Lamarca R, Alonso J, Gómez G, Muñoz A
Health Services Research Unit, Institut Municipal d'Investigació Mèdica (IMIM), Barcelona, Spain.
J Gerontol A Biol Sci Med Sci. 1998 Sep;53(5):M337-43. doi: 10.1093/gerona/53a.5.m337.
The standard approach for survival analysis of the elderly population is to define the survival time as the elapsed time from entry into the study until death, and to adjust by age using stratification and regression procedures. However, the interest is in the study of the aging process and the risk factors related to it, not in the use of time-on-study as the time scale. Here, we present methods to use age as the time scale and compare inferences and interpretations with those obtained using the standard approach.
A total of 1,315 individuals aged 65 years or older from the city of Barcelona, Spain, were interviewed in 1986 (baseline). The vital status of the cohort was assessed in October 1994. To illustrate the usefulness of age as time scale (alternative approach) instead of time-on-study in the survival analysis of the elderly population, both methods were used to assess the relationship between baseline functional capacity and mortality.
Using the alternative approach, we observed that 50% of the sample died at age 80.6 years; this information could not be estimated with the standard approach. Using age as a covariate in the standard analysis with time-on-study as the time scale and using age as the time scale in the alternative analysis, the association of functional capacity at baseline and mortality was of similar magnitude under both analyses. Nevertheless, using the alternative approach, relative risks were slightly lower, and the adjustment by age was tight and was not subject to the inherent assumptions in regression models of the functional relationship of independent variables with outcome. We illustrated the methods with fixed covariates (i.e., gender) and baseline values of time-dependent covariates (i.e., functional capacity), but we discussed the extension of our methods for the analysis of time-dependent covariates measured at several visits in a cohort study. Methods proposed here are easily implemented with widely available statistical software packages.
Although the use of standard survival analysis generally produces correct estimates, the use of age as time scale is deemed more appropriate for survival analysis of the elderly: Inferences are easier to interpret and final models are simpler. We therefore recommend the use of age as time scale for survival analysis of the elderly population.
老年人群生存分析的标准方法是将生存时间定义为从进入研究到死亡的时间，并通过分层和回归程序按年龄进行调整。然而，研究兴趣在于衰老过程及其相关风险因素，而非将研究时间作为时间尺度。在此，我们提出以年龄为时间尺度的方法，并将其推断和解释与使用标准方法获得的结果进行比较。
1986年（基线）对来自西班牙巴塞罗那市的1315名65岁及以上个体进行了访谈。1994年10月评估了该队列的生命状态。为说明在老年人群生存分析中以年龄为时间尺度（替代方法）而非研究时间的有用性，两种方法均用于评估基线功能能力与死亡率之间的关系。
使用替代方法，我们观察到样本中有50%在80.6岁时死亡；而使用标准方法无法估计此信息。在以研究时间为时间尺度的标准分析中使用年龄作为协变量，以及在替代分析中以年龄为时间尺度，两种分析下基线功能能力与死亡率之间的关联程度相似。然而，使用替代方法时，相对风险略低，且年龄调整紧密，不受回归模型中自变量与结果功能关系固有假设的影响。我们用固定协变量（即性别）和随时间变化协变量的基线值（即功能能力）说明了这些方法，但我们也讨论了将我们的方法扩展用于队列研究中多次访视时测量的随时间变化协变量的分析。本文提出的方法可通过广泛使用的统计软件包轻松实现。
尽管使用标准生存分析通常能得出正确估计，但在老年人群生存分析中，以年龄为时间尺度被认为更合适：推断更易于解释，最终模型更简单。因此，我们建议在老年人群生存分析中使用年龄作为时间尺度。
