Armstrong B G
School of Occupational Health, McGill U., Montreal, Quebec, Canada.
Am J Epidemiol. 1990 Dec;132(6):1176-84. doi: 10.1093/oxfordjournals.aje.a115761.
This paper concerns the effects of random error in numerical measurements of risk factors (covariates) in relative risk regressions. When not dependent on outcome (nondifferential), such error usually attenuates relative risk estimates (shifts them toward one) and leads to spuriously narrow confidence intervals. The presence of measurement error also reduces precision of estimates and power of significance tests. However, significance levels obtained by using the approximate measurements are usually valid and as powerful as possible given the measurement error. The attenuation in risk estimate depends not only on the size (variance) of the measurement error, but also on its distributional form, on whether it is dependent on the true level of the risk factor (whether it is of "Berkson" type), on the variance and distributional form of true levels of the risk factor, on the functional form of the regression (exponential or linear), and on the confounding variables included in the model. Error in measuring confounding variables leads to loss of control of confounding, leaving residual bias. Uncomplicated techniques of correcting the effects of measurement error in simple models in which distributions are assumed normal are available in the statistical literature. For these corrections, information on measurement error variance is required. Some approaches appropriate for more general models have been proposed, but these appear to be insufficiently developed for routine application.
本文关注相对风险回归中风险因素（协变量）数值测量中的随机误差的影响。当不依赖于结果（无差异）时，这种误差通常会减弱相对风险估计值（使其向1偏移），并导致置信区间虚假变窄。测量误差的存在还会降低估计的精度和显著性检验的功效。然而，使用近似测量值获得的显著性水平通常是有效的，并且在存在测量误差的情况下尽可能具有强大的功效。风险估计值的减弱不仅取决于测量误差的大小（方差），还取决于其分布形式、是否依赖于风险因素的真实水平（是否为“伯克森”类型）、风险因素真实水平的方差和分布形式、回归的函数形式（指数或线性）以及模型中包含的混杂变量。测量混杂变量时的误差会导致对混杂因素的控制失效，从而留下残余偏差。统计文献中提供了在假设分布为正态的简单模型中校正测量误差影响的简单技术。对于这些校正，需要测量误差方差的信息。已经提出了一些适用于更一般模型的方法，但这些方法似乎尚未充分发展到可用于常规应用的程度。
