Dilutional linearity

VS and QC concentrations should reflect the expected study sample. For example, the plasma sample concentrations from intravenous or inhaler dosing would be very different. The concentration of samples around the Cmax region may exceed the ULOQ. In that case, a VS/QC should be prepared to mimic the high concentration samples and tested for dilution linearity to extend the assay range. 

In general, the functional range of a curvilinear regression model is narrower than that of a linear model the assay range is extended by the dilution of samples with concentrations higher than the ULOQ. Dilution linearity also demonstrates the lack of a prozone or hook effect of the assay. A hook (prozone) effect is the phenomenon where the responses of higher concentrations of analyte are lower than expected. 

Experiment. Two levels of Dilution QC are required. The Dilution QC for dilution integrity is typically at lOx of the High QC. The Dilution QC for dilution linearity should be at a concentration above projected maximum concentration (C ). If the projected Cmix is not available, the recommended concentration would be 50x or lOOx of High QC. To test dilution integrity or linearity, the Dilution QCs need to be diluted at dilution factor (DF) of 10, 50 or 100 to bring the final concentration within the range. It may require multiple steps of dilution. This experiment only needs to be conducted once per each validation. 

Kokorin YuK, Pokrovskii VN (1990) Mechanism of ultra-slow relaxation in non-dilute linear polymers. Polym Sci USSR 32 2532-2540... 

Figure 10.13 Equilibrium isotherms and high-concentration band profiles, (a) Isotherm models 1, linear 2, Langmuir (Eqs. 3.47 and 3.48) 3, bi-Langmuir (Eq. 3.53) 4, quadratic with inflection point (Eq. 3.61 with n = 2). All foiu isotherms have the same initial slope, hence the retention times at infinite dilution (linear chromatography) are the same for all four profiles, (b) Band profiles corresponding to a 1-mg sample with the four isotherms. Reproduced with permission from AM. Katti, M. Diack, M.Z. El Fallah, S. Golshan-Shirazi, S.C. Jacobson, A. Seidel-Morgenstern and G. Guiochon, Acc. Chem. Res., 25 (1992) 366 (Fig. 4). 1992, American Chemical Society.

Dilution linearity was evaluated with three serum samples. Dilution was conducted by preparing 2 folds serial dilution series. Expected values of the diluted samples were calculated from the concentrations measured in the undiluted sample. 

Dilutional linearity Demonstrate that high-concentration samples can be diluted into range with no hook effect Demonstrate low- and high-concentration samples can be diluted into range with acceptable accuracy and precision Demonstrate low- and high-concentration samples can be diluted into range with acceptable accuracy and precision... 

Preliminary analyte stability in biological matrix Parallelism/dilutional linearity Robustness and ruggedness... 

Most LBAs require some level of sample dilution prior to analysis due to either the assay MRD or high analyte concentrations in the study samples. It is imperative to demonstrate during method development that the analyte, when present in levels above the ULOQ, can be diluted to concentrations within the quantitative range. This may be accomplished by illustrating that the analytical recovery of an ultrahigh matrix spike ( 100 1000 times ULOQ), diluted serially in assay matrix, remains acceptable over a wide concentration range (when corrected for the dilution factor). Dilutional linearity experiments often reveal the presence of a prozone or Hook effect, which is discussed in the next section. 

FIGURE 3.13 Hook effect revealed by dilutional linearity experiment, (a) The analyte when assayed neat resulted in a low measured concentration. When reassayed at multiple dilutions, the measured concentration for several dilutions was greater than the assay ULOQ. (b) The results, when corrected for the dilution factor, showed dilutional linearity at dilutions greater than 400 fold, indicating the presence of a HDHE. 

Dilutional linearity Evaluate Establish Monitor and establish dilutions not covered in prestudy validation... 

Procedurally, dilutional linearity should not be confused with the MRD of an assay. The MRD is a designed integral part of an analytical method and involves a predefined dilution of test samples, QC samples and, often, calibrators usually with a buffer-based matrix. In contrast, dilution linearity is used only to support analysis of study samples that exceed the assay s ULOQ and involves dilution(s) intended to result in an analyte concentration within the standard curve s validated range. Another notable difference is that, while MRD is usually performed in buffer, dilutional linearity is performed in matrix, often the same one used to prepare the standard curve. 

The requirements on the calibration curve are frequently confused with the dilutional linearity criteria. Dilutional linearity is the relationship between the... 

The primary performance measures of a ligand-binding assay are bias/trueness and precision. These measures along with the total error are then used to derive and evaluate several other performance characteristics such as sensitivity (LLOQ), dynamic range, and dilutional linearity. Estimation of the primary performance measures (bias, precision, and total error) requires relevant data to be generated from a number of independent runs (also termed as experiments or assay s). Within each run, a number of concentration levels of the analyte of interest are tested with two or more replicates at each level. The primary performance measures are estimated independently at each level of the analyte concentration. This is carried out within the framework of the analysis of variance (ANOVA) model with the experimental runs included as a random effect [23]. Additional terms such as analyst, instmment, etc., may be included in this model depending on the design of the experiment. This ANOVA model allows us to estimate the overall mean of the calculated concentrations and the relevant variance components such as the within-run variance and the between-run variance. 

Parallelism and Dilutional Linearity to Evaluate Matrix Effects... 

Evaluation of parallelism for ligand-binding PK assays is very similar to that for biomarker PD assays since most PK assays that employ commercial kit methods are likely to be for endogenous compounds. This describes the dilution of incurred samples rather than dilution of spiked samples. The dilution of spiked samples is termed dilution linearity [3]. 

Linearity has been described by some workers in a way which, by the current authors, would be interpreted as matrix parallelism, whereas others will use the term to describe the extent to which a calibration curve is linear in nonligand-binding assays. For the purpose of this chapter, the term linearity or dilution linearity is used to describe the results of experiments conducted using spiked samples to demonstrate the potential for high-concentration samples to be able to be diluted into the analytical range and read with acceptable accuracy and precision. It is often used to give an indication that matrix effects will not cause a problem upon sample dilution in circumstances where incurred or volunteer samples are not available with concentrations of analyte sufficiently high to conduct parallelism experiments. 

Dilution linearity is also normally monitored during the study sample analysis phase by using dilution linearity quality control (DLQCs) samples. These samples are prepared at concentrations above the assay range and then diluted into range at the same time as the study samples. The dilutions performed for these DLQCs should be representative of how the samples are diluted. 

Dilution linearity can be performed using the kit standard material if required or appropriate. Here, the highest standard could be prepared as instructed in the kit insert and then a 9/10 dilution made. This may be used as the 100% value and 9/10,8/10,6/10,... 

For PK assays, it may be the case that a human-derived molecule is being dosed to a different species. In this case, an assessment should be made of whether structurally similar molecules in that species are likely to cross-react. If the molecule does not appear naturally in the species, for example, a humanized monoclonal antibody, then the assay can be used for that species, but potential matrix differences have to be investigated and solved, that is, parallelism, dilution linearity, and so on. 

A bioequivalence study was conducted in nonhuman primates to assess in vivo equivalence for the two forms of the drug. In preparation for sample analysis, the assays were optimized and standard curves were prepared using each form of the protein in study matrix. In addition, spiked controls were serially diluted and each series was measured in the N-and C-terminus-specific assays. The results for the C-terminus assay were equivalent, as shown in Fig. 9.3, demonstrating acceptable dilutional linearity with either sample type. However, as one can see in Fig. 9.4, the N-terminus assay clearly does not equivalently recognize the two forms of the drug. 

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