Hospices Civils de Lyon, Service de Biostatistique, Lyon, F-69424, France.
Stat Med. 2010 Oct 15;29(23):2453-68. doi: 10.1002/sim.4005.
Prognostic studies often involve modeling competing risks, where an individual can experience only one of alternative events, and the goal is to estimate hazard functions and covariate effects associated with each event type. Lunn and McNeil proposed data manipulation that permits extending the Cox's proportional hazards model to estimate covariate effects on the hazard of each competing events. However, the hazard functions for competing events are assumed to remain proportional over the entire follow-up period, implying the same shape of all event-specific hazards, and covariate effects are restricted to also remain constant over time, even if such assumptions are often questionable. To avoid such limitations, we propose a flexible model to (i) obtain distinct estimates of the baseline hazard functions for each event type, and (ii) allow estimating time-dependent covariate effects in a parsimonious model. Our flexible competing risks regression model uses smooth cubic regression splines to model the time-dependent changes in (i) the ratio of event-specific baseline hazards, and (ii) the covariate effects. In simulations, we evaluate the performance of the proposed estimators and likelihood ratio tests, under different assumptions. We apply the proposed flexible model in a prognostic study of colorectal cancer mortality, with two competing events: 'death from colorectal cancer' and 'death from other causes'.
预后研究通常涉及建模竞争风险，其中个体只能经历替代事件之一，目标是估计与每种事件类型相关的风险函数和协变量效应。Lunn 和 McNeil 提出了数据处理方法，允许将 Cox 的比例风险模型扩展到估计每个竞争事件的风险的协变量效应。然而，竞争事件的风险函数被假设在整个随访期间保持比例，这意味着所有特定于事件的风险具有相同的形状，并且协变量效应也被限制随时间保持不变，即使这些假设通常存在疑问。为了避免这种限制，我们提出了一种灵活的模型来 (i) 为每种事件类型获得基线风险函数的独特估计值，以及 (ii) 在一个简洁的模型中允许估计时变协变量效应。我们的灵活竞争风险回归模型使用平滑三次回归样条来对 (i) 特定于事件的基线风险的比例，以及 (ii) 协变量效应的时间依赖性变化进行建模。在不同的假设下，我们在模拟中评估了所提出的估计量和似然比检验的性能。我们将所提出的灵活模型应用于结直肠癌死亡率的预后研究中，有两个竞争事件：“结直肠癌死亡”和“其他原因死亡”。
