionally, the melatonin secretion profile could be represented by slopes during the increasing and decreasing phases; namely, one for melatonin concentrations from before the start of secretion (around sunset) to after the start of secretion, and the other for those from the beginning to the end of secretion (after waking). If DLMO can be estimated using two slopes, the melatonin sampling points required for DLMO evaluation can be reduced to three (first: before the start of secretion; second: after the start of secretion; and thrid: at the end of secretion).

In this study, we aimed to establish a method for estimating the DLMO using slopes calculated from melatonin concentrations at a few sampling points before and after sleep. In particular, we examined a method that uses two slopes calculated from three melatonin sampling points. Additionally, we examined a method that uses the difference between the two slopes for simplicity. For each method, we established a model for the DLMO estimation using multiple regression analysis, and verified its estimation accuracy.

Materials and methods

Participants

The subjects of this study included 30 children (mean age ± SD: 10.2 ± 1.3 years, age range: 9–14 years, male% = 76.7%) who participated in long-term residential activities during the summer of 2019 and winter of 2020. Based on their self-reports, we confirmed that none of the participants had color vision deficiency. Habitual sleep schedules were confirmed using the Japanese versions of the Children’s ChronoType Questionnaire (CCTQ) [10, 11] for elementary school participants, and the Japanese versions of the Munich ChronoType Questionnaire (MCTQ) [12, 13] for junior high school participants. The participants’ wake and bedtimes on school days were 6:27 ± 0:32 h (mean ± SD) and 21:29 ± 0:35 h, respectively, whereas their wake and bedtimes on free days were 7:09 ± 1:07 h and 21:55 ± 0:42 h, respectively. Written informed consent for participation in the study was obtained from each child’s parents. The study was conducted with the approval of the Nippon Sport Science University.

Phase determination

Saliva samples were collected from children using a cotton plug (Salivette, Sarstedt) up to six times every hour from 17:30 (t17) to 23:30 (t23); namely, 17:30 (t17), 18:30 (t18), 19:30 (t19), 20:30 (t20), 21:30 (t21), 22:30 (t22), and 23:30 (t23) on the evening of the first (2020) or second (2019) day of each residential activity. Saliva samples were collected at 6:00 (t30) the following morning in both the 2019 and 2020 groups. From the beginning to the end of saliva collection, the vertical illuminance was set to less than 30 lx, and the children engaged in quiet activities (reading, talking, homework, etc.) in a sitting position. Eating and drinking were prohibited 15 min prior to saliva collection. The collected saliva samples were frozen at or below  – 10 °C and transported to Kyushu University. The delivered saliva samples were thawed and quantified by a radioimmunoassay (RIA) kit (RK-DSM2-U; Novolytix). The detection limit of the assay was 0.2 pg/mL (0.9 pmol/L). The circadian phase is determined by the onset time of salivary melatonin secretion in the evening, known as the DLMO. The time of DLMO was determined by linear interpolation between two time points at which the melatonin concentration crossed the 4.0 pg/mL threshold [14, 15].

Parameterizing the slope of melatonin secretion

The slope of melatonin secretion was calculated as follows.

First, the following slopes were obtained:

$$SLOP{E}_{\mathit{on}}=\left(Me{l}_{2nd}-Me{l}_{1st}\right)/\left(t_2-t_1\right)$$

$$SLOP{E}_{\mathit{off}}=\left(Me{l}_{3rd}-Me{l}_{2nd}\right)/\left(t_3-t_2\right)$$

Mel_1st, Mel_2nd, and Mel_3rd are the melatonin concentrations at the time points before the start of melatonin secretion (t18), melatonin secretion (t₂₀, t₂₁, or t₂₂), and the end of melatonin secretion (t30), respectively. The melatonin concentration at t₂₀, t₂₁ or t₂₂ was used as Mel_2nd. t₁, t₂, and t₃ are the collection times of saliva samples Mel_1st, Mel_2nd, and Mel_3rd, respectively (Figure S1A–C). DLMO was estimated by the following equation using ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$:

$$DLM{O}_{\mathit{est}}=\beta +{\alpha }_{1}SLOP{E}_{\mathit{on}}+{\alpha }_{2}SLOP{E}_{\mathit{off}}$$

As there are three Mel_2nd sampling time points, namely, t₂₀, t₂₁, and t₂₂, there are also three ${\mathit{SLOPE}}_{\mathit{on}}$/ ${\mathit{SLOPE}}_{\mathit{off}}$ values; therefore, three DLMO_est values are obtained depending on the used Mel_2nd. Furthermore, $\mathrm{\Delta }SLOPE$ was calculated from ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$ as follows:

$$\mathrm{\Delta }SLOPE=SLOP{E}_{\mathit{off}}-SLOP{E}_{\mathit{on}}$$

In general, melatonin secretion profiles show high and low values at night and in the early morning, respectively, resulting in negative $\mathrm{\Delta }SLOPE$ values. However, when the circadian rhythm phase was delayed, namely, in the eveningness chronotype, melatonin secretion was low at night and persisted in the morning, resulting in positive $\mathrm{\Delta }SLOPE$ values (Figure S1D). Using the $\mathrm{\Delta }SLOPE$ obtained from the three Mel_2nd values, the DLMO_est values were calculated using the following equation:

$$DLM{O}_{\mathit{est}}=\beta +{\alpha }_1\mathrm{\Delta }SLOPE$$

Statistical analyses

DLMO estimations using the melatonin secretion slope were conducted using the leave-one-out cross-validation (LOOCV) method, wherein the DLMO of one subject was used as the objective variable and estimated using the slope of the other subjects. Multiple regression analysis was conducted using the DLMO of each individual as the objective variable and ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$, or $\mathrm{\Delta }SLOPE$ as the explanatory variables. The root mean square error (RMSE), R-squared (R²) value, and mean absolute error (MAE) were calculated to determine the accuracy of the LOOCV prediction. The final model, including the partial regression coefficients and constant terms, was obtained using the data from all participants as the objective and explanatory variables. The intraclass correlation coefficient (ICC) was calculated between the estimated DLMO obtained from the multiple regression equations and the measured DLMO, and was used as a reference for accuracy.

Bland–Altman analysis [16], using the estimated and measured DLMOs, was used to evaluate the systematic error in the estimated DLMOs. The presence or absence of systematic error was determined by the following two methods: (1) the limits of agreement (LoA) were considered as standard deviations (SDs) of ± 1.96 of the differences to determine the presence of an additive error. If the LoA did not contain zero, we concluded that an additive error was present because the distribution was biased in a certain direction, positive or negative, from the x-axis. (2) To determine the presence of a proportional error, a regression equation was calculated for the Bland-Altoman plot, and the significance of the regression was examined. A significant regression equation indicated that the proportional error was present. Data are presented as mean ± SD. p < 0.05 was considered statistically significant in all statistical analyses. We used R 4.2.2 (R Core Team) for statistical analyses and R packages “caret (6.0–94),” “irr (0.84.1),” and “blandr (0.5.1)” for conducting LOOCV, to calculate the the ICC [17], and for the Bland–Altman analysis, respectively.

Results

Melatonin profile and dim light melatonin onset (DLMO)

Among the hourly saliva samples collected from 17:30 (t₁₇) to 23:30 (t₂₃), those from all 30 participants were collected at five time points, from t₁₇ to t₂₁, but those from only 22 and three participants were collected at t₂₂ and t₂₃, respectively. The next morning at 6:00 (t₃₀), saliva from all 30 participants was collected. Among those for the 30 subjects, DLMO calculations could not be conducted in five subjects (four subjects did not exceed the 4 pg/mL threshold for melatonin secretion onset, and one subject’s melatonin secretion exceeded the threshold at all collection points). Therefore, subsequent analyses were conducted with 25 participants (n = 25 for t₁₇–t₂₁ and t30, n = 21 for t₂₂, and n = 3 for t₂₃).

At t₁₇ and t₁₈, melatonin secretion was below the threshold in all 25 subjects (t₁₇: 0.77 ± 0.68 pg/ml, t₁₈: 0.72 ± 0.53 pg/ml); 5/25 subjects (20.0%) at t₁₉, 17/25 subjects (68.0%) at t₂₀, 24/25 subjects (96.0%) at t21, 20/22 subjects (95.2%) at t₂₂, and 3/3 subjects (100%) at t₂₃ had melatonin secretion levels above the threshold (Figure S2). The mean DLMO in 25 subjects was 20.03 ± 0.81 h (mean ± SD, range 18.62–21.68 h).

Estimating DLMO using the slope of three-point melatonin data

Multiple regression analysis with LOOCV using the slope from t₁₈ to any point between t₂₀ and t₂₂ (${\mathit{SLOPE}}_{\mathit{on}}$) and that from any point between t₂₀ and t₂₂ to t₃₀ the next morning (${\mathit{SLOPE}}_{\mathit{off}}$) yielded significant multiple regression equations for t₂₀, t₂₁, and t₂₂. The mean ± SD of estimated DLMOs were 20.00 ± 0.92, 20.00 ± 0.77, and 20.20 ± 0.74 h for t₂₀, t₂₁, and t₂₂, respectively. The mean RMSE, R², and MAE were 0.739, 0.393, and 0.521 for t₂₀; 0.711, 0.334, and 0.534 for t₂₁; and 0.760, 0.213, and 0.569 for t₂₂, respectively, showing certain explanatory rates. The ICC values between estimated and measured DLMOs using each multiple regression equation were significant, with the largest at t₂₀ (ICC = 0.634), followed by t₂₁ (ICC = 0.591), and the smallest at t₂₂ (ICC = 0.477) (Fig. 1).

Fig. 1.

Accuracy of DLMO estimates obtained from ${\mathit{SLOPE}}_{\mathit{on}}and{\mathit{SLOPE}}_{\mathit{off}}$. Correlations between the estimated and measured DLMO when melatonin concentrations were obtained at A t₂₀, intraclass correlation coefficient (ICC) = 0.634 (p < 0.001); B t21, ICC = 0.591 (p < 0.001); and C t22, ICC = 0.477 (p = 0.011). The horizontal and vertical axes show the measured and estimated DLMOs, respectively. The data points overlap on the diagonal line when the estimated values coincide with the measured values

Estimating DLMO using ΔSlope of three-point melatonin data

Multiple regression equations with LOOCV using $\mathrm{\Delta }SLOPE$ calculated from the difference between ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$ were also significant, wherein the mean ± SDs of estimated DLMOs were 20.00 ± 0.81, 20.00 ± 0.71, and 20.10 ± 0.58 h for t₂₀, t₂₁, and t₂₂, respectively. Additionally, the mean RMSE, R², and MAE were 0.606, 0.515, and 0.451 for t₂₀, 0.630, 0.420, and 0.478 for t₂₁, and 0.551, 0.447, and 0.474 for t₂₂, respectively, indicating a higher explanatory rate than multiple regression equations using ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$ (Fig. 2). The estimated DLMOs using each multiple regression equation with $\mathrm{\Delta }SLOPE$ yielded a significant ICC higher than that of the multiple regression equation using ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$ in the following order of coefficients: t₂₀ (ICC = 0.726), t₂₂ (ICC = 0.661), and t₂₁ (ICC = 0.654).

Fig. 2.

Accuracy of DLMO estimates obtained from $\mathrm{\Delta }SLOPE$. Correlations between the estimated and measured DLMOs when melatonin concentrations were obtained at A t₂₀, intraclass correlation coefficient (ICC) = 0.726 (p < 0.001); B t21, ICC = 0.654 (p < 0.001); and C t22, ICC = 0.661 (p < 0.001). The horizontal and vertical axes show the measured and estimated DLMO, respectively. The data points overlap on the diagonal line when the estimated values coincide with the measured values

Bland–Altman analysis

For the ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ model, the estimated biases (mean difference between the estimated and measured DLMOs) were  – 0.006 h (upper LoA: 1.47 h, lower LoA:  – 1.48 h),  – 0.013 h (upper LoA: 1.41 h, lower LoA:  – 1.44 h), and  – 0.067 h (upper LoA: 1.45 h, lower LoA:  – 1.59 h) for t₂₀, t₂₁, and t₂₂, respectively, resulting in no additive errors. Additionally, for the $\mathrm{\Delta }SLOPE$ model, the estimated biases were 0.046 h (upper LoA: 1.25 h, lower LoA:  – 1.16 h), 0.033 h (upper LoA: 1.29 h, lower LoA:  – 1.23 h), and 0.009 h (upper LoA: 1.11 h, lower LoA:  – 1.10 h) for t₂₀, t₂₁, and t₂₂ respectively. These results indicate that the estimated and measured DLMOs were almost identical, and no additional errors were observed for either ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ or $\mathrm{\Delta }SLOPE$. However, Spearman’s rank correlation showed significant positive correlations between the ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ model and t20 (ρ = 0.421, p = 0.037), and $\mathrm{\Delta }SLOPE$ model and t₂₀ (ρ = 0.533, p = 0.007) and t₂₁ (ρ = 0.518, p = 0.009), suggesting the existence of proportional errors, wherein the error increases as the circadian phase is delayed (Fig. 3).

Fig. 3.

Bland–Altman plot between the estimated DLMO using cross-validation method and measured DLMO. A–C The Bland–Altman plot showing agreement between the measured and estimated DLMOs using the cross-validation method with ${\mathit{SLOPE}}_{\mathit{on}}and{\mathit{SLOPE}}_{\mathit{off}}$ when melatonin concentrations were obtained at (A) t20, $\rho$ = 0.421 (p = 0.037); B t21, $\rho$ = 0.389 (p = 0.055); and C t22, $\rho$ = 0.230 (p = 0.315). D–F Bland–Altman plot showing agreement between the measured and estimated DLMOs with $\mathrm{\Delta }SLOPE$ when melatonin concentrations were obtained at (A) t₂₀, $\rho$ = 0.533 (p = 0.007); (B) t₂₁, $\rho$ = 0.518 (p = 0.009); and (C) t22, $\rho$ = 0.390 (p = 0.082). The horizontal axis shows the mean values of the estimated and measured DLMOs, and the vertical axis shows the difference between the estimated and measured DLMOs. The solid horizontal line represents the average difference between the estimated and measured DLMOs. The dashed horizontal full lines represent the limits of agreement (LoA) as the standard deviations of ± 1.96 of the differences between the estimated and measured DLMOs

Determining the estimation equation using the final model

Cross-validation yielded significant estimation equations for ${\mathit{SLOPE}}_{\mathit{on}}$, ${\mathit{SLOPE}}_{\mathit{off}}$, and $\mathrm{\Delta }SLOPE$ all at t₂₀, t₂₁, and t₂₂. Therefore, a single DLMO estimation equation was derived from the final model (prediction using all data), and the DLMO was estimated for each subject (Tables S1 and S2). Using the final model, the mean ± SDs of estimated DLMOs for ${\mathit{SLOPE}}_{\mathit{on}}$/ ${\mathit{SLOPE}}_{\mathit{off}}$ were 20.00 ± 0.66, 20.00 ± 0.61, and 20.10 ± 0.55 h for t₂₀, t₂₁, and t₂₂, respectively, and those for $\mathrm{\Delta }SLOPE$ were 20.00 ± 0.66, 20.00 ± 0.61, and 20.10 ± 0.55 h for t₂₀, t₂₁, and t₂₂, respectively. The ICCs for ${\mathit{SLOPE}}_{\mathit{on}}$/ ${\mathit{SLOPE}}_{\mathit{off}}$ ranged from 0.714 to 0.809 and those for $\mathrm{\Delta }SLOPE$ ranged from 0.713 to 0.809, which were generally higher than those in the cross-validation (Figures S3 and S4, all p < 0.001). Significant positive correlations were obtained for the Bland–Altman plots in all final models as well as for the LOOCV, suggesting the presence of proportional errors, wherein the errors increased as the circadian phase was delayed (Figure S5).

Discussion

In this study, the slope between two time points of melatonin secretion (${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$) and the difference between the two slopes ($\mathrm{\Delta }SLOPE$) were calculated from salivary melatonin concentrations collected from 25 out of 30 children at three time periods before (t₁₈), during (t₂₀–t₂₂), and after (t₃₀) the start of melatonin secretion, which represented the periods before and after sleep. The DLMO estimation was conducted with multiple regression equations using LOOCV, ICC, and Bland–Altman analysis to evaluate the estimation accuracy.

The independent estimation by LOOCV showed that both ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ and $\mathrm{\Delta }SLOPE$ had mean values that were mostly consistent with the actual DLMO, although each model showed a certain range of SD. The R² and MAE of the estimation equation for DLMO in the LOOCV and ICC methods were most desirable at t₂₀ for both ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ and $\mathrm{\Delta }SLOPE$; this may be attributed to the fact that the average DLMO of the subjects in this study was approximately 20:00. As 17 of the 25 participants (68%) showed melatonin levels above the threshold at t₂₀, and 24 of the 25 participants (96%) showed melatonin levels above the threshold at t₂₁, it is likely that the estimation accuracy decreased at or after t₂₁. Overall, the estimation of the DLMO equations using $\mathrm{\Delta }SLOPE$ showed a higher rate of explanation than that using ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$. This suggests that $\mathrm{\Delta }SLOPE$ reflects the contrast between the increase and decrease in melatonin secretion; thus, the use of $\mathrm{\Delta }SLOPE$ as a composite variable may enable the extraction of more characteristics of the melatonin secretion profile.

In the Bland-Altmann plot, the bias (mean difference between estimated and actual DLMO) for each model was less than 0.1 h (0.3–4 min for ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ and 0.5–2.7 min for $\mathrm{\Delta }SLOPE$), indicating the absence of an additive error. Furthermore, most of the differences were within the range of 1 h, suggesting that the accuracy of these models is equivalent or much better for circadian phase predictions using a multi-omics approach [18–22] or predictions using behavioral and environmental information [23–27]. However, both the estimated DLMOs using ${\mathit{SLOPE}}_{\mathit{on}}$/${\mathit{SLOPE}}_{\mathit{off}}$ and $\mathrm{\Delta }SLOPE$ showed significant proportional errors, wherein errors were more than 30 min for individuals with a delayed circadian phase, especially those with DLMO after t₂₁. As the number of subjects decreased after saliva collection at t₂₂ in this study, individuals in the late circadian phase were not included in our estimation of the DLMO equation, and sufficient estimation accuracy was not achieved.

The estimated DLMO equation using the final model for DLMO showed the highest ICC at t20, similar to that in LOOCV, and overall, a higher ICC than that obtained using LOOCV. As their validity was confirmed with LOOCV, the coefficients of the final model could be used to estimate children’s DLMO using only three melatonin data points.

In studies of circadian rhythms, it is important to measure DLMO as a circadian phase marker. However, as mentioned in the introduction, DLMO measurement is not easy from sampling to assay. The magnitude of light-induced melatonin suppression is often examined to determine the effects of nighttime light on circadian rhythms [28–31]. Although melatonin suppression is closely linked to circadian phase resetting [32], the proposed functional separation between the two [33] necessitates a separate evaluation for a thorough understanding of the non-image-forming effect of light in humans. Our proposed method, which can estimate the DLMO using only 3 points sampling, reduces the burden of circadian phase measurements in field studies. This approach can advance our understanding of the interplay between light and human circadian functions.

Our study had some limitations. First, the sample size was small (30 subjects; 25 subjects for analysis). Therefore, cross-validation was used and the evaluation was not conducted in an independent population. Second, there are age- and sex-related biases. The majority of the participants in this study (76.7%) were boys, and the standard deviation of age was narrow (1.3 years old). Therefore, the applicability of this study to populations with age and sex ratios differing from those in the present study should be carefully considered. Third, many of the subjects in this study had relatively early circadian rhythm phases and few had late circadian phases. The mean DLMO for the present subjects (20.03 ± 0.81 h) is 40–60 min earlier than the DLMOs of previous studies for children [34–37]. Therefore, in populations that exhibit late DLMOs, the estimation accuracy may vary.

Conclusions

DLMO can be estimated with a certain level of accuracy from salivary melatonin levels at three time points: before and after sleep. Additionally, the difference between the slopes of the increase and decrease in melatonin secretion ($\mathrm{\Delta }SLOPE$) may be a better indicator of an individual's melatonin secretion profile. Future studies with more diverse populations (age, sex, and circadian rhythm phases) are required to verify the applicability of the estimation accuracy and establish more accurate estimation equations.

Supplementary Information

Below is the link to the electronic supplementary material.

List of Symbols

DLMO

Dim light melatonin onset

t18, t20, t21, t22, and t30

Salivary melatonin measured at 18:30, 20:30, 21:30, 22:30 and 6:00 (the next morning)

Mel_1st

Melatonin concentration at t18

Mel_2nd

Melatonin concentration at t20, t21, or t22

Mel_3rd

Melatonin concentration at t30

${\mathit{SLOPE}}_{\mathit{on}}$

Slope between Mel_1st and Mel_2nd

${\mathit{SLOPE}}_{\mathit{off}}$

Slope between Mel_2nd and Mel_3rd

$\mathrm{\Delta }SLOPE$

Difference between ${\mathit{SLOPE}}_{\mathit{on}}$ and ${\mathit{SLOPE}}_{\mathit{off}}$

DLMO_act

Measured DLMO value

DLMO_est

Estimated DLMO value

LOOCV

Leave-one-out cross-validation

RMSE

Root mean square error

MAE

Mean absolute error

ICC

Intraclass correlation coefficient

LoA

Limit of agreement

Author contributions

SK, AS, and SN designed the study. AS and SN acquired the samples. TE, SK, and SH analyzed the data. TE and SK drafted the manuscript. AS, KT, SH, and SN reviewed the manuscript. All the authors have read and approved the final version of the manuscript.

Funding

This study was supported in part by the JSPS KAKENHI (JP19K21785). The funders had no role in the study design, data collection and analysis, decision to publish, or manuscript preparation.

Declarations

Competing interests

The authors declare that they have no competing interests.

Ethical approval

This study was approved by the Institutional Review Board of Nippon Sport Science University, Japan (Approval No. 019-H057). All procedures involving human participants were conducted in accordance with the ethical standards of institutional and/or national research committees. All participants provided informed consent.

Consent for publication

Not applicable.