1 Department of Statistics, University of Pittsburgh, Pittsburgh, PA, USA.
2 Department of Psychiatry, University of Pittsburgh School of Medicine, Western Psychiatric Institute and Clinic, Pittsburgh, PA, USA.
Stat Methods Med Res. 2018 Jun;27(6):1661-1682. doi: 10.1177/0962280216667645. Epub 2016 Sep 19.
We aim to close a methodological gap in analyzing durations of successive events that are subject to induced dependent censoring as well as competing-risk censoring. In the Bipolar Disorder Center for Pennsylvanians study, some patients who managed to recover from their symptomatic entry later developed a new depressive or manic episode. It is of great clinical interest to quantify the association between time to recovery and time to recurrence in patients with bipolar disorder. The estimation of the bivariate distribution of the gap times with independent censoring has been well studied. However, the existing methods cannot be applied to failure times that are censored by competing causes such as in the Bipolar Disorder Center for Pennsylvanians study. Bivariate cumulative incidence function has been used to describe the joint distribution of parallel event times that involve multiple causes. To the best of our knowledge, however, there is no method available for successive events with competing-risk censoring. Therefore, we extend the bivariate cumulative incidence function to successive events data, and propose non-parametric estimators of the bivariate cumulative incidence function and the related conditional cumulative incidence function. Moreover, an odds ratio measure is proposed to describe the cause-specific dependence, leading to the development of a formal test for independence of successive events. Simulation studies demonstrate that the estimators and tests perform well for realistic sample sizes, and our methods can be readily applied to the Bipolar Disorder Center for Pennsylvanians study.
我们旨在填补分析连续事件持续时间的方法学空白，这些事件受到诱导的相依删失和竞争风险删失的影响。在宾夕法尼亚州双相情感障碍中心研究中，一些从症状进入期成功恢复的患者后来出现了新的抑郁或躁狂发作。量化双相情感障碍患者从恢复到复发的时间关联具有重要的临床意义。具有独立删失的间隔时间的双变量分布的估计已经得到了很好的研究。然而，现有的方法不能应用于因竞争原因而被删失的失效时间，例如在宾夕法尼亚州双相情感障碍中心研究中。双变量累积发生率函数已被用于描述涉及多个原因的平行事件时间的联合分布。据我们所知，然而，对于具有竞争风险删失的连续事件，尚无可用的方法。因此，我们将双变量累积发生率函数扩展到连续事件数据，并提出了双变量累积发生率函数和相关条件累积发生率函数的非参数估计。此外，提出了一个优势比度量来描述特定原因的依赖性，从而开发了用于独立连续事件的正式检验。模拟研究表明，对于现实的样本量，估计量和检验表现良好，并且我们的方法可以很容易地应用于宾夕法尼亚州双相情感障碍中心研究。
