Comparisons of standard curve-fitting methods to quantitate Neisseria meningitidis group A polysaccharide antibody levels by enzyme-linked immunosorbent assay

Abstract

We examined several of the more commonly used models (log-log, two forms of the logit-log, and the fourparameter logistic-log transformations) for forming standard or calibration curves by using a standardized enzyme-linked immunosorbent assay (ELISA). Assay range, accuracy, and error for each function were measured and compared. Antibody levels to Neisseria meningitidis group A polysaccharide were estimated by calculating antibody concentrations of a serially diluted standard reference serum of known concentration. Each function achieved a high squared correlation coefficient (r2> 0.97), indicating a high degree of accuracy in forming the standard curves. However, when predicted antibody concentrations were compared with the known values, the log-log function exhibited the least precision, with extreme percentages of error occurring at several dilutions. A partially specified logit-log transformation performed better than the log-log model over a reduced range of standard dilutions. This indicated that a high r2 alone was not a reliable measure of the accuracy of the standard curve. Of the methods surveyed, the logistic-log and fully specified logit-log functions were the most accurate models for forming standard curves and for interpolating antibody concentrations from the standard curve. The accuracy of the fully specified logit-log function is highly dependent on the precise specification of two unknown quantities, the optical densities at zero and infinite concentrations, prior to fitting the model to a typical set of calibration data. The four-parameter logistic-log function was the preferred choice for quantitating N. meningitidis group A total polysaccharide antibody by using a standardized ELISA. The function does not require prespecification of any parameters before estimating the standard curve, and the four parameters are readily interpretable in terms of identifiable physical quantities. This model also has the advantage that it is easiest to visualize since it does not incorporate complex transformations of the optical density scale.

Assignment of Additional Anticapsular Antibody Concentrations to the Neisseria meningitidis Group A, C, Y, and W-135 Meningococcal Standard Reference Serum CDC1992

“…The quality control sera were assigned anticapsular antibody concentrations for groups Y and W-135 after the antibody concentrations were assigned to CDC1992. Data analysis for ELISA antibody concentrations was done by using a four-parameter logistic log curve-fitting technique (6,7). All antibody concentrations were calculated within the working range of the standard curve.…”

Quantifying Antibody Binding on Protein Microarrays using Microarray Nonlinear Calibration

“…Thus, no single approach to curvefitting will be appropriate for all applications. In the context of calibration, fixed-form methods using logistic and power curves are commonlyused (17)(18)(19). Alternative methods based upon flexible splines or hierarchical models have also been proposed (20-21).…”

Transition models for change‐point estimation in logistic regression

“…In the toxicological and risk assessment literature, intersecting linear-linear models with constant slope below the change-point, so-called no-observed-e ect level (NOEL) models, are used routinely to establish reference doses for regulatory decision making [19][20][21]. In the bioassay and radioligand assay ÿelds, transition functions for horizontal asymptotes, referred to as four-parameter logistic-log models, have been used to model sigmoidal calibration curves between the optical density and the log dilution scale [22], but exible statistical methods seem to be lacking for linear-linear relationships with dichotomous outcomes. Finally, our analysis of the association of the 2-hour glucose levels after an oral glucose tolerance test with mortality highlights the need to assess potential threshold e ects for clinical decision making and for evaluating epidemiological associations.…”