Whitmore G A, Crowder M J, Lawless J F
McGill University, Montreal, Canada.
Lifetime Data Anal. 1998;4(3):229-51. doi: 10.1023/a:1009617814586.
Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.
已经提出了许多将失效时间与随机时变协变量联系起来的模型。在其中一些模型中，当某个特定的可观测指标超过阈值水平时，失效就会发生。我们感兴趣的是更困难且通常更现实的情况，即失效并非确定性地与某个可观测指标相关。在这种情况下，用于指标演变和失效的联合模型往往会导致诸如失效时间的边际分布或失效时失效时间与指标值的联合分布等特征的复杂计算。本文提出了一种基于二元维纳过程的模型，其中一个分量表示指标，另一个潜在（不可观测）分量决定失效时间。特别地，当潜在分量超过阈值水平时，失效就会发生。该模型为上述特征给出了相当简单的表达式，并且易于拟合常见的数据，这些数据包括存活病例在删失时间的指标值以及失效病例的指标值和失效时间。讨论了参数推断和预测推断以及模型检验。该模型的一个扩展允许从几个可能可用的候选指标构建一个复合指标。通过一个模拟示例和一个案例应用展示了该方法。
