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).