Adiposity and the isotemporal substitution of physical activity, sedentary time and sleep among school-aged children: a compositional data analysis approach

Participants were from four study sites (Australia, Canada, United Kingdom and Finland) included in the larger cross-sectional 12-nation International Study of Childhood Obesity, Lifestyle and the Environment (ISCOLE) [15]. The four sites were chosen based on previous findings suggesting relative homogeneity of lifestyle behaviours among children at these sites [16]. Site investigators aimed to recruit a sex-balanced sample of 500 children from each site, based on a priori power calculations [15]. Children aged 9–11 years (n = 2156) were recruited from schools in urban and suburban settings, and stratified by socioeconomic status [15]. Data were collected between September 2011 and December 2013. Children were excluded if they had incomplete data for any of the following parameters; activity behaviours (n = 319), as well as body fat% (n = 28) and covariates (highest education level of either parent, number of parents and siblings in the home; n = 81), resulting in a final sample of 1728 children.

The Pennington Biomedical Research Center in Baton Rouge, Louisiana coordinated ISCOLE and received ethical approval for the overall study protocol from their Institutional Review Board. The four sites also received approval from local ethics committees and school boards. Parents provided signed informed consent and child assent was attained prior to inclusion in the study. ISCOLE is registered on ClinicalTrials.gov, Identifier: NCT01722500.

Activity behaviours were measured during the school year over 7 days, by 24-h accelerometry. Actigraph GT3X+ Accelerometers (ActiGraph LLC, Pensacola, FL) were worn on the right hip, with instruction to remove the device only for water-based activities. Wear time compliance in ISCOLE was high (daily average = 22.8 h). Participants were required to have at least 4 days of valid accelerometry data (with ≥10 h of waking wear/day, including at least one weekend day [17]). Data were downloaded in 1-s epochs using the low-frequency extension filter (ActiLife software version 5.6). A fully automated algorithm was used to estimate nocturnal sleep duration (from data aggregated to 60-s epochs) [18, 19]. Waking behaviours were determined (from data aggregated to 15-s epochs), once nocturnal sleep time and awake non-wear time (any sequence of ≥20 consecutive minutes of 0 activity counts) were removed. Evenson’s cut-points were used to define sedentary time (≤25 counts per 15 s), LPA (26–573 counts per 15 s), and MVPA (≥574 counts per 15 s) [20]. These cut-points have been shown to provide acceptable classification accuracy for 5–15 year old children [21]. The daily average for each part of the composition (sleep, sedentary time, LPA and MVPA) was weighted for week:weekend days at 5:2.

Body fat% was used to indicate children’s overall adiposity. Body fat% was measured during school visits using a portable Tanita SC-240 bioelectrical impedance scale (TANITA Corporation, Tokyo, Japan) [22]. Two measurements were taken, and the average was used in analysis (if measurements were >2.0% apart, a third measurement was taken, and the closest two were averaged for analysis). Bioelectrical impedance analysis is a valid (r = 0.69–0.79) and reliable (CV_intra = 3%, SEM_intra = −0.91 to 1.61 body fat%) estimate of body fat for school-age children compared to gold standards of underwater weighing and dual-energy X-ray absorptiometry (DXA) [23, 24]. The Tanita SC-240 has acceptable accuracy for estimating body fat% in this age group when assessed against DXA [22]. Body mass index (BMI) z-score, used to classify children into weight-status sub-groups, was calculated from measured height (Seca 213 portable stadiometer, Hamburg, Germany) and weight (TANITA Corporation, Tokyo, Japan [22]), using BMI = weight (kg)/height (m²) and age- and sex-specific World Health Organization reference data [25] for standardisation as z-scores.

The highest education level of either parent, and the number of parents and siblings in the home were reported by parents [15]. These sociodemographic factors were selected as covariates due to their potential influence on both activity behaviours and adiposity [26‐28].

Analysis was conducted in R (R Development Core Team, Vienna, Austria), using the packages Compositions [29] and robCompositions [30]. The daily behaviour composition was described in terms of centre (geometric mean of each behaviour, adjusted to collectively sum to 1440 min) [8, 31] and dispersion (variation matrix) [8, 10]. Analysis consisted of exploring the relationship between isotemporal substitution of one behaviour for another behaviour and children’s body fat%, using (i) traditional isotemporal substitution [4] and (ii) compositional isotemporal substitution. All analyses were stratified by sex.

Traditional isotemporal substitution analysis followed the procedure outlined by Mekary et al. [4]. Four linear regression models were created with body fat% as the dependent variable. The explanatory variables of the first model included each daily behaviour (sedentary time, LPA, MVPA) except one (sleep). Total time was also included; with the effect of constraining the linear model so that the regression coefficients represented the estimated change in adiposity associated with the substitution of one unit of sleep (i.e., 30 min) for one unit of the corresponding remaining behaviours. To capture all isotemporal eventualities, the remaining three linear models each omitted a different behaviour, while adjusting for all remaining behaviours, total wear time and covariates.

Compositional isotemporal substitution used multiple linear regression models with the activity behaviour composition (expressed as ilr coordinates) and sociodemographic covariates as explanatory variables. A comprehensive explanation of the compositional analysis and sample R code is included in Additional file 1. The ilr model was used to estimate body fat% at a baseline composition (e.g., the mean daily activity behaviour composition), and subsequently at new compositions (e.g., sleep = mean sleep +30 min, sedentary time = mean sedentary −30 min, LPA = mean LPA and MVPA = mean MVPA). The estimated absolute differences in body fat percentage units was calculated using predictions from the model (i.e., estimated difference in body fat% = estimated body fat% at baseline composition – estimated body fat% at new composition). Estimates were calculated for time reallocations of 30 min. Effect sizes (ES) were calculated by dividing the estimated differences by the mean standard deviation of body fat%. Additionally, estimated changes in body fat% across the continuum of reallocations in 5-min increments up to 70 min were graphically illustrated, using MVPA as an example.

This method of compositional isotemporal substitution uses a different approach from the change-matrix procedure outlined in Chastin et al. [8], where pairwise log ratios obtained by applying the inverse ilr transformation to the regression coefficients are introduced to facilitate the interpretation of the change in response variable. Each of these pairwise log-ratios is analogous to one of the three ilr coordinates of a four-part composition. However, the remaining ilr will necessarily contain information regarding the two components involved in the pair-wise log ratio. The method in Chastin et al. [8] is a useful tool, but prediction and inference are more comprehensive when made using the complete set of ilr coordinates.

Compositional isotemporal substitution was conducted in sex-stratified cohorts, at the daily behaviour mean composition (geometric mean of each behaviour, adjusted to collectively sum to the daily total of 1440 min) for all children, and repeated at the daily mean composition for (i) normal weight children (−2 ≤ zBMI≤1); (ii) overweight children (1 < zBMI≤2); and (iii) obese children (zBMI>2) [25].

The absolute differences in estimated body fat% appeared to be the greatest when time was reallocated between LPA and MVPA (boys) or either LPA or sedentary time and MVPA (girls) (Table 1).

For both sexes, higher estimated body fat% was associated with the reallocation of time from MVPA to other behaviours (Table 1). Notably, the estimated difference in adiposity was not exactly symmetrical, e.g., a reallocation of 30 min from MVPA to sedentary time was associated with a larger estimated absolute difference in body fat% (+2.31 ES = 0.36 for boys; +2.94 ES 0.41 for girls) than when 30 min was reallocated from sedentary to MVPA (−1.54 ES = 0.24 for boys; −1.78 ES = 0.25 for girls). For boys, the reallocation of any given time spent in MVPA to LPA tended to predict the largest positive (unfavourable) difference in body fat% (Fig. 1), whereas for girls, the reallocation of any given time spent in MVPA to either sedentary time or LPA appeared to predict the largest positive difference in body fat% (Fig. 2).

Reallocations modeled at the mean daily behaviour composition for different weight status subgroups (Additional file 4) demonstrated larger differences in estimated body fat% for overweight and obese children, compared to those classified as ‘normal weight’, particularly when the reallocated behaviour was MVPA (Figs. 3 and 4).

Both statistical techniques found that the largest differences in estimated body fat% were associated with reallocations of time away from MVPA. However, there were some important differences between the findings from the two approaches. The relative difference between the estimates for 30-min reallocations ranged from 0.2% to 121% (median = 18%) (calculated as the absolute difference between estimates from traditional and compositional models divided by a pooled estimate from both models). Larger absolute differences between the traditional and compositional models seem to be associated with higher estimates. Compositional isotemporal substitution findings also differed from traditional isotemporal substitution findings in the following ways: (i) the amount of difference in estimated body fat% when a behaviour was higher or lower was not exactly symmetrical, (Figs. 5 and 6), (ii) the difference in estimated body fat% was not linearly proportional to the amount of time reallocated (Figs. 5 and 6), and (iii) traditional isotemporal models indicated the estimated change in a continuous outcome was associated with same time reallocations irrespective of the starting/reference durations of activity behaviours (in other words, estimated change in body fat% was identical when 30 min of MVPA was reallocated from a starting duration of, for example, either 0 min/day or 150 min/day, whilst in contrast, estimates of change in outcome from compositional models were relative to a starting/reference composition, thus respecting the relative nature of compositional data [Figs. 3 and 4]).

This study estimated the difference in adiposity associated with the isotemporal substitution of daily activity behaviours. For both traditional and compositional models, the greatest differences in body fat% were estimated for the reallocation of time from MVPA to other behaviours, and vice versa. The estimated differences in body fat% for 30-min reallocations with MVPA were relatively modest, with standardised effect sizes ranging between 0.2 and 0.4.

There appeared to be sex differences between the findings. Both models estimated favourable absolute differences in body composition when sedentary behaviour replaced LPA (significant only in the compositional model) among boys, but not among girls. Furthermore, among boys estimated body composition was not most favourable when MVPA replaced sedentary time, whereas it was among girls. This unexpected finding may be an artefact of the cross-sectional study design; there may be a sub-population of lean boys who accumulate large amounts of sedentary time. A number of previous studies have detected clusters of boys with high screen time [32‐34]. Interestingly, membership of these clusters was not associated with higher adiposity.

There were some similarities between findings from traditional and compositional models, however there were fundamental differences between the two analytical approaches. The distinguishing feature of the compositional approach is that the inherent compositional nature and corresponding geometry of the data are not violated by the mathematical operations applied [12].

Unlike traditional isotemporal substitution, the compositional method produces asymmetrical estimates. That is, a quantum reallocation of one behaviour for another does not predict the exact inverse effect as the reverse reallocation. In the present study, asymmetry was most notably observed for reallocations with MVPA. Similar asymmetry with reallocation of MVPA was reported for other adiposity indicators by Fairclough et al. [14]. Essentially, adding MVPA appears to yield lower returns, while reducing MVPA seems to be associated with higher expected differences in fatness. In addition, the amount of time reallocated between behaviours was not linearly related to the difference in estimated body fat%. These findings are consistent with dose-response curves observed in experimental studies (e.g. Sattelmair et al. [35]), where marginal increases in exposures regularly predict diminishing benefits [36]. The non-linearity of findings has two implications. Firstly, they suggest that adiposity interventions should encourage children (particularly those with low levels of physical activity) to be more physically active. Secondly, the asymmetry in the estimated dose-response curves suggests that interventions aimed at defending (i.e. maintaining) MVPA may be of great importance, even if MVPA is not increased. However, the cross-sectional nature of the findings and the relatively modest effect sizes should be noted when considering the implications of this study.

This study has drawn on a large multi-national dataset using standardised measurements, including accelerometer-based measures of activity behaviours and objective measures of body fat% [15]. We used compositional data analysis techniques to quantify the adiposity association of isotemporal substitutions of activity behaviours.

Nonetheless, the study has several limitations. Accelerometers cannot distinguish completely between sitting and standing postures, with both potentially being classified as sedentary time. Whilst the analyses were adjusted for sociodemographic variables, there may be potential residual confounding from other lifestyle, social and environmental factors, such as diet, parental influence and perceived neighbourhood safety that were not included as covariates in our analyses. Furthermore, in ISCOLE, the participants were sampled from urban and suburban centres and were not nationally representative, limiting the generalisability of results [37]. Most importantly, due to the cross-sectional nature of the present isotemporal substitution analyses, findings are more correctly conceptualised as snapshots of adiposity associations with various daily behaviour compositions, than as adiposity associations of various behaviour substitutions within one day. It is therefore not possible to interpret the findings as the effect on adiposity for isotemporal substitutions of time between activity behaviours.