Nakamura T, Akazawa K
School of Allied Medical Sciences, Nagasaki University, Japan.
Comput Methods Programs Biomed. 1994 Nov;45(3):203-12. doi: 10.1016/0169-2607(94)90204-6.
The Cox-regression analysis based on the partial likelihood assumes that the covariates, or independent variables, are exactly measured without error. If the covariates are subject to measurement error and the error-prone observed values are used in the analysis by simply ignoring the measurement error, the results are generally biased and misleading; the bias does not diminish as the sample size is increased. The objective of the paper is to briefly describe a method searching for asymptotically unbiased estimates of the parameters correcting for the measurement error in the Cox-regression model and to present a FORTRAN program to perform the correction method; asymptotic standard errors of the corrected estimates are also obtained. The measurement error distribution, that is the conditional distribution of the observed values given the true value, must be specified. An advantage of the method described is that it does not require any assumption on the distribution of the true values; in other words, <--> values are treated as unknown fixed constants. It can accommodate tied failure times unless ties are very frequent, and any censorship or loss to follow-up are allowed as long as they are 'independent of survival'.
基于偏似然的Cox回归分析假定协变量或自变量的测量是完全准确无误的。如果协变量存在测量误差，而在分析中只是简单地忽略测量误差，直接使用容易出错的观测值，那么结果通常会有偏差且具有误导性；这种偏差不会随着样本量的增加而减小。本文的目的是简要描述一种在Cox回归模型中寻找针对测量误差校正的参数渐近无偏估计的方法，并给出一个执行该校正方法的FORTRAN程序；同时还能得到校正估计的渐近标准误差。必须指定测量误差分布，即给定真实值时观测值的条件分布。所描述方法的一个优点是它不需要对真实值的分布做任何假设；换句话说，真实值被视为未知的固定常数。该方法可以处理删失的失效时间，除非删失非常频繁，并且只要删失或失访是“与生存无关的”，那么任何删失或失访情况都是允许的。
