Directly testing the linearity assumption for assay validation

The ICH Q2(R1) (International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use) guideline for testing linearity in validation of analytical procedures suggests that “linearity should be evaluated by visual inspection of a plot of signals as a function of analyte concentration or content.” The EP6-A guideline recommends more quantitative methods that compare straight-line and higher-order polynomial curve fits. In this paper, a new equivalence test is proposed to compare the quality of a straight-line fit to that of a higher-order polynomial. By using orthogonal polynomials and generalized pivotal quantity analysis, one may estimate the probability of equivalence between a straight line and a polynomial curve fit either in the assay signal space (the Y values) or in the concentration space (the X values). In the special case of the linear-to-quadratic polynomial comparison, an equivalence test may be constructed via a two one-sided T test. Copyright © 2013 John Wiley & Sons, Ltd.