Effects of correlated and uncorrelated measurement error on linear regression and correlation in medical method comparison studies.

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.