Individual Barriers to an Active Lifestyle at Older Ages Among Whitehall II Study Participants After 20 Years of Follow-up

Code for functional and multivariate linear regression to analyse the association between socio-demographic, behavioural, and health-related factors with a functional (activity intensity distribution function) or a scalar (time spent in a specific activity intensity range) outcome, respectively.

Data were analysed using R 3.6.1 (http://www.r-project.org), analyses required downloading of the following packages:

• GGIR for accelerometer data processing (version 2.0-0, https://cran.r-project.org/web/packages/GGIR/vignettes/GGIR.html)
• ks for kernel smoothing (version 1.11.7, https://cran.r-project.org/web/packages/ks/ks.pdf)
• REFUND for function-on-scalar regressions (version 0.1-21, https://cran.r-project.org/web/packages/refund/refund.pdf)
• pracma for trapezoidal integration of functional coefficients (version 2.2.9, https://cran.r-project.org/web/packages/pracma/pracma.pdf)

Here is a schema of the workflow:

More details on each steps are provided in the following sections:

Step 0 - Data & activity distribution computation

Computation of activity distribution function from accelerometer data. It involves differents steps that are represented in the workflow:

• characterise the PDF of each individual using the kernel smoothing method
• standardize kernel densities
• estimate activity distribution

More information on the computation of the activity distribution function in the following document: Kernel_density_computation.pdf

Step 1 - Building datasets

Data from Whitehall II accelerometer-substudy.

Data should include:

• the functional outcome for functional data analysis: individual activity intensity distribution function (a matrix with N lines and P columns, N corresponding to the number of subjects, P the number of points of the functional outcome)
• the scalar outcome for multivariate linear: individual daily duration of different activity behaviors (sedentary behaviour, ligh-intensity physical activity, moderate-to-vigorous physical activity)
• the scalar exposures: mean daily waking time, socio-demographics factors, behavioural factors, health related factors, the interaction terms, if necessary

Step 2 - Load functions

Specific functions to fit the models, extract coefficients and p values, and to plot the associations (heatmap for function-on-scalar regressions, table of coefficients for multivariate linear regressions)

Step 3 - Model fitting

Function-on-scalar regressions (conducted on the full study population, then stratified by sex) Multivariate linear regressions (conducted on the full study population, then stratified by sex)

Step 4 - Tables & Figures

Ploting the association between exposures and functional outcome using heatmaps.