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

Abstract

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).

Associations of Objectively-Assessed Physical Activity and Sedentary Time with Hippocampal Gray Matter Volume in Children with Overweight/Obesity

“…For example, γ > 0 for z 1 in Equation (A1) would be interpreted as SB relative to LIPA, MVPA, and sleep as positively associated with GMV in the hippocampus. Likewise, 95% confidence intervals (CIs) and p-values for the γ were calculated using a likelihood ratio test [57]. Since we aim to investigate the association of each behavior relative to the remaining behaviors, we report estimates from the z 1 coordinate of the equations above.…”

“…Isotemporal substitution plots were drawn to estimate the effect size of the association resulting from reallocating time from SED into either LPA or MVPA. Isotemporal substitution models with compositional data [57] were used to calculate the expected HRs associated with the range of compositions arising from two-way reallocations of time between behaviors. The compositional mean was calculated and used as the reference.…”

Compositional Data Analysis in Time-Use Epidemiology: What, Why, How

“…Regression analyses have typically used isometric logratio coordinates [46] as these enable meaningful interpretation of individual regression coefficients [47]. The word "coordinates" refers to a more generic mathematical concept of the resulting logratios being points/coordinates in the real space.…”

“…MPA per se is therefore not associated with greater cardiovascular risk, but its net reallocation (relative to VPA and SB) in this population is. This difficulty could be addressed by analyzing the association of other general logratios with cardiometabolic risk [35,47,61]. In addition, thinking in terms of time reallocations is helpful when interpreting CoDA results.…”

Risk Perception Sensitivity of Cyclists Based on the Cox Risk Perception Model

“…This method can be applied to investigate the relationships and influence degrees between survival time and influencing factors. It has also been applied in the field of traffic engineering in recent years [33][34][35]. Survival analysis focuses on not only the survival time but also the continuous change process of a termination event.…”