Piao Jin, Ning Jing, Shen Yu
The University of Southern California, Los Angeles, USA.
The University of Texas MD Anderson Cancer Center, Houston, USA.
J R Stat Soc Series B Stat Methodol. 2019 Apr;81(2):409-429. doi: 10.1111/rssb.12308. Epub 2019 Jan 6.
To better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence, it is of interest to identify patients with the intermediate event and then analyze their residual survival data. One challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population, since patients who die before experiencing the intermediate event are excluded from the identified cohort. We propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias. We develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model, and use a two-stage expectation-maximization algorithm. Using empirical process theory, we prove that the estimators have strong consistency and asymptotic normality. We conduct simulations studies to evaluate the finite sample performance of the proposed method. We apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival.
为了更好地理解患者特征与诸如局部癌症复发等中间事件后的剩余生存期之间的关系，识别发生中间事件的患者并分析他们的剩余生存数据很有意义。分析此类数据的一个挑战是，观察到的剩余生存时间往往比目标人群中的更长，因为在经历中间事件之前死亡的患者被排除在已识别的队列之外。我们建议使用copula模型对有序双变量生存数据进行联合建模，并对抽样偏差进行适当调整。我们开发了一种估计程序，以同时估计边际生存函数的参数和copula模型中的关联参数，并使用两阶段期望最大化算法。利用经验过程理论，我们证明了估计量具有强一致性和渐近正态性。我们进行模拟研究以评估所提方法的有限样本性能。我们将所提方法应用于两项队列研究，以评估患者特征与剩余生存期之间的关联。
