Incorrect least-squares regression coefficients in method-comparison analysis.

Abstract

The least-squares method is frequently used to calculate the slope and intercept of the best line through a set of data points. However, least-squares regression slopes and intercepts may be incorrect if the underlying assumptions of the least-squares model are not met. Two factors in particular that may result in incorrect least-squares regression coefficients are: (a) imprecision in the measurement of the independent (x-axis) variable and (b) inclusion of outliers in the data analysis. We compared the methods of Deming, Mandel, and Bartlett in estimating the known slope of a regression line when the independent variable is measured with imprecision, and found the method of Deming to be the most useful. Significant error in the least-squares slope estimation occurs when the ratio of the standard deviation of measurement of a single x value to the standard deviation of the x-data set exceeds 0.2. Errors in the least-squares coefficients attributable to outliers can be avoided by eliminating data points whose vertical distance from the regression line exceed four times the standard error the estimate.

Performance of non‐traditional hyperglycemia biomarkers by chronic kidney disease status in older adults with diabetes: Results from the Atherosclerosis Risk in Communities Study

“…Ordinary regression requires one variable to be the dependent variable, whereas in Deming regression both variables have the same status. 15,16 When the slope is equal to 1, then the dependent variable and the independent variable are the same; otherwise, the two variables are different from each other. When the distributions of variables are different between groups, the RMSE is more relevant because Spearman's rank correlation coefficient is a function of the distribution of the explanatory variable.…”

Linear regression analysis for comparing two measurers or methods of measurement: But which regression?

“…40,41 It again may be coincidental, but in the studies that favour the MA technique samples were taken from populations in which b was close to 1.0. 34,42 In the only study that favours the P-B technique, samples were taken from populations in which there was heteroscedasticity. 22 In the only study of BLMS, outliers were introduced into the bivariate normal population.…”

Comparing methods of measurement: Extending the LoA by regression

“…The regression model where both variables are subject to error can only be identified for data with one measurement per item and method if one is willing to assume a fixed value for ratio of the variances. This is called Deming regression; Cornbleet and Gochman [4] and Jensen [5] provide the maximum-likelihood estimator in the model (2) (with the usual bias correction for the variance), under the assumption that the ratio of the variances is known. This highlights the desirability to have replicate measurements on each item by both methods, so that the method-specific variances, and hence their ratio can be estimated.…”