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

Abstract

In a previous paper, a computational method was presented for determining statistically rigorous limits of detection and quantification. The main purpose of this study is to evaluate similar but less computationally complex methods. These “approximate” methods use data at multiple spiking concentrations, are iterative, can be derived from either prediction intervals or statistical tolerance intervals, and require at a minimum ordinary least-squares regression for calculating the intercept and slope. Approximate detection and quantification limits calculated for various PCB congeners were similar to those calculated using the computationally exact method. Although the exact methods should be employed whenever possible (they include uncertainty in the calibration function and provide greater weight to less variable data), approximate methods can provide detection and quantification limits that are sufficiently accurate for most applications. Practical application of multiconcentration-based methods may involve the use of routinely generated quality control data in the statistical calculations.

Assessing the Detection Capacity of Microarrays as Bio/Nanosensing Platforms

“…The LOD and LOQ based on the weighted prediction intervals (one-sided) are estimated by [11, 18] $\begin{array}{c}\text{LOD}=L_C+\frac{t_{(\mathrm{1}-\beta ,\hspace{0.17em}n-p-\mathrm{2})}{s}_W}{b_{\mathrm{1}W}}\\ \hspace{1em}{\times \left[\frac{\mathrm{1}}{w_{\text{LOD}}}+\frac{\mathrm{1}}{false\sum w_i}+\frac{{\left(\text{LOD}-{\overline{X}}_W\right)}^{\mathrm{2}}}{Sx{x}_W}\right]}^{\mathrm{1}/\mathrm{2}},\\ \text{LOQ}=L_Q+\frac{t_{(\mathrm{1}-\beta ,\hspace{0.17em}n-p-\mathrm{2})}{s}_W}{b_{\mathrm{1}W}}\\ \hspace{1em}\times {\left[\frac{\mathrm{1}}{w_{L_Q}}+\frac{\mathrm{1}}{false\sum w_i}+\frac{{\left(L_Q-{\overline{X}}_W\right)}^{\mathrm{2}}}{Sx{x}_W}\right]}^{\mathrm{1}/\mathrm{2}},\end{array}$ where L C is the critical level, L Q is the determination limit, w is the weight at specific data, t (1− β ,  n − p −2) is (1 − β )100% percentile of Student's t -distribution with n − p − 2 degrees of the freedom, p is the number of parameters used to model the weight, b 1 W is Sxy W / Sxx W , Sxx W is ${false\sum }_{}^{}{w}_i{false(X_i-{\stackrel{}{X}}_{}}^{}$…”

“…The LOD and LOQ based on the weighted tolerance interval are estimated by [11, 18] $\begin{array}{c}\text{LOD}=L_C\\ \hspace{1em}+\frac{s_W}{b_{\mathrm{1}W}}\{t_{\left(\mathrm{normal1}-\beta ,\hspace{0.17em}n-\mathrm{normal2}\right)}{\left[\frac{\mathrm{1}}{false\sum w_i}+\frac{{\left(\text{LOD}-{\overline{X}}_W\right)}^{\mathrm{2}}}{Sx{x}_W}\right]}^{\mathrm{1}/\mathrm{2}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\left(\frac{\mathrm{1}}{w_{\text{LOD}}}\right)}^{\mathrm{1}/\mathrm{2}}N\left(P\right){\left(\frac{n-p-\mathrm{2}}{{{}^{\beta }\chi }_{n-p-\mathrm{2}}^{\mathrm{2}}}\right)}^{\mathrm{1}/\mathrm{2}}\},\\ \text{LOQ}=L_Q+\frac{s_W}{b_{\mathrm{1}W}}\{t_{\left(\mathrm{normal1}-\beta ,\hspace{0.17em}n-\mathrm{normal2}\right)}{\left[\frac{\mathrm{1}}{false\sum w_i}+\frac{{\left(L_Q-{\overline{X}}_W\right)}^{\mathrm{2}}}{Sx{x}_W}\right]}^{\mathrm{1}/\mathrm{2}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\end{array}$…”

Fusarium head blight and associated mycotoxin occurrence on winter wheat in Luxembourg in 2007/2008

“…An Altima HP RP-C 18 column was used (150 Â 2.1 mm; 3 mm; Grace Davison, Deerfield, IL, USA) with a mobile phase consisting of methanol/water (80 : 20, v/ v) containing 2.5 mM ammonium acetate. The detection and quantification limits obtained by extracting 5 g of sample were 35 and 70 ng/g for the trichothecenes and 20 and 40 ng/g wheat for ZON, following the US-EPA approach (Zorn et al, 1999). Quantification was based on external standards and by measuring the following fragment ions of the parent molecules: 371 !…”

Effectiveness of activated carbon disk for the analysis of iodine in water samples using wavelength dispersive X-ray fluorescence spectrometry

“…The LOD and MDL values were calculated and compared to those of other conventional methods to assess analytical sensitivity. The LOD and MDL values were defined as three times the standard deviation of blank measurements (r b ) divided by the slope of the calibration line (p) and the standard deviation of seven replicates of sample measurements (r S ) multiplied by Student's t-value at the 99% confidence level (t = 3.143 at 6 degrees of freedom), respectively (Zorn et al, 1999;ICH, 1999).…”