On Statistical Evaluation of the Linearity in Assay Validation

Abstract

Linearity is one of the most important characteristics for evaluation of the accuracy in assay validation. The current statistical method for evaluation of the linearity recommended by the Clinical Laboratory Standard Institute (CLSI) guideline EP6-A is reviewed. The method directly compares the point estimates with the pre-specified allowable limit and completely ignores the sampling error of the point estimates. An alternative method for evaluation of linearity, proposed by Kroll et al. (2000), considers the statistical test procedure based on the average deviation from linearity (ADL). However this procedure is based on an inappropriate formulation of hypotheses for the evaluation of linearity. Consequently, the type I error rates of both current methods may be inflated for inference of linearity. To claim the linearity of analytical methods, we propose that the hypothesis of proving the linearity should be formulated as the alternative hypothesis. Furthermore, any procedures for assessment of linearity should be based on the sampling distributions of the proposed test statistics. Therefore, we propose a two one-sided test (TOST) procedure and a corrected Kroll's procedure. The simulation studies were conducted to empirically compare the size and power between current and proposed methods. The simulation results show that the proposed methods not only adequately control size but also provide sufficient power. A numeric example illustrates the proposed methods.

Statistical methods for evaluating the linearity in assay validation

“…However, Hsieh and Liu [2] pointed out that the formulation of hypothesis given in Equation (3) is not appropriate for linearity validation and they suggested that the hypothesis of proving the linearity formulated as the alternative hypothesis as follows:…”

“…Throughout the simulation, mean concentration m is assumed to be 4 and the allowable margin of linearity based on ADL, u 0 , is specified 0.05 as recommended by Kroll et al [1]. From the relationship that SSDL ¼ L(mu) 2 , it follows that the margin for SSDL for 5 and 7 concentrations are 0.2 and 0.28, respectively. In addition, standard deviation of normal random error is specified as 0.1 and 0.2.…”

“…On the other hand, Hsieh and Liu [2] pointed out that the Kroll's method based on the ADL is derived from an improper formulation of hypotheses and suggested that the hypothesis of proving the linearity should be formulated as the alternative hypothesis. They termed their proposed procedure as the corrected Kroll's method.…”

“…In addition, we also apply the bootstrap method [12] to linearity validation. In Section 2, we review experiment designs for evaluation of linearity recommended by the approved CLSI guideline EP6-A [4] as well as the corrected Kroll's methods proposed by Hsieh and Liu [2]. The impact of ignoring the variability of estimated non-centrality parameters on the size of the corrected Kroll's method is highlighted.…”

“…Hsieh and Liu [2] suggested that hypothesis for proving the linearity be formulated as the alternative hypothesis and proposed the corrected Kroll's method. However, the issue concerning the variability in estimation of the non-centrality parameter is still unresolved.…”