Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, Canada H3A 1A1.
Stat Med. 2011 May 30;30(12):1351-65. doi: 10.1002/sim.4208. Epub 2011 Mar 22.
Relative survival methods permit separating the effects of prognostic factors on disease-related 'excess mortality' from their effects on other-causes 'natural mortality', even when individual causes of death are unknown. As in conventional 'crude' survival, accurate assessment of prognostic factors requires testing and possibly modeling of non-proportional effects and, for continuous covariates, of non-linear relationships with the hazard. We propose a flexible extension of the additive-hazards relative survival model, in which the observed all-causes mortality hazard is represented by a sum of disease-related 'excess' and natural mortality hazards. In our flexible model, the three functions representing (i) the baseline hazard for 'excess' mortality, (ii) the time-dependent effects, and (iii) for continuous covariates, non-linear effects, on the logarithm of this hazard, are all modeled by low-dimension cubic regression splines. Non-parametric likelihood ratio tests are proposed to test the time-dependent and non-linear effects. The accuracy of the estimated functions is evaluated in multivariable simulations. To illustrate the new insights offered by the proposed model, we apply it to re-assess the effects of patient age and of secular trends on disease-related mortality in colon cancer.
相对生存方法允许将预后因素对疾病相关“超额死亡率”的影响与对其他原因“自然死亡率”的影响分开，即使不知道死亡的具体原因。与传统的“粗死亡率”相比，准确评估预后因素需要测试并可能对非比例效应进行建模，对于连续协变量，还需要对与危险的非线性关系进行建模。我们提出了一种灵活的加性风险相对生存模型扩展，其中观察到的所有原因死亡率风险由疾病相关的“超额”和自然死亡率风险之和表示。在我们灵活的模型中，代表（i）“超额”死亡率的基线风险、（ii）时变效应和（iii）连续协变量的非线性效应的三个函数，都通过低维三次样条回归来建模。提出了非参数似然比检验来检验时变效应和非线性效应。在多变量模拟中评估了估计函数的准确性。为了说明所提出模型提供的新见解，我们将其应用于重新评估患者年龄和时间趋势对结肠癌相关死亡率的影响。
