Cox regression survival analysis with compositional covariates: application to modelling mortality risk from 24-h physical activity patterns

Survival analysis is commonly conducted in medical and public health research to assess the association of an exposure or intervention with a hard end outcome such as mortality. The Cox (proportional hazards) regression model is probably the most popular statistical tool used in this context. However, when the exposure includes compositional covariables (that is, variables representing a relative makeup such as a nutritional or physical activity behaviour composition), some basic assumptions of the Cox regression model and associated significance tests are violated. Compositional variables involve an intrinsic interplay between one another which precludes results and conclusions based on considering them in isolation as is ordinarily done. In this work, we introduce a formulation of the Cox regression model in terms of log-ratio coordinates which suitably deals with the constraints of compositional covariates, facilitates the use of common statistical inference methods, and allows for scientifically meaningful interpretations. We illustrate its practical application to a public health problem: the estimation of the mortality hazard associated with the composition of daily activity behaviour (physical activity, sitting time and sleep) using data from the U.S. National Health and Nutrition Examination Survey (NHANES)

Differences in physical activity time-use composition associated with cardiometabolic risks

This study investigates the association between the overall physical activity composition of the day (sedentary behavior (SB), light intensity physical activity (LIPA) and moderate-to-vigorous physical activity (MVPA)) and cardiometabolic health, and examines whether improved health can be associated with replacing SB with LIPA. A cross-sectional analysis of the Health Survey for England 2008 on N = 1411 adults was undertaken using a compositional analysis approach to examine the relationship between cardiometabolic risk biomarkers and physical activity accounting for co-dependency between relative amounts of time spent in different behavior. Daily time spent in SB, LIPA and MVPA was determined from waist-mounted accelerometry data (Actigraph GT1M) and modelled against BMI, waist circumference, waist-to-hip ratio, blood pressure, total and HDL cholesterol, HbA1c, and VO2 maximum. The composition of time spent in SB, LIPA and MVPA was statistically significantly associated with BMI, waist circumference, waist-to-hips ratio, HDL cholesterol and VO2 maximum (p < 0.001), but not HbA1c, systolic and diastolic blood pressure, or total cholesterol. Increase of relative time spent in MVPA was beneficially associated with obesity markers, HDL cholesterol, and VO2 maximum, and SB with poorer outcomes. The association of changes in LIPA depended on whether it displaced MVPA or SB. Increasing the proportion of MVPA alone may have the strongest potential association with adiposity outcomes and HDL cholesterol but similar outcomes could also be associated with a lower quantity of MVPA provided a greater quantity of SB is replaced overall with LIPA (around 10.5 min of LIPA is equivalent to 1 min of MVPA). Keywords: MVPA, Sedentary behavior, Physical activity, Compositional data analysis, Cardiometabolic health, Adipoisit

Extreme events and predictability of catastrophic failure in composite materials and in the Earth

Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a ‘black swan’. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify ‘characteristic’ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragon’s domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models

Differences in physical activity time-use composition associated with cardiometabolic risks

This study investigates the association between the overall physical activity composition of the day (sedentary behavior (SB), light intensity physical activity (LIPA) and moderate-to-vigorous physical activity (MVPA)) and cardiometabolic health, and examines whether improved health can be associated with replacing SB with LIPA. A cross-sectional analysis of the Health Survey for England 2008 on N = 1411 adults was undertaken using a compositional analysis approach to examine the relationship between cardiometabolic risk biomarkers and physical activity accounting for co-dependency between relative amounts of time spent in different behavior. Daily time spent in SB, LIPA and MVPA was determined from waist-mounted accelerometry data (Actigraph GT1M) and modelled against BMI, waist circumference, waist-to-hip ratio, blood pressure, total and HDL cholesterol, HbA1c, and VO2 maximum. The composition of time spent in SB, LIPA and MVPA was statistically significantly associated with BMI, waist circumference, waist-to-hips ratio, HDL cholesterol and VO2 maximum (p < 0.001), but not HbA1c, systolic and diastolic blood pressure, or total cholesterol. Increase of relative time spent in MVPA was beneficially associated with obesity markers, HDL cholesterol, and VO2 maximum, and SB with poorer outcomes. The association of changes in LIPA depended on whether it displaced MVPA or SB. Increasing the proportion of MVPA alone may have the strongest potential association with adiposity outcomes and HDL cholesterol but similar outcomes could also be associated with a lower quantity of MVPA provided a greater quantity of SB is replaced overall with LIPA (around 10.5 min of LIPA is equivalent to 1 min of MVPA). Keywords: MVPA, Sedentary behavior, Physical activity, Compositional data analysis, Cardiometabolic health, Adipoisit

Mobility in community dwelling older adults: predicting successful mobility using an instrumented battery of novel measures

Mobility in older adults is associated with better quality of life. However, evidence suggests that older people spend less time out-of-home than younger adults. Traditional methods for assessing mobility have serious limitations. Wearable technologies provide the possibility of objectively assessing mobility over extended periods enabling better estimates of levels of mobility to be made and possible predictors to be explored. Eighty-six community dwelling older adults (mean age 79.8 years) had their mobility assessed for one week using GPS, accelerometry and self-report. Outcomes were: number of steps, time spent in dynamic outdoor activity, total distance travelled and total number of journeys made over the week. Assessments were also made of personal, cognitive, psychological, physical and social variables. Four regression models were calculated (one for each outcome). The models predicted 32 to 43% of the variance in levels of mobility. The ability to balance on one leg significantly predicted all four outcomes. In addition, cognitive ability predicted number of journeys made per week and time spent engaged in dynamic outdoor activity, and age significantly predicted total distance travelled. Overall estimates of mobility indicated step counts that were similar to those shown by previous research but distances travelled, measured by GPS, were lower. These findings suggest that mobility in this sample of older adults is predicted by the ability to balance on one leg. Possible interventions to improve out-of-home mobility could target balance. The fact that participants travelled shorter distances than those reported in previous studies is interesting since this high-functioning subgroup would be expected to demonstrate the highest levels

Is the association between physical activity and fatigue mediated by physical function or depressive symptoms in symptomatic knee osteoarthritis? The Multicenter Osteoarthritis Study

Objectives: To examine whether physical activity (PA) was associated with fatigue, and quantify the extent of potential mediation through depressive symptoms or physical function (PF) on the relationship between PA and fatigue in symptomatic knee osteoarthritis (KOA). Method: This longitudinal study used data from the Multicenter Osteoarthritis Study (n = 484), comprising subjects aged ≥ 50 years. Baseline PA was quantified via an ankle-worn accelerometer. The outcome was fatigue, measured using a 0–10 rating scale at 2 year follow-up. Mediators included gait speed as a measure of PF and depressive symptoms at 2 year follow-up. Mediation analysis was carried out after adjustment for baseline confounders. Stratified analysis by baseline fatigue status [no/low (< 4) and high (≥ 4) fatigue] was performed. Results: A significant direct association was found between PA and fatigue at 2 years [unstandardized coefficient (B) = −0.054; 95% confidence interval (CI) −0.107, −0.002, p = 0.041]. The PA–fatigue relationship was not mediated by gait speed (B = −0.006; 95% CI −0.018, 0.001) or depressive symptoms (B = 0.009; 95% CI 0.009, 0.028). In the subgroup with high baseline fatigue, direct associations were found between PA and fatigue (gait speed model:, B = −0.107; 95% CI −0.212, −0.002, p = 0.046; depressive symptoms model: B = −0.110; 95% CI −0.120, −0.020, p = 0.017); but in the no/low baseline fatigue group, no significant association was found between PA and fatigue. Conclusion: In the symptomatic KOA population, higher baseline PA was directly associated with reduced fatigue 2 years later, especially in those with high baseline fatigue. However, this relationship was not mediated by depressive symptoms or PF

Systematic comparative validation of self-report measures of sedentary time against an objective measure of postural sitting (activPAL)

Background: Sedentary behaviour is a public health concern that requires surveillance and epidemiological research. For such large scale studies, self-report tools are a pragmatic measurement solution. A large number of self-report tools are currently in use, but few have been validated against an objective measure of sedentary time and there is no comparative information between tools to guide choice or to enable comparison between studies. The aim of this study was to provide a systematic comparison, generalisable to all tools, of the validity of self-report measures of sedentary time against a gold standard sedentary time objective monitor. Methods: Cross sectional data from three cohorts (N = 700) were used in this validation study. Eighteen self-report measures of sedentary time, based on the TAxonomy of Self-report SB Tools (TASST) framework, were compared against an objective measure of postural sitting (activPAL) to provide information, generalizable to all existing tools, on agreement and precision using Bland-Altman statistics, on criterion validity using Pearson correlation, and on data loss. Results: All self-report measures showed poor accuracy compared with the objective measure of sedentary time, with very wide limits of agreement and poor precision (random error &gt; 2.5 h). Most tools under-reported total sedentary time and demonstrated low correlations with objective data. The type of assessment used by the tool, whether direct, proxy, or a composite measure, influenced the measurement characteristics. Proxy measures (TV time) and single item direct measures using a visual analogue scale to assess the proportion of the day spent sitting, showed the best combination of precision and data loss. The recall period (e.g. previous week) had little influence on measurement characteristics. Conclusion: Self-report measures of sedentary time result in large bias, poor precision and low correlation with an objective measure of sedentary time. Choice of tool depends on the research context, design and question. Choice can be guided by this systematic comparative validation and, in the case of population surveillance, it recommends to use a visual analog scale and a 7 day recall period. Comparison between studies and improving population estimates of average sedentary time, is possible with the comparative correction factors provided.</p