Xu R, O'Quigley J
Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, Boston, MA 02115, USA.
Biostatistics. 2000 Dec;1(4):423-39. doi: 10.1093/biostatistics/1.4.423.
We present an estimator of average regression effect under a non-proportional hazards model, where the regression effect of the covariates on the log hazard ratio changes with time. In the absence of censoring, the new estimate coincides with the usual partial likelihood estimate, both estimates being consistent for a parameter having an interpretation as an average population regression effect. In the presence of an independent censorship, the new estimate is still consistent for this same population parameter, whereas the partial likelihood estimate will converge to a different quantity that depends on censoring. We give an approximation of the population average effect as integral beta(t)dF(t). The new estimate is easy to compute, requiring only minor modifications to existing softwares. We illustrate the use of the average effect estimate on a breast cancer dataset from Institut Curie. The behavior of the estimator, its comparison with the partial likelihood estimate, as well as the approximation by integral beta(t)dF(t)are studied via simulation.
我们提出了一种在非比例风险模型下平均回归效应的估计方法，其中协变量对对数风险比的回归效应随时间变化。在无删失的情况下，新估计值与通常的偏似然估计值一致，这两种估计值对于一个可解释为总体平均回归效应的参数都是一致的。在存在独立删失的情况下，新估计值对于同一个总体参数仍然是一致的，而偏似然估计值将收敛到一个依赖于删失的不同量。我们给出了总体平均效应的一个近似值，即积分β(t)dF(t)。新估计值易于计算，只需对现有软件进行微小修改。我们说明了在居里研究所的一个乳腺癌数据集上使用平均效应估计值的情况。通过模拟研究了估计量的行为、它与偏似然估计值的比较以及积分β(t)dF(t)的近似值。
