Song Xiao, Ma Shuangge, Huang Jian, Zhou Xiao-Hua
Department of Biostatistics, University of Washington, Seattle, WA 98195, USA.
Biostatistics. 2007 Apr;8(2):197-211. doi: 10.1093/biostatistics/kxl001. Epub 2006 May 2.
The nonparametric transformation model makes no parametric assumptions on the forms of the transformation function and the error distribution. This model is appealing in its flexibility for modeling censored survival data. Current approaches for estimation of the regression parameters involve maximizing discontinuous objective functions, which are numerically infeasible to implement with multiple covariates. Based on the partial rank (PR) estimator (Khan and Tamer, 2004), we propose a smoothed PR estimator which maximizes a smooth approximation of the PR objective function. The estimator is shown to be asymptotically equivalent to the PR estimator but is much easier to compute when there are multiple covariates. We further propose using the weighted bootstrap, which is more stable than the usual sandwich technique with smoothing parameters, for estimating the standard error. The estimator is evaluated via simulation studies and illustrated with the Veterans Administration lung cancer data set.
非参数变换模型对变换函数的形式和误差分布不做参数假设。该模型在对删失生存数据进行建模时具有灵活性，很有吸引力。当前估计回归参数的方法涉及最大化不连续的目标函数，在有多个协变量的情况下，在数值上难以实现。基于偏秩（PR）估计量（Khan和Tamer，2004），我们提出了一种平滑的PR估计量，它最大化PR目标函数的平滑近似。结果表明，该估计量与PR估计量渐近等价，但在有多个协变量时计算起来要容易得多。我们还提出使用加权自助法来估计标准误差，它比带有平滑参数的常用三明治技术更稳定。通过模拟研究对该估计量进行了评估，并用退伍军人管理局肺癌数据集进行了说明。
