Participants were drawn from the Generation R Study, a birth cohort from Rotterdam, the Netherlands. All pregnant women with a delivery date between April 2002 and January 2006 were invited to participate . Since recruitment, the children and their families have been invited for multiple waves of data collection. At 10 years of age 8548 children were invited to visit the research center, of those, 7968 were invited again at 13 years of age. Actigraphic sleep patterns were estimated in a subsample of Generation R, for which in total 1910 children were invited in two separate waves. A detailed description of the sampling strategy for this subsample has been described previously . Briefly, included participants had high follow-up rates, premature born participants were oversampled, and were more often of Western decent. The first actigraphy data collection started nearly 1 year after the 10-year assessment (n = 915) and the second was conducted nearly 1 year after the 13-year assessment (n = 490), these assessments included no repeated measurements. Children were excluded from analyses if the reported sleep or behavioral data was missing at the corresponding age and when outliers corresponding to impossible or highly unlikely values were detected, resulting in a total of 788 children who were included at 10–11 years of age and 344 children at 13–14 years of age. Figure 1 presents a flowchart of the study sample. The Medical Ethics Committee of the Erasmus Medical Center approved all study procedures, and all parents and participants provided written informed consent or assent if appropriate.
Child behavior checklist (CBCL)
The CBCL is a widely used parent-reported screening questionnaire to assess child behavior. The CBCL version 6–18  was used in both waves and consists of 112 items scored on a three point Likert scale (0 = not true, 1 = somewhat true, 2 = very/often true). It is a reliable and valid questionnaire assessing mental health problems in school age children and adolescents . The questionnaire was completed at both age waves by the primary caregiver, which was in the majority of the cases the mother. Specifically, at 10 years of age all data was obtained from maternal report, and at 13 years of age, 8.3% of the CBCL reports were obtained from fathers. Symptom severity is scored with eight empirically derived syndrome scales, being anxious/depressed, withdrawn/depressed, somatic complaints, social problems, thought problems, attention problems, rule-breaking behavior, and aggressive behavior. From these syndrome scales, three broadband scales can be derived, the internalizing scale consists of anxious/depressed, withdrawn/depressed and somatic complaints, (range 0–64), the externalizing scale consists of rule-breaking behavior, and aggressive behavior (range 0–70) and the dysregulation profile scale comprises subscales from both domains as it is a sum score of the anxiety/depressed, attention problems, and aggressive behavior scales (range 0–82), with a higher score reflecting more problems. In the current sample, the dysregulation profile is highly correlated with the total problems score of the CBCL, that includes all 113 items, at both age waves the correlation is 0.96. Further, since this study is embedded in a population-based study, all measures of mental-health were positively skewed. Given that the range was different for the broad domains of mental health, we standardized all mental health measures to a mean of 0 with a standard deviation of 1.
Sleep patterns and the 24 h activity rhythm were estimated with wrist tri-axial actigraphy (GENEActiv; Activinsights, UK) worn on non-dominant wrist for 9 subsequent days (5 school days and 4 weekend days) . Each morning children filled out sleep diaries answering questions about their sleep timing (e.g., the time they went to bed). All data from the diaries was manually entered in a database and checked for outliers; no human censoring of bedtime/rise-time was performed. This data was used as input to guide fully automated actigraphy analyses. The binary files were processed using the R-package GGIR . This procedure generated the following sleep measures: total sleep time, sleep onset, sleep onset latency, sleep efficiency, and the total number of awakenings after sleep onset. Total sleep time is the duration of epochs classified as sleep during the night. Sleep onset is the time of falling asleep. Sleep onset latency indicates the time between the reported bedtime and the sleep onset. Sleep efficiency is the total sleep time divided by time in bed. Additionally, we calculated 24 h activity rhythm parameters: the interdaily stability (IS), the intradaily variability (IV), and the onset of the least active 5-h period in 24-h (L5 onset), according to a method described by Van Someren et al. . Due to the nonparametric nature of the variables no specific waveform is assumed. IS indicates the resemblance of the rhythm between different days. IV indicates the fragmentation of the rhythm to its 24 h amplitude; i.e., the frequency of alterations between active and rest states. L5 is defined as resting levels during the 5 h period when there was the least activity, the L5 onset indicates the timing of the 24 h activity rhythm. Most actigraphy-estimated sleep measures were normally distributed, with the exception of the sleep onset latency, which was right-skewed.
Self reported sleep problems (10–11 years)
Child reported sleep problems were assessed by self-report questionnaire with six questions about their perceived sleep in general: “Do you find it difficult to go to bed?”; “Do you find it difficult to fall asleep?”; “Do you think you get enough sleep?”; “If you wake up at night, do you find it difficult to fall asleep again?”; “Do you feel rested when you wake in the morning?”; “When you come out of your bed in the morning, do you feel rested?”. These questions were derived from the widely used Sleep Disturbance Scale for Children (SDSC)  and slightly rephrased for our pediatric population. Similar questions can be found in other sleep scales for children such as the Sleep Self Report , and the Sleep Habits Survey . The three possible responses for each item: “No”, “Sometimes” or “Yes” were scored on a Likert scale. Responses from all six items were summed to calculate a total score; the total score had an internal consistency of α = 0.65; higher scores indicate more sleep problems.
Self reported sleep problems (13–14 years)
Child reported sleep problems in general were assessed via a questionnaire consisting of questions derived from the Sleep Habits Survey (SHS)  and the Youth Self Report (YSR) . Sleep problems were assessed using four items from the SHS: “How many minutes do you need to fall asleep after the light is shut off”; “How many times do you wake up during the night?” (never, once, two or three times, more than three times); “Do you feel like you normally sleep enough?” (too little, enough, too much); “Do you think you are a good or a poor sleeper?”, and two items from the YSR: “I sleep less than most boys and girls” and “I have trouble sleeping”. Items were individually standardized between 0 and 1, to give all items the same the same weight and summed to make a total sleep problems score; the total score had an internal consistency of α = 0.69; higher scores indicate more sleep problems. For ease of comparison, we standardized both sleep problem scale scores.
Mother-reported sleep problems
Mother-reported sleep problems were obtained during a structured interview that took place during the home-visits performed in the actigraphy subsample. Mothers were asked to report their children’s experienced difficulties initiating or maintaining sleep by using this subscale of the Sleep Disturbance Scale for Children (SDSC) . Seven items were included: “How many hours of sleep does your child get on most nights”, “How long after going to bed does your child usually fall asleep”, “The child goes to bed reluctantly”, “The child has difficulty getting to sleep at night”; “The child feels anxious or afraid when falling asleep”, “The child wakes up more than twice per night”; “After waking up in the night, the child has difficulty to fall asleep again”. All items were scored on a five-point Likert scale. Items were summed to create the sum score; the total score had an internal consistency of α = 0.63, with higher scores indicating more sleep problems. Both child- and mother-reported sleep problems were positively skewed.
To address potential confounding, sex, age at assessment, child national origin, gestational age at birth, maternal education and maternal psychopathology were included as covariates. Child national origin was based on the birth country of the parents and categorized as Western (American Western, Asian Western, Dutch, European, Indonesian & Oceania) and Non-Western (Moroccan, Surinamese & Turkish, Dutch Antilles, African, American Non-Western, Asian Non-Western, Cape Verdean). Gestational age was entered in the model, because in the actigraphy subsample we oversampled children with a lower gestational age at birth . Maternal education was assessed through questionnaire at birth and divided into three categories, being low (no education, primary school), middle (high school, vocational training), and high (higher vocational training, university). Maternal psychopathology was included using measures of the anxiety and depression subscales of the brief symptom inventory (BSI), which was completed when the child was 9 years of age .
We assessed the cross-sectional relation between self- and mother-reported sleep problems and parent-reported mental health problems (internalizing, externalizing, dysregulation profile) at age 10–11 and 13–14. Linear regression analyses were used with sleep problems as the dependent and mental health problems as independent variables in separate models. Similarly, we analyzed the association between actigraphic sleep patterns (sleep duration, sleep onset, sleep onset latency, sleep efficiency, nocturnal awakenings) mental health problems. Lastly, we assess the relationship between the 24 h activity rhythm (IS, IV, L5 onset), and mental health problems.
All analyses were adjusted for different covariates in two step-wise models. The first model was adjusted for age and sex. The second model was additionally adjusted for gestational age at birth, child national origin, maternal educational level, and maternal psychopathology.
All analyses were performed in R 3.6.3 . Our analyses include separate models for ten measures of sleep and three domains of mental health problems, performed at two different ages, resulting in a total of 60 tests. Because of the high number of models we adjusted for multiple testing using the Benjamini-Hochberg procedure . Missing values on covariates, with a maximum of 6.1% missing, were imputed with multiple imputation through chained equations, using the mice package  (30 imputed datasets with 30 iterations).
Sensitivity and exploratory analyses
To assess the robustness of our findings, we performed two sensitivity analyses. First, as the actigraphy subsample might be affected by selection bias, we reran the analyses of self-reported sleep problems and mental health within the larger full samples of children that have self-reported sleep measures and CBCL data (10–11 years: n = 4180; 13–14 years: n = 3468). Second, we assessed whether individual domains of mental health underlie the associations between sleep measures (sleep patterns, 24 h activity rhythm and reported sleep) and the broad domains of mental health. The six syndrome scales that were used to calculate sum scores for the broad domains (anxious/depressed, withdrawn/depressed, somatic complaints, attention problems, rule-breaking behavior and aggressive behavior) were entered into separate models and analyzed using the same models and covariates used in the primary analyses.
To explore whether sleep problems and patterns are related to the two syndrome scales not included in the broad domains (social problems and thought problems), these syndrome scales were entered as independent variables in separate models as exploratory analyses.