Xu R, Harrington D P
Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA.
Biometrics. 2001 Sep;57(3):875-85. doi: 10.1111/j.0006-341x.2001.00875.x.
A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect beta(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in k-sample transformation models when the random error belongs to the G(rho) family of Harrington and Fleming (1982, Biometrika 69, 553-566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression.
最近在Cox型模型下提出了一种对具有右删失失效时间数据的平均回归效应的半参数估计，其中回归效应β(t)允许随时间变化。在本文中，当随机误差属于Harrington和Fleming（1982年，《生物统计学》69卷，553 - 566页）的G(ρ)族时，我们推导了这种平均回归效应与k样本变换模型中组间差异度量之间的简单代数关系，后者等同于伽马脆弱模型中的条件回归效应。这里考虑的模型适用于实践中经常出现的衰减风险比。结果揭示了上述三类模型作为比例风险假设替代方案之间的有趣联系，并加深了我们对非比例风险下部分似然估计行为的理解。该代数关系在变换模型下提供了一个简单的估计量。我们基于经验影响函数开发了一个方差估计量，它比之前建议的重采样方法更容易计算。当失效时间的右尾存在截断时，我们提出一种偏差校正方法来改善置信区间的覆盖性质。估计量、其估计方差和偏差校正项都可以通过对比例风险回归的标准软件进行微小修改来计算。
