Jewell N P, Kalbfleisch J D
Department of Statistics, University of California, Berkeley 94720, USA.
Lifetime Data Anal. 1996;2(1):15-29. doi: 10.1007/BF00128468.
In the development of many diseases there are often associated variables which continuously measure the progress of an individual towards the final expression of the disease (failure). Such variables are stochastic processes, here called marker processes, and, at a given point in time, they may provide information about the current hazard and subsequently on the remaining time to failure. Here we consider a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. We develop some basic calculations based on this model. Interest is focused on statistical applications for markers related to estimation of the survival distribution of time to failure, including (i) the use of markers as surrogate responses for failure with censored data, and (ii) the use of markers as predictors of the time elapsed since onset of a survival process in prevalent individuals. Particular attention is directed to potential gains in efficiency incurred by using marker process information.
在许多疾病的发展过程中，通常存在相关变量，这些变量持续衡量个体朝着疾病最终表现（衰竭）发展的进程。此类变量是随机过程，在此称为标记过程，并且在给定时间点，它们可以提供有关当前风险的信息，以及随后关于剩余衰竭时间的信息。在此，我们考虑一个关于时间(t)时的风险函数与直至时间(t)的标记过程历史之间关系的简单加法模型。我们基于此模型进行一些基本计算。重点在于与衰竭时间生存分布估计相关的标记的统计应用，包括（i）将标记用作删失数据情况下衰竭的替代反应，以及（ii）将标记用作现患个体中自生存过程开始以来所经过时间的预测指标。特别关注利用标记过程信息所带来的潜在效率提升。
