Accelerometer-derived movement phenotypes and adolescent mental health in pediatric obesity: A causal machine-learning study

Abstract

Background

Children with overweight or obesity are at elevated risk for later-life mental health challenges, but the role of accelerometer-derived waking movement behaviors remains uncertain. Thus, we examined longitudinal associations of sedentary behavior (SB), light-intensity physical activity (LPA), and moderate-to-vigorous-intensity physical activity (MVPA) at age 7 with later-life internalizing and externalizing problems.

Method

We used data from the UK Millennium Cohort Study, focusing on children with overweight or obesity at age 7 who had valid accelerometer data and a complete set of predefined analytic variables (N = 858). Exposures were average daily minutes of SB, LPA, and MVPA. Outcomes were parent-reported Strengths and Difficulties Questionnaire-based internalizing and externalizing problems scores at ages 11 and 14. A generalized random forests approach was used to estimate average treatment effects (ATEs) and conditional average treatment effects (CATEs), adjusted for relevant demographic, socioeconomic, body mass index, parental distress, baseline mental health, and co-occurring movement intensities; day-of-week activity-pattern variables were used as exploratory candidate moderators.

Results

Estimated ATEs were small. After applying the Benjamini-Hochberg false-discovery-rate (FDR) correction across the 12 primary exposure-outcome tests, only the association between higher SB and lower internalizing problems at age 11 remained statistically significant (ATE = -0.013 SDQ points per additional min/day; 95% CI, -0.019 to -0.007; q < 0.001). No other pathway survived FDR correction, and other nominal or directionally suggestive estimates were interpreted as exploratory. CATE summaries and calibration tests provided limited evidence of reproducible heterogeneity.

Conclusions

Accelerometer-derived waking movement behaviors at age 7 were associated with later SDQ problems scores in small and outcome-specific ways among children with overweight or obesity. Since the study is based on observational data and relies on measured-confounder assumptions, the findings should be interpreted cautiously, and as model-based estimates rather than definitive causal evidence.

Introduction

Childhood overweight and obesity are increasingly recognized as developmental health challenges with social, psychological, and behavioral consequences (Ahmed & Mohammed, 2025; NCD Risk Factor Collaboration, 2024; Sahoo et al., 2015). Children with overweight or obesity are at elevated risk of emotional difficulties, low self-esteem, peer victimization, and weight-related stigma, and may also show co-occurring behavioral or neurodevelopmental difficulties (Agranat-Meged et al., 2005; Alimoradi et al., 2020; Gray et al., 2009; Reeves et al., 2008; Russell-Mayhew et al., 2012; Strauss, 2000). Furthermore, obesity may have a complex and yet-to-be fully understood relationship with neurodevelopmental disorders. For example, there is evidence that attention-deficit/hyperactivity disorder often predates weight gain Agranat-Meged et al. (2005); Brandt et al. (2021); van Egmond-Fröhlich et al. (2012). However, the timing and direction of these potential associations remain to be investigated. In this study, we focused on two broad dimensions of child mental health challenges: (i) internalizing problems, reflecting emotional and peer-related difficulties, and (ii) externalizing problems, reflecting conduct and hyperactivity-related difficulties (Fernandez de la Cruz et al., 2018; Liu, 2004; Liu et al., 2011). Indeed, the basis for our foci stems from data derived from the UK Millennium Cohort Study (MCS) indicating that obesity and emotional problems co-develop from mid-childhood through adolescence (Patalay & Hardman, 2019), making it relevant to identify modifiable behavioral correlates during this developmental period and for informing prevention- and intervention-based research and practice.

Physical activity (PA) is defined as any bodily movement produced by skeletal muscles that results in energy expenditure (Caspersen et al., 1985) and has been identified, as a protective factor for mental health in youth (Chan et al., 2019, Gao et al., 2024, Pinto-Escalona et al., 2024, Mahindru et al., 2023), with a growing body of evidence informed by longitudinal studies and meta-analyses indicate that higher PA levels are associated with reduced risks of depression, anxiety, and broader internalizing and externalizing symptomatology in children and adolescents (Kandola et al., 2020, Recchia et al., 2023; Rodriguez-Ayllon et al., 2019; Vella et al., 2023). However, recent global surveillance showed that adolescent MVPA opportunities can vary by different factors, including but not limited to region and gender and thus serves to underscore the need to interpret youth activity patterns within broader social and access contexts (Araujo et al., 2024). Such longitudinal and population-level evidence is particularly valuable because it can reveal whether waking movement behaviors during the early years of life contribute to later mental health risk, help identify subgroups that may be especially vulnerable to adverse outcomes, and provide an empirical basis for earlier and more targeted intervention efforts. Among children with obesity, planned and structured PA interventions, also referred to as physical exercise, have been shown to improve depressive and anxiety symptoms (King et al., 2020; Li et al., 2025; Recchia et al., 2023; Zhou et al., 2025), self-esteem (King et al., 2020, Gow et al., 2020, Liu et al., 2015), and quality of life (Marker et al., 2018, Shoup et al., 2008, Diao et al., 2020) – improvement that have been reported often independently of changes in body weight.

In addition to PA, sedentary behavior (SB), which is commonly defined as any waking behavior characterized by energy expenditure ≤1.5 metabolic equivalents while sitting, reclining, or lying (Tremblay et al., 2017), is increasingly recognized as a modifiable lifestyle factor related to, yet distinct from PA. For example, several longitudinal observational studies and meta-analyses have reported an association between higher SB, particularly screen-based SB, and poorer mental health outcomes in children and adolescents (Asare, 2015; Rodriguez-Ayllon et al., 2019; Wang et al., 2019; Zhang et al., 2022). Moreover, studies have shown that SB is shaped by social, household, and broader behavioral environments (Hatakeyama et al., 2022; Yang et al., 2019). However, the evidence on this phenomenon is not unequivocal because some studies report null or conflicting associations (Hoare et al., 2016), and accelerometer-defined SB cannot distinguish qualitative SB characteristics such as how much time is spent on mentally passive (e.g., watching television) versus mentally active (e.g., reading, homework, quiet play, or socially supportive seated activities) SB – which can modify associations between SB exposure and mental health (Hallgren et al., 2020; Zhang et al., 2025; Zou et al., 2024). For example, analyses of the general MCS child population found that accelerometer-derived MVPA at age 7 was associated with higher conduct and hyperactivity problems at age 11, whereas overall SB exposure at age 7 was associated with lower hyperactivity scores at age 11 (Ahn et al., 2018).

In addition to gaps on the longitudinal association of waking movement behavior exposure and mental health in nationally representative samples of children with overweight and obesity, this study seeks to address three additional limitations of previous work. First, the majority of previous studies relied on self-reported PA and SB patterns, whereas accelerometry provides a more reliable measure, especially in younger children (Griffiths et al., 2013; Nigg et al., 2020; Rich et al., 2013). At the same time, recent work on wearable validation emphasizes that device placement, algorithms, protocols, and construct definitions can affect estimates of 24-hour movement behaviors, supporting cautious interpretation of accelerometer-derived phenotypes (Giurgiu et al., 2025). Second, previous MCS-based work in the general child population reported counterintuitive associations between accelerometer-derived MVPA, SB, and later SDQ outcomes (Ahn et al., 2018); however, it did not focus specifically on children with overweight or obesity. This is a salient issue because this is a subgroup in wherein movement contexts may differ from those of non-obese children because of active commuting, structured activity opportunities, stigma, body image concerns, weight-focused social comparison, peer influence, and participation barriers (Aparicio-Ugarriza et al., 2020; Gray et al., 2009; Rancourt et al., 2015; Salvy et al., 2012). Third, prior analyses mainly emphasized average associations, leaving limited evidence about whether estimated associations vary across children.

To address the above-mentioned limitations, this study used a generalized random forests approach, often described as causal forests, to provide a flexible framework for estimating population-average and conditional associations under explicit causal assumptions (Athey & Imbens, 2016; Athey et al., 2019; Wager & Athey, 2018), using nationally representative data from the MCS (Giurgiu et al., 2025). Related causal machine-learning work has emphasized the value of flexible nuisance-function adjustment and heterogeneous treatment-effect estimation when the aim is to explore variation in model-based effects rather than assume a single homogeneous association (Belloni et al., 2014; Feuerriegel et al., 2024; Naimi & Whitcomb, 2023). This approach is also aligned with recent work describing how artificial intelligence and machine-learning methods can identify behavioral patterns and support more personalized PA interventions, while recognizing that model performance is task- and dataset-dependent (An et al., 2024). In observational cohort data, however, these estimates should not be equated with effects from randomized trials. Their causal interpretation depends on assumptions such as measured-confounder adjustment, positivity, consistency, and no interference. We therefore use cautious terminology and treat the estimates as model-based causal forest estimates that may inform, but cannot by themselves establish, causality. Focusing on children classified as overweight or obese at age 7, we address two research questions (RQs).

RQ1: Among children with overweight or obesity, how are accelerometer-derived SB, LPA, and MVPA at age 7 associated with internalizing and externalizing problems at ages 11 and 14 in generalized random forest models?

RQ2: To what extent do these model-based estimates vary across individual characteristics and candidate moderators?

Materials and methods

Study design

This longitudinal observational cohort study evaluated whether accelerometer-derived PA intensity and SB at age 7 years were associated with subsequent SDQ internalizing and externalizing problems at ages 11 and 14 years among children classified as overweight or obese at baseline. Based on the observational study design and data, causal interpretation depends on strong assumptions about measured confounding, positivity, and model specification. Thus, the estimates should not be interpreted as equivalent to evidence from randomized controlled trials. The overall study framework is summarized in Fig. 1, and the analytic sample construction is shown in Fig. 2.

Fig. 1.

Conceptual overview of exposure measurement, covariate adjustment, outcome assessment, and generalized random forest analysis. Note: ATE (average treatment effects) and CATE (conditional average treatment effects) are retained as generalized random forest estimands but are interpreted as observational, model-based estimates under measured-confounder assumptions.

Fig. 2.

Screening and analytic sample flow. Note: Counts are based on the MCS cohort description, the MCS age-7 accelerometer activity file, and the prepared analytic source file. Detailed BMI/weight-status denominators before the prepared source file could not be fully reconstructed from the available analytic files. BMI = body-mass index; SDQ = Strengths and Difficulties Questionnaire.

Data source

Data were drawn from the MCS, a nationally representative birth cohort that followed 19,519 children born between 2000 and 2002 across England, Wales, Scotland, and Northern Ireland, with repeated assessments spanning family- and child-level characteristics (Connelly & Platt, 2014). The MCS data have been widely used to study child development, obesity, accelerometer-derived movement behaviors, and mental health (Ahn et al., 2018; Brandt et al., 2021; Griffiths et al., 2013; Patalay & Hardman, 2019; Werneck et al., 2026). The MCS was conducted in compliance with the Declaration of Helsinki for human rights, with ethical approval obtained from the NHS Research Ethics Committee and informed consent obtained from parents or primary caregivers.

Analytic sample

At age 7 years, height (nearest 0.1 cm) and weight (nearest 0.1 kg) were measured by trained staff and used to calculate body mass index (BMI, kg/m2). Children were classified as overweight or obese using age- and sex-specific International Obesity Task Force (IOTF) cut-off values (Cole et al., 2000). The available MCS age-7 accelerometer activity file contained 6675 valid child activity records; prior work has described participation, non-response, and accelerometer-derived activity patterns in this MCS sweep (Griffiths et al., 2013; Rich et al., 2013). In the prepared age-7 analytic source file, 1142 records had IOTF-defined overweight or obesity and valid accelerometer-derived movement variables. We excluded records with incomplete baseline covariates and/or follow-up SDQ outcomes, resulting in a final analytic sample of 858 children (Fig. 2). A stricter weekday/weekend robustness sample retained 668 of these children who had at least one valid weekday and at least one valid weekend day.

Measurements

At age 7 years (2008–2009), physical activity was assessed using Actigraph GT1M accelerometers worn on the right hip for seven consecutive days and removed only for water-based activities; devices recorded activity in 15-second epochs. A valid day required at least 10 h of wear time, and participants were included if they provided at least two valid days, consistent with the MCS accelerometer protocol used in previous analyses (Brandt et al., 2021; Griffiths et al., 2013; Rich et al., 2013). Non-wear periods were defined as at least 20 consecutive minutes of zero counts. Intensity thresholds were defined as SB <100 counts per minute (cpm), LPA 100–2240 cpm, and MVPA 2241–11,714 cpm; counts >11,714 cpm were treated as likely spurious. Exposures were expressed as average minutes/day across valid wear days and not as standardized units. The raw daily accelerometer files included valid-day indicators, weekday/weekend indicators, total valid time, total valid time including unclassified activity time, and non-wear time. We therefore added sensitivity analyses that restricted the sample to children with at least one valid weekday and one valid weekend day and that additionally adjusted for mean daily valid wear time. Average treatment effects (ATE) and conditional average treatment effects (CATE) represent the estimated change in raw SDQ problems score associated with a one-minute/day higher exposure, conditional on the modeled covariates and other movement intensities where included.

The Strengths and Difficulties Questionnaire (SDQ) is a widely used measure of child mental health (Goodman, 1997). The parent/primary-caregiver reported SDQ includes five subscales: emotional problems, peer problems, conduct problems, hyperactivity, and prosocial behavior. Each subscale contains five items rated 0 = not true, 1 = somewhat true, and 2 = certainly true. Internalizing problems were computed as emotional problems plus peer problems, and externalizing problems were computed as conduct problems plus hyperactivity, following evidence on the structure of child psychopathology symptoms (Fernandez de la Cruz et al., 2018). The resulting composite scores for internalizing and externalizing problems ranged from 0 to 20, with higher scores indicating more difficulties. The present analyses used internalizing and externalizing problems scores at ages 11 and 14 as outcomes. The baseline SDQ covariate available in the analytic file ranged from 2 to 10 in the study sample and was used for baseline mental health adjustment rather than as a follow-up outcome score.

Covariates

Covariates were selected a priori based on temporal ordering and plausible common causes of both movement behaviors and later mental health. Core baseline covariates included sex, ethnicity, BMI, baseline SDQ score, parental psychological distress, parental education, and household poverty. These variables precede or coincide with the age-7 exposure assessment and were used to reduce measured confounding. However, it is worth noting that this adjustment strategy cannot rule out unmeasured confounding or reverse/bidirectional processes between obesity, activity, and mental health (Ekelund et al., 2008).

Demographic covariates included sex and ethnicity (White; Indian; Pakistani and Bangladeshi; Black or Black British, Mixed, or Other). Health-related covariates included measured BMI and the baseline SDQ score. Family factors included parental psychological distress (Kessler-6 score), parental education level according to the National Vocational Qualifications (NVQ) framework, and household poverty, defined as equivalized household income below 60% of the UK national median.

Day-of-week activity-pattern variables were derived from available daily accelerometer records and used only as exploratory candidate moderators. Missing day-of-week values were imputed using k-nearest-neighbor imputation (k = 5). These variables were not used to define the primary SB, LPA, or MVPA exposures. Weekday-weekend patterning was considered relevant because children's movement behaviors can differ between school days, weekends, and other structured settings (Brazendale et al., 2017; McMinn et al., 2013; Noonan et al., 2017; Tassitano et al., 2020).

Estimands and interpretation

The primary estimands were model-based ATEs for age-7 SB, LPA, and MVPA in relation to SDQ internalizing and externalizing problems at ages 11 and 14, and CATEs describing variation in these estimates across covariate profiles. We retained the conventional ATE and CATE terminology because these are the estimands returned by the generalized random forest framework, but we interpret them cautiously as observational, model-based estimates under measured-confounder assumptions.

Statistical analysis

We estimated ATEs and CATEs using generalized random forests implemented with the R grf package. The treatment variable was continuous in minutes/day. Separate causal forests were fitted for each exposure-outcome pair. The model matrix included core covariates, the two non-focal movement intensities, and candidate day-of-week activity-pattern features. Since day-of-week activity-pattern variables were derived from the same accelerometer assessment as the focal exposures, they were not interpreted as confounders; their role was limited to exploratory heterogeneity assessment. Forests used 2000 trees, honesty-based sample splitting (honesty = TRUE; honesty.fraction = 0.5), internal tuning of grf parameters (tune.parameters = 'all'), and fixed model-specific random seeds for reproducibility. Forest-based asymptotic standard errors were used for ATE inference. Altogether 12 primary exposure-outcome tests were conducted. To account for the multiple-comparison problem, Benjamini-Hochberg false-discovery-rate (BH-FDR) with adjusted p-values was calculated and reported (Benjamini & Hochberg, 1995). Heterogeneity was evaluated descriptively using CATE distribution summaries and formally using grf::test_calibration(), focusing on the differential forest prediction term as an exploratory calibration test for heterogeneity (Athey et al., 2019; Wager & Athey, 2018). Descriptive statistics were computed in Stata 18.0.

Results

Sample characteristics and baseline activity

The analytical sample included 858 children with overweight or obesity at age 7 years (mean age, 7.21 years; 42.54% male). Most participants were White (87.76%), with a mean BMI of 19.90 kg/m² (SD, 1.99); 75.17% were classified as overweight and 24.83% as obese. Socioeconomic disadvantage was present in 22.72% of participants, and mean parental psychological distress was 3.05 (SD, 3.81). The sample provided a mean of 5.49 valid accelerometer days (SD, 1.55), including 4.27 valid weekdays (SD, 1.18) and 1.22 valid weekend days (SD, 0.81); mean daily valid wear time was 737.32 min/day (SD, 62.36). At age 7 years, average daily movement time was 395.40 min/day (SD, 67.23) in SB, 283.95 min/day (SD, 43.11) in LPA, and 56.44 min/day (SD, 20.75) in MVPA. Mean SDQ internalizing and externalizing problems scores were 3.17 (SD, 3.27) and 3.82 (SD, 3.30) at age 11, and 3.81 (SD, 3.78) and 3.80 (SD, 3.39) at age 14 (Table 1). In the available unique source-ID comparison, excluded source IDs had slightly higher BMI, lower baseline SDQ scores, a higher prevalence of household poverty, and a different ethnicity distribution, whereas SB, LPA, MVPA, sex, and parental psychological distress were not statistically significant (Table S4).

Table 1.

Baseline characteristics of the analytic sample of children with overweight or obesity (N = 858).

Characteristic	Value
Age, years, mean (SD)	7.21 (0.24)
Sex, n (%)
Male	365 (42.54%)
Female	493 (57.46%)
Ethnicity, n (%)
White	753 (87.76%)
Black or Black British	40 (4.66%)
Indian	18 (2.10%)
Pakistani and Bangladeshi	23 (2.68%)
Mixed	17 (1.98%)
Other ethnic group	7 (0.82%)
BMI and weight status
BMI, kg/m2, mean (SD)	19.90 (1.99)
Overweight, n (%)	645 (75.17%)
Obesity, n (%)	213 (24.83%)
Family and socioeconomic factors
Household income below 60% of national median, n (%)	195 (22.73%)
Parental psychological distress, mean (SD)	3.05 (3.81)
Parental education, n (%)
NVQ level 1 (foundation-level qualifications)	55 (6.41%)
NVQ level 2 (GCSE or equivalent)	246 (28.67%)
NVQ level 3 (A-level or equivalent)	123 (14.34%)
NVQ level 4 (higher education certificate, diploma, or degree)	311 (36.25%)
NVQ level 5 (postgraduate degree or higher)	56 (6.53%)
Other/overseas/none of these	67 (7.81%)
Movement behaviors at age 7, min/day, mean (SD)
Sedentary behavior	395.40 (67.23)
Light-intensity physical activity	283.95 (43.11)
Moderate-to-vigorous physical activity	56.44 (20.75)
Mental health variables, mean (SD)
Baseline SDQ score at age 7 (range in analytic sample: 2–10)	8.93 (1.39)
Internalizing problems at age 11 (0–20)	3.17 (3.27)
Externalizing problems at age 11 (0–20)	3.82 (3.30)
Internalizing problems at age 14 (0–20)	3.81 (3.78)
Externalizing problems at age 14 (0–20)	3.80 (3.39)

Note: Continuous variables are reported as mean (SD), and categorical variables as n (%). The baseline SDQ score is the age-7 SDQ covariate available in the analytic file (range in this sample: 2–10). Internalizing and externalizing problems scores each range from 0 to 20. BMI, body mass index; SB, sedentary behavior; LPA, light-intensity physical activity; MVPA, moderate-to-vigorous-intensity physical activity; SDQ, Strengths and Difficulties Questionnaire; NVQ, National Vocational Qualifications.

Average model-based estimates of activity intensity and sedentary time on later SDQ problems

Across the 12 primary exposure-outcome combinations, estimated ATEs were small (Table 2). After BH-FDR correction, only the SB-age-11 internalizing pathway remained statistically significant. LPA showed no statistically significant average association with SDQ externalizing or internalizing problems at either age 11 or age 14.

Table 2.

Model-based average treatment-effect estimates for accelerometer-derived sedentary behavior, light physical activity, and moderate-to-vigorous physical activity at age 7 years on Strengths and Difficulties Questionnaire internalizing and externalizing problems at ages 11 and 14 years.

Exposure	Outcome	ATE estimate	95% CI	p value	BH-FDR q value
SB	Externalizing problems at age 11	−0.006	[−0.013, −0.0001]	0.046	0.104
SB	Internalizing problems at age 11	−0.013	[−0.019, −0.007]	< 0.001	< 0.001
SB	Externalizing problems at age 14	−0.007	[−0.013, −0.001]	0.025	0.099
SB	Internalizing problems at age 14	−0.008	[−0.017, −0.0002]	0.045	0.104
LPA	Externalizing problems at age 11	0.007	[−0.004, 0.017]	0.210	0.252
LPA	Internalizing problems at age 11	−0.001	[−0.012, 0.009]	0.828	0.828
LPA	Externalizing problems at age 14	0.007	[−0.003, 0.018]	0.177	0.236
LPA	Internalizing problems at age 14	0.003	[−0.009, 0.015]	0.635	0.692
MVPA	Externalizing problems at age 11	0.019	[−0.001, 0.039]	0.060	0.104
MVPA	Internalizing problems at age 11	−0.025	[−0.046, −0.003]	0.025	0.099
MVPA	Externalizing problems at age 14	0.019	[−0.001, 0.039]	0.060	0.104
MVPA	Internalizing problems at age 14	−0.020	[−0.046, 0.005]	0.123	0.185

Note: ATEs were estimated using generalized random forests. The exposure unit is one additional minute/day, and outcomes are raw SDQ internalizing or externalizing problems scores. BH-FDR q values were calculated across the 12 primary exposure-outcome tests. SB, sedentary behavior; LPA, light-intensity physical activity; MVPA, moderate-to-vigorous-intensity physical activity; ATE, average treatment effect; CI, confidence interval; BH-FDR, Benjamini-Hochberg false-discovery-rate correction.

For MVPA, the estimate for internalizing problems at age 11 was nominally negative (ATE, −0.025; 95% CI, −0.046 to −0.003; p = 0.025; q = 0.099), but it did not remain statistically significant after BH-FDR correction. MVPA estimates for externalizing problems at ages 11 and 14 were directionally positive but imprecise (both p values approximately 0.060; q = 0.104), and the age-14 internalizing estimate was not significantly different from zero.

For SB, estimates were negative across all four outcomes. The strongest estimate was for lower internalizing problems scores at age 11 (ATE, −0.013; 95% CI, −0.019 to −0.007; p < 0.001; q < 0.001). The remaining SB estimates were small and nominally distinguishable for age-11 externalizing, age-14 externalizing, and age-14 internalizing problems, but none survived BH-FDR correction (q-values = 0.099–0.104). Because ATEs are expressed per one additional minute/day, a 30-minute/day difference corresponds to approximately −0.39 SDQ points for SB and internalizing problems at age 11.

Robustness analyses addressed the two-valid-day criterion and wear time (Table S3). In the stricter weekday/weekend sample (N = 668), the SB-age-11 internalizing estimate remained directionally similar (ATE, −0.010; 95% CI, −0.017 to −0.003; p = 0.006), although it did not survive BH-FDR correction across 12 tests (q = 0.073). No pathway survived FDR correction in this restricted sample. In the full sample additionally adjusted for mean daily valid wear time, the SB-age-11 internalizing estimate remained statistically significant after FDR correction (ATE, −0.012; 95% CI, −0.019 to −0.005; p < 0.001; q = 0.008).

Heterogeneity of effects and candidate moderators

CATE distributions are shown for SB, LPA, and MVPA across outcomes (Fig. 3, Fig. 4, Fig. 5), with vertical reference lines for the mean CATE and the empirical 2.5th and 97.5th percentiles. In the primary sample, CATE standard deviations ranged from 0.0039 to 0.0191 SDQ points per one min/day, and the percentage of individual 95% CATE intervals excluding zero was usually low (0% to 3.15%), except for LPA and age-11 externalizing problems (20.86%). This latter pattern was not supported by calibration evidence for differential prediction. The grf::test_calibration() differential forest prediction term was nominal only for the SB-age-11 internalizing pathway (estimate, 0.840; SE, 0.487; p = 0.042) and was not corrected for multiple calibration tests. Given that calibration evidence for differential prediction was limited and the only nominal signal was not corrected for multiple calibration tests, we interpret the observed heterogeneity as exploratory rather than as evidence of reproducible subgroups that could guide clinical or intervention decisions, including but not limited to differences between children with overweight versus obesity. CATE summaries and calibration tests are reported in Tables S1-S2, and feature-importance rankings are shown descriptively in Figs. S1-S3.

Fig. 3.

Distribution of conditional average treatment effects (CATEs) for sedentary behavior (SB) across Strengths and Difficulties Questionnaire (SDQ) outcomes. Note: CATEs are expressed as the estimated change in raw SDQ problems score per one additional minute/day of SB. The solid vertical line marks the mean CATE; dashed vertical lines mark the empirical 2.5th and 97.5th percentiles.

Fig. 4.

Distribution of conditional average treatment effects (CATEs) for light-intensity physical activity (LPA) across Strengths and Difficulties Questionnaire (SDQ) outcomes. Note: CATEs are expressed as the estimated change in raw SDQ problems score per one additional minute/day of LPA. The solid vertical line marks the mean CATE; dashed vertical lines mark the empirical 2.5th and 97.5th percentiles.

Fig. 5.

Distribution of conditional average treatment effects (CATEs) for moderate-to-vigorous-intensity physical activity (MVPA) across Strengths and Difficulties Questionnaire (SDQ) outcomes. Note: CATEs are expressed as the estimated change in raw SDQ problems score per one additional minute/day of MVPA. The solid vertical line marks the mean CATE; dashed vertical lines mark the empirical 2.5th and 97.5th percentiles.

Discussion

This study used MCS data to employ a generalized random forests approach to examine longitudinal, model-based associations between accelerometer-derived waking movement behaviors at age 7 and SDQ internalizing and externalizing problems at ages 11 and 14 among children with overweight or obesity. The main findings indicate small, outcome-specific estimates. After FDR correction, the most robust finding was the association between higher SB exposure and lower internalizing problems scores at age 11; the MVPA findings and the age-14 SB finding should be considered exploratory and thus interpreted with caution.

Moderate-to-vigorous-intensity physical activity and mental health: a dual-edged pattern

The MVPA findings were directionally mixed. Nominal estimates suggested that higher MVPA was associated with lower internalizing problems scores at age 11 but higher externalizing problems scores at ages 11 and 14. These estimates were small in raw SDQ units and did not remain statistically significant after multiple comparison correction. Therefore, they should be interpreted as hypothesis-generating rather than as evidence that high levels of MVPA exacerbate externalizing problems.

One possible explanation for this unexpected finding is measurement overlap: the SDQ hyperactivity subscale includes items such as being restless or overactive, which may partly capture high activity levels rather than symptoms of lower mental health. Notably, this finding is similar to previous studies using the MCS dataset, which reported positive associations between accelerometer-derived PA and later ADHD symptoms or externalizing-related outcomes, underscoring the need to distinguish motor activity from clinically relevant symptoms of ADHD (Ahn et al., 2018; Brandt et al., 2021; van Egmond-Fröhlich et al., 2012). A second possible explanation is residual or bidirectional confounding, because children with pre-existing externalizing tendencies may engage in more high-intensity PA. A third – and not mutually exclusive explanation – may be that some contexts in which unstructured high-intensity PA occurs may involve peer conflict or low adult supervision. However, as the present study did not directly test these potential explanations, future research should seek to elucidate the aforementioned phenomenon to allow for more robust conclusions.

The attenuation of the MVPA-internalizing estimate at age 14 may reflect developmental changes in PA, school context, puberty, peer relationships, or other unmeasured time-varying factors. PA and SB often change across the transition from primary to secondary school, and single-wave exposure measurement cannot capture later trajectories or changing social contexts (Atkin et al., 2021; Chong et al., 2020). Although PA may relate to mood and stress through monoaminergic, neurotrophic, and hypothalamic-pituitary-adrenocortical pathways (Chaouloff, 1989; Martikainen et al., 2014; Phillips, 2017), these mechanisms were not directly measured, but are promising candidates whose roles remain to be investigated in future studies. Since the PA and SB exposure was measured only at age 7, the study cannot determine whether later changes in those waking movement behaviors explain the attenuation of the observed association.

Sedentary behavior and lower internalizing problems scores

The inverse association observed between SB and internalizing problems should not be interpreted as evidence that SB is beneficial to aspects of mental health. First, accelerometer-defined SB captures low movement but not the type or context in which SB occurs. Thus, overall SB exposure may combine adverse SB types, particularly mentally passive SB (screen time such as television viewing) and potentially positive SB, namely mentally active SB (e.g., reading, homework, drawing, quiet play, or socially supportive seated activities). As a result, the combination of mentally active and passive SBs may have driven the unexpected observations between SB and internalizing problems reported here (Brechet et al., 2022; Hallgren et al., 2020; Hoare et al., 2016; Lopes et al., 2005; Ramdass & Zimmerman, 2011; Vasconcellos et al., 2025; Wang et al., 2019). Second, among children with overweight or obesity, some PA settings may involve weight-related stigma, social comparison, or negative peer experiences, and contexts of SB may provide respite from these exposures (Alimoradi et al., 2020; Gray et al., 2009; Rancourt et al., 2015; Salvy et al., 2012). Third, residual confounding, wear-time differences, measurement error, and selection into the accelerometer substudy may contribute to the pattern. Unfortunately, these explanations cannot be tested with the present MCS data, so future research is required to verify or refute our assumptions.

Light-intensity physical activity: a null signal

LPA showed no evidence of average model-based association with any outcome at either follow-up. This null pattern may indicate that total LPA minutes are too heterogeneous to capture psychologically relevant activity contexts, such as active play, walking, transport, or school-based activities. Prior reviews suggest that the effects of LPA on mental health may differ from those of MVPA, but evidence is less consistent and context-dependent (Felez-Nobrega et al., 2021; Vella et al., 2023). Moreover, a recent editorial argued that LPA has public-health relevance and should not be dismissed simply because it is lower intensity, particularly when replacing time spent on SB is the behavioral target (Ross et al., 2024). The present null finding concerning LPA should therefore be interpreted in the context of the current study and cohort and not as evidence that LPA is generally ineffective to benefit aspects of mental health, with effects that may emerge when SB is replaced by LPA; an assumption that requires further investigation (Parfitt et al., 2009; Yan et al., 2024).

Heterogeneity in model-based estimates

An important contribution of this study is the exploratory assessment of heterogeneity using CATEs, distributional summaries, and formal calibration tests. Although the CATE distributions showed some variation across children, calibration evidence for differential prediction was limited and did not support strong claims about clinically actionable subgroups. This cautious interpretation is consistent with recommendations that heterogeneous-effect estimates from flexible causal machine-learning methods require careful calibration, transparent reporting, and external replication before being used for individual-level decision-making (Feuerriegel et al., 2024; Sharma et al., 2025; Varidel et al., 2025; Wager & Athey, 2018). We therefore interpret the heterogeneity results as exploratory and as a basis for future studies with larger samples and richer contextual waking movement behavior data.

Strengths

This study has several strengths. First, PA and SB were measured using accelerometry, avoiding key limitations of self-report in young children (Griffiths et al., 2013; Nigg et al., 2020). Second, the longitudinal design placed exposure assessment at age 7 before SDQ outcomes at ages 11 and 14. Third, adjustment for baseline mental health and family/socioeconomic factors reduced several major sources of measured confounding. Fourth, the focus on children with overweight or obesity addresses a clinically relevant subgroup that is often underrepresented in 24-hour movement behavior and mental health research (Andrade et al., 2025; Galler et al., 2024; King et al., 2020; Zhou et al., 2025).

Limitations

Several limitations merit consideration. First, despite the causal forest framework, the study is observational; causal interpretation depends on measured-confounder assumptions, and residual confounding from unmeasured factors such as sleep quality, diet, temperament, pubertal timing, school environment, neighborhood context, and family health climate cannot be excluded (Ekelund et al., 2008; Iob et al., 2023, Richmond et al., 2014, Ziegeldorf et al., 2024). Second, the analytic sample was restricted to children with overweight or obesity at age 7 who had valid accelerometer data and complete analytic variables. As such, selection into accelerometer wear and retention to follow-up may have favored families with greater study engagement or more stable circumstances, which could limit generalizability within the overweight/obesity subgroup (Rich et al., 2013). Third, detailed sample-flow information before the prepared overweight/obesity analytic source file, including the full BMI/weight-status denominator, could not be fully reconstructed from the available analytic files. Fourth, accelerometer-derived SB does not distinguish screen time, homework, reading, transport, or social context, and wearable-derived 24-hour movement estimates can vary across measurement protocols and validation assumptions (Giurgiu et al., 2025). Fifth, the two-valid-day inclusion criterion may not fully capture habitual waking movement behavior patterns, especially weekday-weekend differences, although robustness analyses using at least one valid weekday and one valid weekend day were added. Sixth, the estimates are per minute/day and should not be interpreted as isotemporal substitution effects. Finally, the SDQ captures continuous symptom domains rather than clinical diagnoses.

Implications for research and practice

The present findings do not support the direct recommendation that more MVPA or less SB will uniformly improve mental health later in life among children with overweight or obesity. Interventions may need to consider quality exposure characteristics, social context, supervision, enjoyment, and exposure to weight-related stigma, consistent with evidence that the context of PA matters for mental health and social experience (Alimoradi et al., 2020; Salvy et al., 2012; Vella et al., 2023). SB recommendations should also distinguish between mentally passive and mentally active SB, with the latter including socially supportive seated activities, which may offer benefits for aspects of mental health (Hallgren et al., 2020; Zhang et al., 2025; Zou et al., 2024).

For research, future studies should use repeated exposure assessments, richer contextual information about PA and SB type, and designs capable of addressing time-varying confounding and behavioral substitution (Athey & Imbens, 2016, Runge et al., 2023, Wang et al., 2025). A complex-systems perspective may also help future work integrate individual, social, and environmental determinants of 24-hour movement behavior without reducing intervention targets to total minutes alone (Schüler et al., 2025). This direction is consistent with calls for more precise 24-hour movement behavior recommendations that account for different compositions of PA, SB, and sleep across individuals and contexts (Tremblay et al., 2024). Larger samples are also needed before day-specific candidate moderators from causal forest models can be interpreted substantively.

Conclusion

In conclusion, among children with overweight or obesity from the UK Millennium Cohort Study, accelerometer-derived movement behaviors at age 7 showed small and outcome-specific associations with later SDQ problems scores. After correcting for multiple comparisons, the most robust finding was an inverse association between higher SB and lower internalizing problems at age 11 – a finding that should not be interpreted as evidence that SB is protective. Nominal MVPA and other SB findings, sensitivity analyses, and heterogeneity results were exploratory and require replication before more solid conclusions can be drawn. Overall, the results support the need for more nuanced research in children with overweight or obesity on how waking movement behavior characteristics and context influence mental health, considering the role of individual heterogeneity.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.