Effects of correlated and uncorrelated measurement error on linear regression and correlation in medical method comparison studies.
Effects of correlated and uncorrelated measurement error on linear regression and correlation in medical method comparison studies.
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医学方法比较研究中相关和不相关测量误差对线性回归和相关性的影响。
DOI：
10.1002/sim.4780140808
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发表时间：
1995
影响因子：
2
通讯作者：
R. Rifkin
中科院分区：
文献类型：
--
作者：
R. Rifkin
众所周知，当测量误差不相关时，线性回归中的两个变量都受到影响，相关系数和回归斜率会衰减。然而，相关测量误差的影响很少受到关注。在医学方法比较研究中，这种误差相关性是由于存在其他未知的解释变量，这些变量会影响新检测方法和与之进行比较的参考检测方法的结果。相关测量误差对观测到的相关系数的贡献可以通过表达式rho t1 t2 = rho 1 rho 2 + rho E1 E2来解释（1-ρ 2（1））1/2（1-rho 2（2））1/2其中rho t1 t2是测试1和2之间观察到的相关性，rho 1和rho 2分别是测试1和2与真实值的相关性，ρ E1 E2是测试误差之间的相关性。第一项描述由于不相关误差引起的衰减，第二项描述相关误差的影响。测量误差之间的正相关性降低了观测相关性和斜率的衰减，但是，当参考方法很好时，这种影响非常小。然而，对于与真实值的相关性小于0.9的较差参考检测，误差相关性可能导致斜率和相关系数与使用不相关误差或无参考检测误差获得的值存在显著差异。负相关测量误差放大了斜率和相关性的衰减。当观察到的回归斜率接近或超过1时，人们可能会怀疑存在相关误差，并且已知参考测试具有次优可靠性。本文提供了几个潜在相关的诊断方法的临床例子。
It is well known that when uncorrelated measurement error affects both variables in linear regression, there is attenuation of the correlation coefficient and regression slope. The effect of correlated measurement error, however, has received little attention. In medical method comparison studies, such error correlation results from the presence of other, unknown explanatory variables that affect the results of the new test method and the reference test method to which it is being compared. The contribution of correlated measurement error to the observed correlation coefficient can be accounted for by the expression rho t1t2 = rho1 rho2 + rho E1E2 (1-rho2(1))1/2(1-rho 2(2))1/2 where rho t1t2 is the observed correlation between tests 1 and 2, rho 1 and rho 2 are the correlation with true values for tests 1 and 2, respectively, and rho E1E2 is the correlation between the test errors. The first term describes the attenuation due to uncorrelated error, the second term describes the effect of correlated error. A positive correlation between the measurement errors reduces the attenuation of observed correlation and slope, but, when the reference method is excellent, the effect is very small. For poorer reference tests whose correlations with true values are less than 0.9, however, error correlation may result in a slope and correlation coefficient that differ importantly from the values obtained with either uncorrelated error or with no reference test error. Negatively correlated measurement errors magnify the attenuation of slope and correlation. One might suspect the presence of correlated error when the observed regression slope is close to or exceeds 1 and the reference test is known to have suboptimal reliability. This paper provides several clinical examples of potentially correlated diagnostic methods.