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

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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).
Keywords
Survival analysis, Cox regression, compositional data, time use, accelerometry, physical activity, sedentary behaviour, NHANES, HEALTH, TIME

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MLA
McGregor, DE, et al. “Cox Regression Survival Analysis with Compositional Covariates : Application to Modelling Mortality Risk from 24-h Physical Activity Patterns.” STATISTICAL METHODS IN MEDICAL RESEARCH, vol. 29, no. 5, 2020, pp. 1447–65, doi:10.1177/0962280219864125.
APA
McGregor, D., Palarea-Albaladejo, J., Dall, P., Hron, K., & Chastin, S. (2020). Cox regression survival analysis with compositional covariates : application to modelling mortality risk from 24-h physical activity patterns. STATISTICAL METHODS IN MEDICAL RESEARCH, 29(5), 1447–1465. https://doi.org/10.1177/0962280219864125
Chicago author-date
McGregor, DE, J Palarea-Albaladejo, PM Dall, K Hron, and Sebastien Chastin. 2020. “Cox Regression Survival Analysis with Compositional Covariates : Application to Modelling Mortality Risk from 24-h Physical Activity Patterns.” STATISTICAL METHODS IN MEDICAL RESEARCH 29 (5): 1447–65. https://doi.org/10.1177/0962280219864125.
Chicago author-date (all authors)
McGregor, DE, J Palarea-Albaladejo, PM Dall, K Hron, and Sebastien Chastin. 2020. “Cox Regression Survival Analysis with Compositional Covariates : Application to Modelling Mortality Risk from 24-h Physical Activity Patterns.” STATISTICAL METHODS IN MEDICAL RESEARCH 29 (5): 1447–1465. doi:10.1177/0962280219864125.
Vancouver
1.
McGregor D, Palarea-Albaladejo J, Dall P, Hron K, Chastin S. Cox regression survival analysis with compositional covariates : application to modelling mortality risk from 24-h physical activity patterns. STATISTICAL METHODS IN MEDICAL RESEARCH. 2020;29(5):1447–65.
IEEE
[1]
D. McGregor, J. Palarea-Albaladejo, P. Dall, K. Hron, and S. Chastin, “Cox regression survival analysis with compositional covariates : application to modelling mortality risk from 24-h physical activity patterns,” STATISTICAL METHODS IN MEDICAL RESEARCH, vol. 29, no. 5, pp. 1447–1465, 2020.
@article{8650772,
  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).},
  author       = {McGregor, DE and Palarea-Albaladejo, J and Dall, PM and Hron, K and Chastin, Sebastien},
  issn         = {0962-2802},
  journal      = {STATISTICAL METHODS IN MEDICAL RESEARCH},
  keywords     = {Survival analysis,Cox regression,compositional data,time use,accelerometry,physical activity,sedentary behaviour,NHANES,HEALTH,TIME},
  language     = {eng},
  number       = {5},
  pages        = {1447--1465},
  title        = {Cox regression survival analysis with compositional covariates : application to modelling mortality risk from 24-h physical activity patterns},
  url          = {http://dx.doi.org/10.1177/0962280219864125},
  volume       = {29},
  year         = {2020},
}

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