Division of Biostatistics, College of Public Health, The Ohio State University, 320 West 10th Avenue, Columbus, OH 43210, USA.
Biostatistics. 2010 Jan;11(1):111-26. doi: 10.1093/biostatistics/kxp041. Epub 2009 Oct 14.
In epidemiological and clinical studies, time-to-event data often violate the assumptions of Cox regression due to the presence of time-dependent covariate effects and unmeasured risk factors. An alternative approach, which does not require proportional hazards, is to use a first hitting time model which treats a subject's health status as a latent stochastic process that fails when it reaches a threshold value. Although more flexible than Cox regression, existing methods do not account for unmeasured covariates in both the initial state and the rate of the process. To address this issue, we propose a Bayesian methodology that models an individual's health status as a Wiener process with subject-specific initial state and drift. Posterior inference proceeds via a Markov chain Monte Carlo methodology with data augmentation steps to sample the final health status of censored observations. We apply our method to data from melanoma patients with nonproportional hazards and find interesting differences from a similar model without random effects. In a simulation study, we show that failure to account for unmeasured covariates can lead to inaccurate estimates of survival probabilities.
在流行病学和临床研究中，由于存在时变协变量效应和未测量的风险因素，事件时间数据经常违反 Cox 回归的假设。一种替代方法是使用首次到达时间模型，该模型将受试者的健康状况视为潜在的随机过程，当达到阈值时就会失效。虽然比 Cox 回归更灵活，但现有方法并未考虑初始状态和过程速率中的未测量协变量。为了解决这个问题，我们提出了一种贝叶斯方法，该方法将个体的健康状况建模为具有特定个体初始状态和漂移的 Wiener 过程。后验推断通过马尔可夫链蒙特卡罗方法进行，并使用数据增强步骤对删失观测的最终健康状态进行采样。我们将我们的方法应用于具有非比例风险的黑色素瘤患者的数据，并发现与没有随机效应的类似模型有有趣的差异。在一项模拟研究中，我们表明，不考虑未测量的协变量会导致生存概率的估计不准确。
