Huang Yijian
Department of Biostatistics and Bioinformatics, Emory University.
Scand Stat Theory Appl. 2013 Dec;40(4). doi: 10.1111/sjos.12031.
Weighted log-rank estimating function has become a standard estimation method for the censored linear regression model, or the accelerated failure time model. Well established statistically, the estimator defined as a consistent root has, however, rather poor computational properties because the estimating function is neither continuous nor, in general, monotone. We propose a computationally efficient estimator through an asymptotics-guided Newton algorithm, in which censored quantile regression methods are tailored to yield an initial consistent estimate and a consistent derivative estimate of the limiting estimating function. We also develop fast interval estimation with a new proposal for sandwich variance estimation. The proposed estimator is asymptotically equivalent to the consistent root estimator and barely distinguishable in samples of practical size. However, computation time is typically reduced by two to three orders of magnitude for point estimation alone. Illustrations with clinical applications are provided.
加权对数秩估计函数已成为删失线性回归模型或加速失效时间模型的标准估计方法。从统计学角度来看，这种方法已得到充分确立，然而，将估计量定义为一致根时，其计算性质相当糟糕，因为估计函数既不连续，一般也不单调。我们通过一种渐近引导的牛顿算法提出了一种计算效率高的估计量，在该算法中，删失分位数回归方法经过调整，以产生极限估计函数的初始一致估计和一致导数估计。我们还通过一种新的三明治方差估计方法开发了快速区间估计。所提出的估计量与一致根估计量渐近等价，在实际规模的样本中几乎无法区分。然而，仅就点估计而言，计算时间通常会减少两到三个数量级。文中提供了临床应用示例。
