The AAPS Journal OF Education
Abstract
The accuracy of reported sample results is contingent upon the quality of the assay calibration curve, and as such, calibration curves are critical components of ligand binding and other quantitative methods. Regulatory guidance and lead publications have defined many of the requirements for calibration curves which encompass design, acceptance criteria, and selection of a regression model. However, other important aspects such as preparation and editing guidelines have not been addressed by health authorities. The goal of this publication is to answer many of the commonly asked questions and to present a consensus and the shared views of members of the ligand binding assay (LBA) community on topics related to calibration curves with focus on providing recommendations for the preparation and editing of calibration curves.
KEY WORDS
accuracy profile calibration curve curve editing ligand binding assay non-linear regressionAbbreviations
Introduction
Calibration curves illustrate the relationship between the detected response variable and the concentration of a reference standard that is presumed to be representative of the analyte of interest in a test sample. They are used to estimate the unknown concentration of the analyte of interest in a test sample by dose interpolation. Calibration curves are prepared by spiking the target analyte into a matrix that has been judged to be representative of the test sample matrix. The instrument read-out values for unknown samples and quality controls (QCs) are subsequently used to interpolate their concentrations from the calibration (or standard) curve. Three factors should be given consideration for optimal fitting of non-linear calibration curves. These include fitting the mean concentration response relationship, use of an appropriate weighting to account for the known heteroscedasticity (non-constant response-error relationship) in non-linear dose response curves, and a suitable curve fitting algorithm to estimate the curve fit parameters.
The accuracy of sample quantitation depends on the robustness and reproducibility of the assay calibration curve, which is in turn dependent upon the performance of the reference material and other assay components. Performance characteristics of ligand binding assay (LBA) components which include but are not limited to the solid or immobilized surfaces such as microtiter plates and the capture and detection antibodies should be thoroughly evaluated in the method development phase, and appropriate plans should be put in place to monitor lot to lot reagent consistency. The general requirements for the design of calibration curves, the acceptance criteria for individual calibrators, and the guidelines for the selection of an appropriate regression model have been defined in regulatory guidance documents and lead publications by subject matter experts . Compliance with these guidelines and adherence to the published requirements would enhance reproducibility of a calibration curve across runs and across studies. Other aspects of calibration curves including editing specifications and preparation guidelines have not been established or adequately addressed. It is ultimately the responsibility of each bioanalytical laboratory to define the criteria for the design, preparation, acceptance, and editing of LBA calibration curves in their standard operating procedures (SOPs). This publication aims to present a collective view from members of the LBA community to fill in gaps by providing recommendations and best practices for the preparation of calibration curves as well as for the treatment of calibrator data points. Although the content of this publication may be applicable to subsets of biomarker assays, its focus remains on calibration curves for quantitative pharmacokinetic (PK) LBAs. All other assay types are outside the scope of this paper.
Calibration Curves in Quantitative Analysis
Non-Linear Nature of Ligand Binding Assay Calibration Curves
There are key differences between calibration curves in LBAs and in chromatographic assays. In LBAs, the instrument response may be directly or inversely related to the analyte concentration depending on the non-competitive or competitive format of the assay. Irrespective of the format, the use of a semi-log scale translates the curve into a sigmodal “S-shaped” relationship between the response and the concentration of the analyte. This is in contrast to the chromatographic assays where response is typically a linear function of the concentration, and the two are proportional over most of the calibration curve range. For chromatographic methods, loss of linearity is an indication that the assay has reached its limits of the detection. LBAs rely upon the interaction of the analyte with a binding agent such as an antibody or a receptor component; this is in contrast to traditional chromatographic assays in which detection of the target analyte is independent of its binding to a macromolecule. The dynamic equilibrium nature of protein-protein interaction leads to a non-linear response in LBAs. Furthermore, since performance of LBAs heavily depends upon the performance of their constituent biological reagents, these assays typically manifest greater variability. The non-linear nature of an LBA curve limits the concentration-response correlation at the upper and lower ends of the curve, resulting in plateaus and therefore an S-shaped curve. Quantitation from the asymptote (upper and lower plateaus) of the calibration curve would result in poor precision and accuracy. These characteristics ultimately narrow the validated quantitative range of LBAs and render the selection of an appropriate non-linear data fitting algorithm all the more important.
Performance and Validation Requirements for Non-Linear Regression Software
There is a wide range of commercial software available to perform non-linear regression for LBAs. Most instrument manufacturers provide a non-linear regression software that is compatible with the equipment. Depending on which better meets their needs and requirements, laboratories may alternatively choose to install a stand-alone software or use their laboratory information management system (LIMS) for regression purposes. There are performance requirements for the software. The software used for LBA calibration curves should have the capability to
- Perform four and five parameter logistic (4 PL and 5 PL) regressions
- Allow for application of various weighting factors
- Calculate %bias
- Determine %CV
- Possess the capability to plot concentration versus %bias for each model with various weighting factors and the response curve
- Allow for editing of the curve and repeat regression after editing
- Be compatible with standard computer equipment, infrastructure, networks, and data processing procedures
- Be compatible with standard or custom system interfaces
- Allow for data acquisition, analysis, and reporting
- Allow for data upload to LIMS
- Include an audit trail feature
- Include an edit lock feature
- Allow for creation of custom immunoassay templates to incorporate the acceptance criteria of the validated method
Software validation is the responsibility of the end user. Additional recommendations and the general requirement for software validation have been provided in Appendix 2.
Calibration Curve Minimum Requirements
Comparison of Requirements from Various Regulatory Agencies
The minimum requirements for calibration standard curves have been established in a number of bioanalytical guidance or in the bioanalytical subsections of regulatory documents. At the same time, several bioanalytical guidance from around the world are still in the draft stage. Guidance documents are generally aligned with regard to the requirements and performance expectations of the LBA curves. Table I summarizes the calibration curve requirements from the US Food and Drug Administration (FDA), European Medicines Agency (EMA), the Japanese Ministry of Health, Labor and Welfare (MHLW), and the Brazilian Sanitary Surveillance Agency (ANVISA) (9, 10, 11, 12, 13, 14). The FDA and EMA guidance are the lead regulatory documents for the vast majority of bioanalytical laboratories; individual groups should assess their regulatory requirements based on the agency they intend to submit to.
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