Department of Statistics, The Hebrew University, Jerusalem, Israel.
Biostatistics. 2010 Apr;11(2):304-16. doi: 10.1093/biostatistics/kxp057. Epub 2010 Jan 11.
Continuous-time Markov processes are frequently used to describe the evolution of a disease over different phases. Such modeling can provide estimates for important parameters that are defined on the paths of the process. A simple example is the mean first hitting time to a set of states. However, more interesting events are defined by several time points such as the first time the process stays in state j for at least Delta time units. These kinds of events are very important in relapsing-remitting diseases such as in multiple sclerosis (MS) where the focus is on a sustained worsening that lasts 6 months or longer. The current paper considers data on independent continuous Markov processes that are only observed intermittently. It reviews modeling and estimation, presents a new general concept of hitting times, and provides point and interval estimates for it. The methodology is applied to data from a phase III clinical trial of Avonex--a drug given to MS patients.
连续时间马尔可夫过程常用于描述疾病在不同阶段的演变。这种建模可以为过程路径上定义的重要参数提供估计。一个简单的例子是到达一组状态的平均首次到达时间。然而，更有趣的事件是由多个时间点定义的，例如过程在状态 j 中停留至少 Delta 时间单位的第一次。这些类型的事件在复发性缓解性疾病中非常重要，例如多发性硬化症（MS），其重点是持续恶化持续 6 个月或更长时间。本文考虑了仅间歇性观察到的独立连续马尔可夫过程的数据。它回顾了建模和估计，提出了一个新的击中时间的一般概念，并提供了它的点估计和区间估计。该方法应用于多发性硬化症患者使用的药物 Avonex 的 III 期临床试验数据。
