Hughes M D
Harvard School of Public Health, Department of Biostatistics, Boston, Massachusetts 02115.
Biometrics. 1993 Dec;49(4):1056-66.
The problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model. The naive approach to parameter estimation is considered whereby observed covariate values are used, inappropriately, in the usual analysis instead of the underlying covariate values. A relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed. With high censorship, adjustment of the naive estimate by the factor 1 + lambda, where lambda is the ratio of within-person variability about an underlying mean level to the variability of these levels in the population sampled, removes the bias. As censorship increases, the adjustment required increases and when there is no censorship is markedly higher than 1 + lambda and depends also on the true risk relationship.
使用比例风险模型对生存数据研究了因协变量测量误差引起的回归稀释问题。考虑了参数估计的朴素方法，即在常规分析中不恰当地使用观察到的协变量值而非潜在协变量值。得到了大样本中估计参数与真实参数之间的关系，表明当误差呈正态分布时，偏差不依赖于基线风险函数的形式。在高删失情况下，用因子1 + λ调整朴素估计值（其中λ是个体围绕潜在均值水平的变异性与所抽样总体中这些水平的变异性之比）可消除偏差。随着删失增加，所需的调整也增加，且在无删失时明显高于1 + λ，并且还取决于真实风险关系。
