Rennert Lior, Xie Sharon X
Department of Biostatistics and Epidemiology, University of Pennsylvania, 607 Blockley Hall, 423 Guardian Drive, Philadelphia, Philadelphia 19104, U.S.A.
Biometrics. 2018 Jun;74(2):725-733. doi: 10.1111/biom.12809. Epub 2017 Oct 26.
Truncation is a well-known phenomenon that may be present in observational studies of time-to-event data. While many methods exist to adjust for either left or right truncation, there are very few methods that adjust for simultaneous left and right truncation, also known as double truncation. We propose a Cox regression model to adjust for this double truncation using a weighted estimating equation approach, where the weights are estimated from the data both parametrically and nonparametrically, and are inversely proportional to the probability that a subject is observed. The resulting weighted estimators of the hazard ratio are consistent. The parametric weighted estimator is asymptotically normal and a consistent estimator of the asymptotic variance is provided. For the nonparametric weighted estimator, we apply the bootstrap technique to estimate the variance and confidence intervals. We demonstrate through extensive simulations that the proposed estimators greatly reduce the bias compared to the unweighted Cox regression estimator which ignores truncation. We illustrate our approach in an analysis of autopsy-confirmed Alzheimer's disease patients to assess the effect of education on survival.
截断是一种在事件发生时间数据的观察性研究中可能存在的已知现象。虽然存在许多方法来调整左截断或右截断，但很少有方法能调整同时存在的左截断和右截断，即所谓的双截断。我们提出一种Cox回归模型，使用加权估计方程方法来调整这种双截断，其中权重通过参数和非参数方式从数据中估计，并且与观察到某个个体的概率成反比。由此得到的风险比加权估计量是一致的。参数加权估计量渐近正态，并提供了渐近方差的一致估计量。对于非参数加权估计量，我们应用自助法技术来估计方差和置信区间。我们通过大量模拟证明，与忽略截断的未加权Cox回归估计量相比，所提出的估计量大大减少了偏差。我们在一项对尸检确诊的阿尔茨海默病患者的分析中阐述我们的方法，以评估教育对生存的影响。
