Linearity

Nonlinear bias is a component of bias that cannot be represented by a linear relationship between the measured and true values.

A measurement procedure is linear when there is a mathematically verified straight-line relationship between the measured and true values. It is an important parameter as it allows linear interpolation of results between points.

A linear (straight-line) fit describes a relationship where the measuring system is linear. A polynomial fit describes a relationship where the measuring system is nonlinear. In evaluating linearity, a nonlinear polynomial fit is compared against a linear fit. Typically the 2nd and 3rd order polynomial fits are of interest:

2nd-order polynomial fit (curved line), where there is nonlinearity due to increasing or decreasing recovery at higher levels.
3rd-order polynomial fit (slanted S-shaped curve), where there is nonlinearity at the ends of the measuring interval due to changing recovery across levels.

Bias due to nonlinearity is measured as the difference between the linear fit and the best fitting polynomial fit.

Related information

Kroll, M. H., & Emancipator, K. (1993). A theoretical evaluation of linearity. Clinical chemistry, 39(3), 405-413.

Emancipator, K., & Kroll, M. H. (1993). A quantitative measure of nonlinearity. Clinical chemistry, 39(5), 766-772.

Hsieh, E., & Liu, J. P. (2008). On statistical evaluation of the linearity in assay validation. Journal of Biopharmaceutical Statistics, 18(4), 677-690.

Hsieh, E., Hsiao, C. F., & Liu, J. P. (2009). Statistical methods for evaluating the linearity in assay validation. Journal of Chemometrics, 23(1), 56-63.

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