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

This cohort study examines sociodemographic, behavioral, and health-related factors associated with sedentary behavior and different intensities of physical activity in older adults after 20 years of follow-up.


Estimation of activity intensity distribution
For each participant, the density function of acceleration during waking period was estimated by kernel density estimation on a logarithmically distributed 150-point grid, using a Gaussian kernel and a plug-in bandwidth selector. As acceleration distribution was skewed, the log transformed (1 + acceleration) was used for the kernel smoothing. The complete diurnal activity intensity distribution function was defined as follows: where and are the daily waking time and the density function for the i th participant, respectively, is the magnitude of acceleration variable which takes its values over the range of the recorded acceleration, and ( ) represents the time spent at magnitude . The integral of over any range of acceleration represents the time (minutes) spent in this acceleration range per day, with integral over the total range of acceleration representing the daily waking time.

Function-on-scalar regression
Equation of the functional model adjusted for all covariates: _ , _ , _0 , _14 , _ ℎ , and _ are "dummy" binary variables indicating the belonging to ex-smokers, current smokers, 0 unit per week alcohol intake, >14 units per week alcohol intake, overweight, and obesity groups, respectively.
In order to facilitate interpretation of results, functional regression coefficients were integrated over 0.005 g intervals to estimate the time difference (in minutes/day) in each acceleration interval between the different subgroups.

Software and packages
All analyses were undertaken using R version 3.6.1 (version 3.6.1, http://www.r-project.org/). Kernel smoothing was implemented using the package ks (version 1.11.7, https://cran.r-project.org/web/packages/ks/ks.pdf) of R. All function-onscalar regressions were conducted using the REFUND package in R (version 0.1-21, https://cran.rproject.org/web/packages/refund/refund.pdf). The trapezoidal integration of functional coefficients was undertaken using the pracma R package (version 2.2.9, https://cran.r-project.org/web/packages/pracma/pracma.pdf). Significance of associations was examined using p-values from function-on-scalar regression, that accounts for the entire activity intensity distribution, after Bonferroni correction leading to p<0.004 (0.05 divided by 14 tests per model). eMethods 2. Exposure Variables: Sociodemographic, Behavioral, and Health-Related Factors Data were drawn from questionnaires and clinical evaluations as well as from electronic health records (Hospital Episode Statistics (HES), cancer registry, and the Mental Health Services Data Set). Socio-demographic factors included age, sex, self-reported ethnicity (categorized as white and non-white (Black; South Asian; other), due to small numbers of non-white groups), marital status (married/cohabitating, divorced/widowed/single), and last occupational position (low, intermediate, high; coded 1, 0.5, and 0, respectively, and entered as an ordinal variable; this is a comprehensive marker of socioeconomic position in the British Civil Service that reflects salary, social status, and level of responsibility at work).
Health-related factors included body mass index (BMI; categorized as <25 (normal), 25-29.9 (overweight), and ≥30 (obese) kg/m²), Short Form 36 Health Survey 1 physical and mental component summary scores, and number of chronic conditions including hypertension (systolic/diastolic blood pressure ≥140/90 mmHg, or use of antihypertensive drugs), diabetes (fasting glucose ≥7.0 mmol/L, self-reported doctor-diagnosed diabetes, use of anti-diabetic medications, or record in HES), coronary heart disease, stroke, heart failure, arthritis, cancer, depression, dementia, Parkinson's disease, and chronic obstructive pulmonary disease (assessed using HES records and data collected at Whitehall clinical exams as well as mental health records for depression and dementia). Time difference (minutes/day) spent over 0.005 g acceleration intervals between different subgroups, computed after integration of activity intensity distribution estimated by function-on-scalar regression model adjusted for all covariates (sociodemographic, behavioral, and healthrelated factors) and waking time. p for association between each covariate and the full activity intensity distribution from function-on-scalar regression mutually adjusted for all covariates and waking time.
Acceleration (g) eFigure 3. Cross-Sectional Association of Behavioral Factors With Activity Intensity Distribution Time difference (minutes/day) spent over 0.005 g acceleration intervals between different subgroups, computed after integration of activity intensity distribution estimated by function-on-scalar regression model adjusted for all covariates (sociodemographic, behavioral, and healthrelated factors) and waking time. p for association between each covariate and the full activity intensity distribution from function-on-scalar regression mutually adjusted for all covariates and waking time.
Acceleration (g) eFigure 4. Cross-Sectional Association of Health-Related Factors With Activity Intensity Distribution Time difference (minutes/day) spent over 0.005 g acceleration intervals between different subgroups, computed after integration of activity intensity distribution estimated by function-on-scalar regression model adjusted for all covariates (sociodemographic, behavioral, and healthrelated factors) and waking time. p for association between each covariate and the full activity intensity distribution from function-on-scalar regression mutually adjusted for all covariates and waking time.  b p for association between covariates and activity intensity distribution from function-on-scalar regression mutually adjusted for all covariates and waking time; *p-values <0.004 were considered significant according to the Bonferroni correction for multiple testing. c Lower MCS and PCS correspond to poorer mental and physical summary score, respectively. d Chronic conditions include hypertension, diabetes, coronary heart disease, stroke, heart failure, arthritis, cancer, depression, dementia, Parkinson's disease, and chronic obstructive pulmonary disease.