Covariates

We considered a number of categorical covariates (Table 1) as potential predictors of the functional PA daily profile. These were classified into three groups: time and place of measurement (country of residence, season of the year, day of the week); socio-demographic (child sex and ethnicity, and maternal socioeconomic and lone parenthood status); and behavioural (children’s screen time, participation in sport/exercise at clubs or school, reading habits, time spent with friends, mode of transport to/from school, and household number of cars/vans in regular use).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Variables considered in the analysis of determinants of functional day profile.

https://doi.org/10.1371/journal.pone.0187677.t001

With the exception of sex and ethnicity, which were reported at the first MCS survey, all other variables were collected during home interviews at the fourth survey (see [26] for further details).

Statistical methods

The term FDA comprises statistical methods aimed to model data sampled at high temporal resolution (high-frequency data) in which the individual unit of analysis is the entire continuous function whence the observations have originated. [16, 17, 27] The main characteristic of FDA is that the vector of high resolution data is modelled as a unique functional object typically defined in terms of a spline basis. This functional object provides a mathematical framework which enables exploratory data analysis and inference to be performed using statistical techniques analogous to standard multivariable methods (e.g. ANOVA, regression models, principal component and cluster analysis). [16, 17, 27]

In the description that follows, we outline the notation and basic idea of FDA applied to accelerometer data.

Let y_il denote counts measured by the accelerometer, where i = 1,…,n is the child for epoch (time) l = 1,…,n_i. Since in our analysis the time unit was the minute and the time interval was 08:30 to 19:30, there were 660 observations of accelerometer counts available for each child, that is, n_i = 660. Let y(t) denote a continuous, latent function assumed to be smooth over time, indexed by t. FDA assumes that the observed accelerometer counts y_it at a particular time t represent a sample from y(t), possibly measured with error. We used these observations to estimate, by means of splines the latent functions y_i(t), for each child i = 1,…,6497.

The first step is to model observed accelerometer data by means of latent smooth functions y_i(t) assumed to be smooth over time t. The linear predictor (1) where, c_i is a k × 1 vector of coefficients, and ϕ(t) is a k–dimensional basis function system (16) as our starting point. Usually k is relatively large thus reflecting the infinite dimensionality of the space of smooth functions where inference takes place in FDA. Within this framework, there are several basis functions ϕ_k(t) among which one can choose, e.g. Fourier, exponential, truncated power functions, orthogonal polynomials and splines. Here we considered spline functions given their computational efficiency. Among these we used a fourth order cubic B–spline basis function system. Numerically, B–splines are attractive because they require an amount of computation that increases linearly with the number of observations. [17] Another desirable property of cubic splines is that they are the smoothest possible interpolant through any set of data. [28] This property implies that estimated cubic splines yield the interpolant function that minimize the curvature (i.e. the integral for the second derivative) of the objective function.

Let ϕ_k(t_m) be the value of the basis function ϕ_k at time t_m. The coefficients c_i can be estimated within the generalised linear models (GLM) framework, so that we define: (2) where μ_im is the conditional mean of y_im, and h is a link function. The distribution of the response variable, and the link function are chosen within the generalized linear models (GLM) family. [29]

To account for over-dispersion, which is often found in accelerometry measures, we considered quasi-likelihood models with identity link functions [29]; and linear variance functions of the mean. Lastly, the degree of smoothing, which is given by the dimension k of the basis function system, was determined. This was selected using the generalised cross validation (GCV) score which is typically used in nonparametric regression settings: The number of functions that defined the basis system, k = 199, was determined by empirically minimising this score.

We then considered the latent functions y_i(t) as the outcome in the functional ANOVA model (3) where the index g = 1,…,G−1 denotes the level of a categorical covariate different from the baseline category g = 0. as described in Ramsay. [16] These parameters have a similar interpretation as in standard ANOVA, however, in functional ANOVA, they are functions of time. The function α₀(t) is the accelerometer profile function in the reference category, while the second term, α_g(t), represents a time-specific contrast of category g to the reference category. The error ε_i,g(t) collects unexplained variation, assumed to be independent of the covariates. This FANOVA model [3] was extended to multiple predictors, as described in Ramsay. [16]

Finally, it is interesting to note that a functional parameter can be averaged over a period of time to obtain a scalar . Averaged parameters over specific time windows, namely 8:30–9:30; 9:30–12:00; 12:00–13:30; or 17:30–19:30 appear in S1 Table.

We initially performed a univariable FANOVA for each of the considered predictors, using a permutation functional F test [17] to assess their association with daily PA profiles. We subsequently included all predictors in the multivariable FANOVA model, which results are presented in this paper. We calculated 95% Confidence Intervals using a bootstrap procedure. Inverse probability weights were used to take into account MCS sampling probability and non-response propensity to the PA study. [30]

Software

We carried out the analyses in the R programming environment for statistical computing version 3.3.2 (19) [31] in a UNIX platform, using functions from the R package fda. [32]

Summary of findings

This study is, to our knowledge, the largest study to use FDA and FANOVA for the analyses of accelerometer-based measures of physical activity. Our findings provide additional insights into variations in children’s activity levels across their waking day. They confirm and extend previous observations that girls are less active and identify periods in the school day where these differences are most apparent. Children whose measurements were obtained in the spring and summer months were significantly more active than those measured in winter, after adjusting for other factors. The importance of social activities for physical activity is underscored by the time-specific differences in activity levels observed in those involved in sport or after school clubs or who played with friends on a regular basis. While children who read for enjoyment were less active than those who did not, from a developmental perspective reading is clearly a beneficial activity and these findings do not suggest a detrimental influence of reading per se. Our findings also extend the existing strong evidence that cycling or walking to school on some or all days of the week is an effective strategy to get children more active and therefore supports schemes encouraging this, such as the UK ‘Walk to School’ campaign. We have demonstrated the value of using FDA to condense the extensive information available from accelerometer-derived measures of total physical activity in a population-based cohort by proposing a novel method to determine the spline basis functions, and using quasi-likelihood procedures to estimate the models’ functional parameters.

Comparisons with other findings

Among the methodological advances advocated [10, 33] there is the need to increase the context specificity on which the correlates are defined. Clarification of the behavioural context could enhance the specificity of behavioural models, with key characteristics of context being person, place, time and activity. Related to this research agenda, there has also been increased interest in the temporal dimension of correlates of physical activity. These studies have been reviewed [34, 35]; Stanley and colleagues [35] considered studies conducted on children (8–14 years) between 1990 and 2011. They focused on studies that evaluated determinants at school break time and after school. The authors found some correlates with consistent associations with physical activity; in particular, sex (with boys more active) was associated with physical activity in both periods. Brooke and colleagues [34] reviewed differences in physical activity in school aged children across different time periods (weekdays vs weekends, in school vs out of school, weekends vs out of school and lesson time vs break time). They found that children were more active on weekdays than during the weekend, while the unit of physical activity measurement was found to influence comparisons across other time-periods. We have found a small number of other papers also exhuming the temporal characteristics of physical activity correlates and published after this review [36–40]. Hesketh and colleagues [36] have previously examined patterns of activity across the day in a sample of 593 preschool-aged children living in Southampton, UK. Their time-specific observations demonstrated the importance of considering temporality for physical activity interventions targeting, for example, sex differences in the morning when girls were less active than boys. Similarly, a study by Li and colleagues [38] in 1075 8-11-year-old children has shown daily variation in activity levels, with periods of higher activity during the commute to school times, morning break and lunch-times. Stanley and colleagues [39] analysed accelerometer data from 423 south Australian children aged between 10 and 14 years. The authors used the correlation component regression models to predict total physical activity during lunch-time and after-school periods for boys and girls separately; they were able to explain 25% and 17% of the variance for boys and girls respectively during lunch time, while the after-school model predicted 20% and 7% of the variability in boys and girls, respectively. Hubbard and colleagues [37] evaluated the difference in different physical activity dimensions between boys and girls, and normal and overweight/obese children in 517 US school children with a mean age of 9 years. They found lower levels of physical activity in girls, and overweight/obese children, in all of the periods investigated (school, weekday out-of-school, weekend). Finally, De Baere and colleagues [40] examined temporal patterns of both physical activity and sedentary behaviour in 211 children aged 10–14 and reported on particularly active periods of the day, like those reported in our study, but also more sedentary periods and periods where these types of activity compete.

Regarding, statistical methods, in another study based on a small sample of school children in the United States, Fan and colleagues [18] used FDA to assess PA differences between adolescent girls in different school years and with high versus low body mass index (BMI) categories. The sample comprised fewer than one hundred pupils in each of the three year groups examined. The authors reported lower activity levels in grade 10 (15 to 16 years) than grade 11 (16 to 17 years) and 12 (17 to 18 years) girls during evening hours; differences in activity levels were also observed for grade 10 girls with low- versus high-BMIs during the morning period, with the low BMI group being more active. Our study did not re-examine the impact of BMI status, but we do concur with Fan and colleagues [18] on the importance of FDA in enhancing this field of research. Another analytic approach has been outlined by Morris and colleagues [41] who used a wavelet-based functional model incorporating covariates and random effects to analyse 550 accelerometer profiles from 112 early adolescents and demonstrated irregular profiles characterised by many peaks representing short bursts of intense activity. The main focus of the study by Morris and colleagues was to sample stochastically missing regions of incomplete profiles, which were not present in our dataset.

In summary we have found the evidence inconclusive, apart from consistently higher levels of physical activity observed in boys across all time periods examined. While patterns of physical activity within and between days have been studied, few studies have analysed correlates associated with different levels of activity within a single day.

Strengths and limitations

There is increasing interest in using the internal clock of the accelerometer to depict daily PA patterns. [42–44] The representation of accelerometer data as a functional data object over time gives a clearer picture of the daily PA patterns. This enables researchers to identify contextual information for periods when children are most or least active. These daily patterns can be identified at a population level using functional descriptive statistics, such as the functional mean.

Linkage of the activity data to a wide range of individual and behavioural information from MCS enabled examination of the effects of these covariates and activity levels and temporal patterns. A strength of our study is the novel application of FANOVA to explain the variability of fitted functional daily PA patterns, in this study using a sample of approximately 6500 daily physical activity profiles. This has allowed us to extend, in a large population-based study of primary school-aged children, our earlier observations of reduced physical activity among girls, those who do not engage in sporting or other social activities, and those who do not ever walk or cycle to school by demonstrating the time of day where these differences are most marked. We believe this provides additional evidence as well as a methodological approach with which to inform and evaluate population level strategies to increase children’s physical activity.

A potential limitation of using accelerometers to define activity is that it underestimates activities that do not include vertical movement of the trunk, such as cycling, and, for the device used in this study, aquatic activities such as swimming. We also did not use all information available on each child; this choice was made to ensure independence of daily profiles, since the methods developed by Ramsay and Silverman [17] as implemented in the R package fda require independence of functional profiles. Further work is needed to develop and evaluate efficient FDA methods that consider dependence structures on the functional profiles in large scale population studies.

FDA requires a common observation time without missing data. The observation period between 8:30 and 19:30 was chosen to maximise the sample size without missing data in the observation period. By using this time window, we may have missed some active transportation to school; however, the average of the functional coefficient between the period 8:30 and 9:30 shows a lower level of physical activity and it seems that some of the effect of active travelling during the before school time period was captured by the functional coefficient (See Fig 4).

Our analysis did not consider interactions between biological and behavioural determinants, this is a limitation of our work as it is important to understand and evaluate how different levels (and types) of determinants interact to promote healthy behaviours; doing this within FDA requires complex computational considerations but this should be considered in future work.

Implications for research and practice

The description and the analysis over time of factors that affect PA patterns can provide information useful for planning tailored public health interventions aimed at increasing PA among children. For example, several studies have highlighted the lower levels of activity in primary school-aged girls, [5] however quantifying these differences more precisely over the waking day, particularly during school time, can be used to inform and evaluate school-based interventions designed to increase participation in more intense PA. For example, our findings suggest that initiatives aimed at increasing activity during the lunchtime period may be particularly beneficial for girls.

Our observation of higher levels of PA in summer and spring, has been previously reported. [45, 46] This supports the implementation of physical activity promotion interventions in children during winter, possibly during the afternoon when the greatest differences are observed relative to activity levels in summer. The approach used in this study enables research to identify and evaluate mediators of seasonal variation in activity, such as social, organisational, and environmental factors, to inform the design of interventions to reduce this variation. [45]

Our findings about the temporal effects on PA of mode of transport to school underscore the importance of policy initiatives to support active walking to school schemes. [47]

Participation in sporting and other social activities outside of school is associated with higher activity levels throughout the day. While the causal direction of these associations cannot be established in an observational study, public health measures are urgently needed to overcome barriers to involvement and to encourage participation in sports and other activities (such as for example dancing) in and out of school, as proposed in the government’s recently published obesity strategy. [48] Finally, we have shown that children who play with friends more often are more active–social aspects of activity and the influence of peer networks should be considered when tailoring interventions to increase activity in children.

Conclusions

We have presented methods based on FDA applied to a large population-based study of children with individual PA profiles based on accelerometer data. These methods are useful to model the temporal and population heterogeneity of physical activities. In particular, our methodological approach and findings related to modifiable behavioural factors may be used to inform and evaluate population-based strategies aimed at increasing activity levels.