Time use of daily work and leisure time behaviours was treated as two compositions of activities performed within a 24-h day. Work and leisure time were defined as a 3-part composition, both consisting of time spent on sedentary (i.e. sitting or lying), standing and active (i.e. walking, running, stair climbing or cycling).

Compositional means were used to describe the day-to-day pattern of work and leisure time physical behaviours [24, 33]. These were obtained by calculating the geometric mean of each physical behaviour of the respective compositions and then normalising the geometric means to the workers’ average accelerometer-derived daily work and leisure time (i.e. 450 min and 450 min, respectively). On non-workdays, the leisure time composition consisted of daily waking time, normalised to the workers’ average accelerometer-derived daily time spent awake (i.e. 960 min).

Daily work and leisure time-use compositions were expressed using pivot isometric log-ratio (ilr) coordinates [34]. The first pivot-coordinate was calculated as the normalised log-ratio of the first compositional part (i.e. behaviour), relative to the geometric mean of the remaining parts within the work and leisure time composition, respectively. The work and leisure time behaviours were sequentially rearranged to place each behaviour in the first position, where after the corresponding ilr-coordinate sets were computed. This way, the relative importance of each behaviour was sequentially represented in the first ilr-coordinate (ilr1) and used in the regression analysis. A detailed description of how the pivot-coordinates were calculated and model development is provided in Additional file 1.

The analysis was performed using two multivariate multilevel models. In both models, the outcome variables were the ilr-coordinates expressing the leisure time-use composition.

In Model 1, we investigated if leisure time physical behaviours differed between each day of the week (e.g. Monday, Tuesday, Wednesday, etc.) and between workday and non-workdays. Thus, day of the week and an interaction between day of the week and type of day (reference = non-workday) were entered as predictors in Model 1. Model 1 was fitted three times. This was done to isolate the association with one of the leisure time behaviours in relation to the others in the first ilr-coordinate (denoted by ilr1).

In Model 2, only workdays were considered as we investigated if work behaviours influenced day-to-day leisure time behaviours. The following predictors were entered in Model 2: the work time-use composition (i.e. work time sent standing, active and sedentary, expressed as ilr-coordinates) and an interaction term between day of the week and the work time-use composition. Model 2 was fitted six times to investigate the association between each part of the leisure time and work compositions, respectively. Of note, only results of the associations between the relative work time spent active and standing (as a proxies of physical work demands) and leisure time physical behaviours are shown. Results on the association between relative work time spent sedentary and day-to-day leisure time physical behaviours are shown in Additional file 2.

Both Model 1 and 2 were adjusted for the following covariates (reference in parenthesis for categorical variables): sex (men), smoking-status (smoker), BMI, and age. Model 2 was further adjusted for work duration. These covariates were chosen as potential confounders based on theoretical assumptions concerning their possible influence on day-to-day pattern of leisure time and work behaviours and work duration [13, 17]. In all models, Monday was selected as the reference category when entering the “type of the day” variable, as this is considered as the first day of the week in Denmark, where the International Standard ISO 8601 is followed.

Compositional isotemporal substitution analysis was used to provide meaningful interpretation of the expected change (in min/day) in leisure time-use compositions when time was reallocated between behaviours during work on workdays. This was done using the multivariate regression Model 2, stratified on each workday of the week. First, a “reference” leisure time-use composition (average daily leisure time spent sedentary, standing and active) was estimated for the workers’ mean work time-use composition (average min of work time spent sedentary, standing and active for that particular day). Second, new work time-use compositions were calculated where time (15, 30 and 45 min) had been reallocated between behaviours. This enabled us to express effect sizes as expected changes in leisure time behaviours in min/day. Note that results are only shown for workdays where the work behaviours were significantly associated with the leisure time behaviours. A detailed description of this method based on ilr linear regression with non-compositional and compositional outcomes can be found in Dumuid et al. [35] and Lund Rasmussen et al. [36].

All analyses were performed in R version 1.1.3 [37], using the compositions [38] and MCMCglmm [39] packages. We used the MCMCglmm package to conduct the multivariate multilevel analysis, following the guide provided by Baldwin et al. [40], by which a Bayesian approach with uninformative priors were used. The assumptions of normality and homoscedasticity of the residuals were assessed for all models by visual inspection of residuals versus predicted values and quantile-quantile plots.

A sensitivity analysis was conducted in which only workers with at least 2 days of measurements were included (N = 831). Results are shown in Additional file 3.

To identify potential selection bias, we compared the characteristics of the blue-collar workers included and excluded from the study. Differences between groups were investigated by calculating means and standard deviations or frequencies and percentages. Group differences were tested using t-test and Chi-squared statistics and a 5% significance threshold. Results are shown in Additional file 4.

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