McGregor D E, Palarea-Albaladejo J, Dall P M, Hron K, Chastin Sfm
School of Health and Life Science, Glasgow Caledonian University, Glasgow, UK.
Biomathematics and Statistics Scotland, Edinburgh, UK.
Stat Methods Med Res. 2020 May;29(5):1447-1465. doi: 10.1177/0962280219864125. Epub 2019 Jul 25.
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).
生存分析在医学和公共卫生研究中经常进行，以评估暴露或干预与诸如死亡率等硬性结局之间的关联。Cox（比例风险）回归模型可能是在此背景下最常用的统计工具。然而，当暴露包括构成协变量（即代表相对构成的变量，如营养或身体活动行为构成）时，Cox回归模型的一些基本假设以及相关的显著性检验会被违反。构成变量之间存在内在的相互作用，这使得像通常那样孤立地考虑它们得出的结果和结论无效。在这项工作中，我们引入了一种基于对数比坐标的Cox回归模型公式，该公式适当地处理了构成协变量的约束，便于使用常见的统计推断方法，并允许进行具有科学意义的解释。我们说明了它在一个公共卫生问题上的实际应用：利用美国国家健康和营养检查调查（NHANES）的数据，估计与日常活动行为（身体活动、久坐时间和睡眠）构成相关的死亡风险。
