Effects of Analytical Calibration Models on Detection Limit Estimates

Abstract

Detection limit estimates derived from confidence bands around analytical calibration curves are highly dependent on the experimental design and on the statistical data treatment. Procedures are described for testing the linearity of data and whether the intercept differs significantly from zero. Insensitivity of the correlation coefficient for the evaluation of goodness of fit of calibration models is emphasized, unweighted linear models with an intercept often yield overly conservative detection limits. Frequently, an unweighted zero-intercept model is justified on both theoretical and statistical grounds. This model yields confidence bands and detection limits consistent with experiment. When the variance of signal measurements increases with concentration, more realistic confidence bands and detection limits are produced by weighting the data. Despite numerous papers dealing with the specification of analytical method detection limits (see, for example 1-6) r much disagreement remains about the choice of both experimental and computational procedures.In part, these disagreements appear to be related to the technical objectives of the experimenter. For example, a detection limit (DL) might be estimated from some multiple of the standard deviation of blank solution signals measured during a short time interval using a painstakingly optimized instrument.Such a DL estimate clearly provides useful information but it would be unrealistic to expect to maintain an equivalent DL during an extended analysis program with real samples.Unfortunately, these differences are frequently ignored, thereby encouraging unproductive controversy.It is important to remember that a DL is not an intrinsic property but rather, it is Current address:

Weighted Least-Squares Approach To Calculating Limits of Detection and Quantification by Modeling Variability as a Function of Concentration

“…The unweighted intervals are wider than the weighted intervals at very low concentration and provide a poor fit to the actual data (see Figure ). As a result, applying unweighted least-squares regression in situations of nonconstant variance generally yields overestimated detection limits. ,, Table lists the unweighted detection limit for all 16 PCB congeners. Unweighted values range from 3 times the weighted value (tolerance interval-based detection limit for PCB congener 128) to nearly 60 times the weighted value (prediction interval-based detection limit for PCB congener 18).…”

“…Also, if the response values are transformed, linearity of the calibration curve will likely be compromised, and an appropriate transformation for the X axis will be required in order to retain linearity. This can be problematic, and, as several previous authors have pointed out, ,, a better solution is to use weighted least-squares regression.…”

Evaluation of Approximate Methods for Calculating the Limit of Detection and Limit of Quantification

“…Often, the errors do not exhibit constant variance; nonconstant variance has been previously documented for various chemical analyses and analytes ( − ). Several authors ( 5 , 11 , 13 , 14 ) have suggested using weighted least-squares (WLS) regression for calculating limits of detection and quantification in situations of nonconstant variance.…”