Validity of linear regression in method comparison studies: is it limited by the statistical model or the quality of the analytical input data?

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Abstract
We compared the application of ordinary linear regression, Deming regression, standardized principal component analysis, and Passing–Bablok regression to real-life method comparison studies to investigate whether the statistical model of regression or the analytical input data have more influence on the validity of the regression estimates. We took measurements of serum potassium as an example for comparisons that cover a narrow data range and measurements of serum estradiol-17β as an example for comparisons that cover a wide data range. We demonstrate that, in practice, it is not the statistical model but the quality of the analytical input data that is crucial for interpretation of method comparison studies. We show the usefulness of ordinary linear regression, in particular, because it gives a better estimate of the standard deviation of the residuals than the other procedures. The latter is important for distinguishing whether the observed spread across the regression line is caused by the analytical imprecision alone or whether sample-related effects also contribute. We further demonstrate the usefulness of linear correlation analysis as a first screening test for the validity of linear regression data. When ordinary linear regression (in combination with correlation analysis) gives poor estimates, we recommend investigating the analytical reason for the poor performance instead of assuming that other linear regression procedures add substantial value to the interpretation of the study. This investigation should address whether (a) the x and y data are linearly related; (b) the total analytical imprecision (sa,tot) is responsible for the poor correlation; (c) sample-related effects are present (standard deviation of the residuals ≫ sa,tot); (d) the samples are adequately distributed over the investigated range; and (e) the number of samples used for the comparison is adequate.