Zhang Song, Müller Peter, Do Kim-Anh
Department of Clinical Sciences, Division of Biostatistics, University of Texas Southwestern Medical Center, Dallas, Texas 75390, USA.
Biometrics. 2010 Jun;66(2):435-43. doi: 10.1111/j.1541-0420.2009.01276.x. Epub 2009 Jun 8.
We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.
我们考虑对转移性前列腺癌治疗的临床试验数据进行推断。患者带着不同的既往治疗史进入试验。当试图预测不同治疗组的疾病进展时间时，由此产生的异质性患者群体引发了具有挑战性的统计推断问题。由于需要将一个纵向标志物作为协变量纳入，推断变得更加复杂。为应对这些挑战，我们开发了一个半参数模型，用于对纵向数据和事件时间进行联合推断。所提出的方法考虑了部分患者可能治愈的情况。事件时间分布基于非参数的波利亚树先验。对于纵向数据，我们假设采用混合效应模型。一般来说，在非参数事件时间模型中纳入协变量回归，特别是对于波利亚树模型，是一个具有挑战性的问题。我们利用协变量本身是一个随机变量这一事实。通过将事件时间和纵向结果的联合模型分解为事件时间的边际模型以及纵向结果对事件时间的回归，我们实现了所需回归的一种实现方式，即我们通过对反向条件分布进行建模来隐式地对所需回归进行建模。
