Department of Health Research & Policy, Stanford University, Stanford, CA 94305, USA.
Biostatistics. 2012 Apr;13(2):256-73. doi: 10.1093/biostatistics/kxr050. Epub 2012 Jan 30.
To estimate an overall treatment difference with data from a randomized comparative clinical study, baseline covariates are often utilized to increase the estimation precision. Using the standard analysis of covariance technique for making inferences about such an average treatment difference may not be appropriate, especially when the fitted model is nonlinear. On the other hand, the novel augmentation procedure recently studied, for example, by Zhang and others (2008. Improving efficiency of inferences in randomized clinical trials using auxiliary covariates. Biometrics 64, 707-715) is quite flexible. However, in general, it is not clear how to select covariates for augmentation effectively. An overly adjusted estimator may inflate the variance and in some cases be biased. Furthermore, the results from the standard inference procedure by ignoring the sampling variation from the variable selection process may not be valid. In this paper, we first propose an estimation procedure, which augments the simple treatment contrast estimator directly with covariates. The new proposal is asymptotically equivalent to the aforementioned augmentation method. To select covariates, we utilize the standard lasso procedure. Furthermore, to make valid inference from the resulting lasso-type estimator, a cross validation method is used. The validity of the new proposal is justified theoretically and empirically. We illustrate the procedure extensively with a well-known primary biliary cirrhosis clinical trial data set.
为了利用随机对照临床试验的数据来估计总体治疗差异，通常会使用基线协变量来提高估计精度。使用协方差分析技术来推断这种平均治疗差异可能并不合适，尤其是当拟合模型是非线性的。另一方面，最近研究的新型增强程序，例如 Zhang 等人（2008. 使用辅助协变量提高随机临床试验推断的效率。生物统计学 64,707-715）非常灵活。然而，一般来说，如何有效地选择增强的协变量并不清楚。过度调整的估计量可能会增加方差，在某些情况下还会产生偏差。此外，忽略变量选择过程中抽样变化的标准推断程序的结果可能是无效的。在本文中，我们首先提出了一种估计方法，直接使用协变量增强简单的治疗对比估计量。新的建议在渐近意义上等同于上述的增强方法。为了选择协变量，我们使用了标准的套索程序。此外，为了从得到的套索型估计量中进行有效的推断，我们使用了交叉验证方法。新建议的有效性在理论和经验上都得到了证明。我们使用一个著名的原发性胆汁性肝硬化临床试验数据集广泛地说明了该过程。
