D ATA A NALYSIS Calculations of sample analyte concentrations in ELISA methods are similar to those

4.2.4 D ATA A NALYSIS Calculations of sample analyte concentrations in ELISA methods are similar to those

used in instrumental methods. A set of standard solutions covering the working range of the method is used to generate the calibration curve, and the concentration of target analyte is calculated according to the calibration data. For the 96-microwell format, it is easy to include a standard curve on each plate along with the samples. Thus, a calibration curve can be generated in the same 96-microwell plate along with the samples. For test tube formats, a standard curve series can be interspersed among the samples. Many mathematical models have been used to construct ELISA calibration curves including four-parameter logistic-log, log –log transforms, logistic-log transforms, and other models. The four-parameter logistic-log model is commonly used for 96-microwell plate assays and is built into commercial data analysis software [65]. The four-parameter logistic-log model is described as fol- lows: y ¼ (A D)=(1 þ (x=C) B ) þ D where x is the concentration of the analyte and y is the absorbance for colorimetric end point determinations.

Specifications are determined from each calibration curve for an expected mid- point on the curve at 50% inhibition (IC 50 ), a maximum absorbance for the lower asymptote (A), and a minimum absorbance for the upper asymptote (D). An estab- lished ELISA method usually has well-documented historical data for the specifica- tions of the curve-fit constants, such as the slope of the curve (B), and central point of the linear portion of the curve (C). The specific curve-fit constants may vary from day to day and the accepted ranges of such variations must be determined and documented. Triplicate analyses of each standard, control, and sample are generally performed for 96-microwell plate assays. The %RSD of measured concentrations

depending on the specific assay and required data quality objectives. Recoveries of positive controls and back-calculated standard solutions typically range from 70% to

Immunoassays and Biosensors 107 sample is diluted and reanalyzed. Effects of the sample matrix can be determined by

analyzing a number of samples at different dilutions. Typically, results from different interference problem, indicating cleanup procedures may be necessary.

When a commercial ELISA testing kit is used as a quantitative ELISA method, similar assay performance is expected as those previously described for laboratory- based 96-microwell plate assays. The samples need to be diluted and reanalyzed if the results of the samples are outside the calibration range. However, some of the commercial magnetic particle ELISA testing kits have a small dynamic optical density range (i.e., 1.0 –0.35 OD) and small changes in OD correlate to large changes in derived concentrations. The differences between absorbance values and duplicate assays are generally small, and are well within the acceptance requirement (<10%) for the calibration standard solutions. However, the percent difference (%D) of the derived concentrations of the standard solution from duplicate assays sometimes may exceed 30%. The greater %D values obtained for some of the measured concentra- tions for the standards and samples may be due to a small volume of standard or sample retained in the pipette tip during the transfer step [8]. If the ELISA testing kit is to be used as a quantitative method, extreme care should be taken when transfer- ring each aliquot of standard or sample. A trace amount of aliquot not delivered may result in a large variation in the data from duplicate analyses. The analyst should be alert in following the protocol when performing the assay.

To ensure the quality of the ELISA data, analytical quality control (QC) meas- ures need to be integrated into the overall ELISA method. The QC samples may include: (1) negative and positive control standard solutions, (2) calibration standard solutions, (3) laboratory and field method blank, (4) fortified matrix samples, and (5) duplicate field samples. The assay performance can be monitored by characterization of the calibration curve and the data generated from the QC samples. The QC results will provide critical information such as assay precision, accuracy, detection limit, as well as overall method precision (including sample preparation and=or cleanup), accuracy, and detection limit when evaluating and interpreting the ELISA data.

Before applying an ELISA method for field application, the ELISA method needs to be evaluated and validated for its performance. The data generated from the ELISA method are usually compared with the data generated by a conventional instrument method (e.g., GC=MS). Various types of statistical analyses have been employed to compare the results between ELISA and GC=MS. For example, the Pearson correlation coefficient, commonly used, measures the extent of a general linear association between the ELISA and GC=MS data, and a parametric statistical test is performed to determine whether the calculated value of this correlation coefficient was significantly positive [66]. The slope of the established linear regres- sion equation can also be used as guidance to determine if a 1:1 relationship exists for the ELISA and GC=MS data. The paired t-test [67] can be used to determine whether the measured ELISA and GC=MS concentrations differ significantly for a given sample at a 0.05 or 0.01 level of significance. Other nonparametric tests, namely, the Wilcoxon signed-rank test and the sign test, can also be performed on the sample-specific differences between ELISA and GC=MS data. These non- parametric tests can be used to determine if the median difference between the

108 Analysis of Pesticides in Food and Environmental Samples from zero [68]. The Wilcoxon signed-rank test is applied to differences between log-

transformed measurements, as this test assumes that the differences have a symmet- ric distribution. In contrast, the sign test does not make this assumption and therefore does not require log transformations of the data. The McNemar’s test of association can also be performed to determine whether there is any significant difference between the two methods in the proportion of samples having measurable levels that were at or above a specified threshold. The false-negative and false-positive rates can then be obtained at the specified concentration level.