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 correlati on coefficient and regression slope. The effect of correlated measurem ent error, however, has received little attention, In medical method c omparison studies, such error correlation results from the presence of other, unknown explanatory variables that affect the results of the n ew test method and the reference test method to which it is being comp ared. The contribution of correlated measurement error to the observed correlation coefficient can be accounted for by the expression rho(t1 t2) = rho(1) rho(2) + rho(E1E2)(1 - rho(1)(2))(1/2)(1 - rho(2)(2))(1/2 ) where rho(t1t2) is the observed correlation between tests 1 and 2, r ho(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 err ors. The first term describes the attenuation due to uncorrelated erro r, the second term describes the effect of correlated error. A positiv e correlation between the measurement errors reduces the attenuation o f observed correlation and slope, but, when the reference method is ex cellent, the effect is very small. For poorer reference tests whose co rrelations with true values are less than 0.9, however, error correlat ion may result in a slope and correlation coefficient that differ impo rtantly from the values obtained with either uncorrelated error or wit h no reference test error. Negatively correlated measurement errors ma gnify the attenuation of slope and correlation. One might suspect the presence of correlated error when the observed regression slope is clo se to or exceeds 1 and the reference test is known to have suboptimal reliability, This paper provides several clinical examples of potentia lly correlated diagnostic methods.