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Methods for the determination of limit of detection and limit of

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Review Article

Methods for the determination of limit of detection and limit of quantitation of the analytical methods
Abstract
The quality of an analytical method developed is always appraised in terms of suitability for its intended purpose, recovery, requirement for standardization, sensitivity, analyte stability, ease of analysis, skill subset required, time and cost in that order. It is highly imperative to establish through a systematic process that the analytical method under question is acceptable for its intended purpose. Limit of detection (LOD) and limit of quantification (LOQ) are two important performance characteristics in method validation. LOD and LOQ are terms used to describe the smallest concentration of an analyte that can be reliably measured by an analytical procedure. There has often been a lack of agreement within the clinical laboratory field as to the terminology best suited to describe this parameter. Likewise, there have been various methods for estimating it. The presented review provides information relating to the calculation of the limit of detection and limit of quantitation. Brief information about differences in various regulatory agencies about these parameters is also presented here.
Key words: Detection limit, limit of detection, limit of quantitation, quantitation limit, methods for determination of LOD and LOQ

Introduction

Analytical method development and validation procedures are vital in the discovery and development of drugs and pharmaceuticals. Analytical methods are used to aid in the process of drug synthesis, screen potential drug candidates, support formulation studies, monitor the stability of bulk pharmaceuticals and formulated products, and test final products for release. The quality of analytical data is a key factor in the success of a drug and formulation development program. During the post approval commercial production stage of bulk drugs and pharmaceutical products, the official or in-house test methods that have resulted from the analytical method development and validation process cycle become indispensable for reliable monitoring of the integrity, purity, quality, strength and potency of the manufactured products. There is often a need to transfer methodology

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DOI: 10.4103/2229-5186.79345

from one laboratory to another and/or to include it in official compendia. Such exercises include the use of a method by large numbers of people, in various laboratories across the globe and on instruments manufactured by different manufacturers, thereby causing a greater probability of decreased reproducibility and reliability. These problems can be foreseen and avoided by thorough validation of the analytical method.[1]
Limit of detection (LOD) and limit of quantitation (LOQ) parameters are related but have distinct definitions and should not be confused. The intent is to define the smallest concentration of analyte that can be detected with no guarantee about the bias or imprecision of the result by an assay, the concentration at which quantitation as defined by bias and precision goals is feasible, and finally the
Alankar Shrivastava, Vipin B. Gupta Department of Pharmaceutical Analysis, B. R. Nahata College of
Pharmacy, Mhow Neemuch Road, Mandsaur, Madhya Pradesh - 458 001, India
Address for correspondence: Dr. Alankar Shrivastava
Department of Pharmaceutical Analysis, BR Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur, Madhya Pradesh 458 001, India. E-mail: [email protected]

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Table 1: Comparison of different guidelines for ‘‘detection limit’’ parameter of analytical method validation[1]

Guidelines ICH

US FDA AOAC

USP

IUPAC

Definition Method
Expression/ calculation Acceptance criteria

Lowest amount of analyte in the sample, which can be detected but not necessarily quantitated under stated experimental conditions
1. By visual evaluation 2. Based on S/N ratio
Applicable to procedure, which exhibits base line noise Low conc. of analyte is compared with blank 3. Based on S.D. of response and slope LOQ=3.3σ/s s – Slope of calibration curve σ – S.D. of response; can be obtained by Standard deviation of blank response Residual standard deviation of the regression line Standard deviation of the y-intercept of the regression line Sy/x, i.e. standard error of estimate
If based on visual examination or S/N ratio - relevant chromatogram is to be presented If by calculation/extrapolation estimate is validated by analysis of suitable no. of samples known to be near or prepared at detection limit
S/N ratio>2–3; not specified in other cases

Explicitly not described Not described
Not specified
Not specified

Lowest content that can be measured with reasonable statistical certainty Based on more than 20 blank readings
The mean value of the matrix blank readings (n≥20) plus three standard deviations of the mean, expressed in analyte concentration Not specified

Lowest amount of analyte in the sample, which can be detected but not necessarily quantitated under stated experimental conditions. For non-instrumental: Analysis of sample with known concentration of analyte and by establishing minimum concentration at which analyte can be reliably detected. For instrumental: Process for non-instrumental can be adopted. Detection limit should be sufficiently low for analysis of samples with known concentration of analyte above and below the required detection limit Not specified
Not specified

Smallest amount of conc. of analyte in the sample that can be reliably distinguished from zero. Not specified
Not specified
Not specified

ICH – International Conference on Harmonisation, US FDA – United states food and drug administration; AOAC – Association of Analytical

Communities; USP – United States Pharmacopoeia; IUPAC – International Union of Pure and Applied Chemistry

concentration at which the analyte can be quantitated with a linear response.[2] Comparison of regulatory authorities such as United States Pharmacopoeia (USP),[3] Foods and Drugs Administration (FDA),[4] International Union of Pure and Applied Chemistry (IUPAC),[5] International Conference on Harmonisation (ICH)[6] and Association of Analytical Communities (AOAC)[7,8] for limit of detection and limit of quantitation are produced in Tables 1 and 2, respectively.
Detection and Quantitation Limits (LOD and LOQ)
There are several terms that have been used to define LOD and LOQ. In general, the LOD is taken as the lowest concentration of an analyte in a sample that can be detected, but not necessarily quantified, under the stated conditions of the test. The LOQ is the lowest concentration of an

analyte in a sample that can be determined with acceptable precision and accuracy under the stated conditions of test.[9]
Although reagent package inserts may state that an assay has a dynamic range that extends from zero concentration to some upper limit, typically an assay is simply not capable of accurately measuring analyte concentrations down to zero. Sufficient analyte concentration must be present to produce an analytical signal that can reliably be distinguished from “analytical noise,” the signal produced in the absence of analyte.[10]
However, some common methods[11] for the estimation of detection and quantitation limit are • Visual definition • Calculation from the signal-to-noise ratio (DL and
QL correspond to 3 or 2 and 10 times the noise level, respectively)

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Table 2: Comparison of different guidelines for ‘quantitation limit’ parameter of analytical method validation[1]

Guidelines ICH

US FDA

AOAC

USP

IUPAC

Definition
Method
Recommendation Expression/ calculation
Acceptance criteria

Lowest amount of analyte in a sample, which can be quantitatively determined with suitable precision and accuracy.
1. By visual evaluation 2. Based on S/N ratio
Applicable to procedure, which exhibits base line noise. Low conc. of analyte is compared with blank 3. Based on S.D. of response and slope LOQ=10σ/s s – Slope of calibration curve σ – S.D. of response; can be obtained by Standard deviation of blank response Residual standard deviation of the regression line Standard deviation of the y-intercept of the regression line Sy/x, i.e. standard error of estimate

The lowest amount of analyte that can be quantitatively determined with suitable precision and accuracy also called LLOQ (Lower limit of quantification).
Preparation of standard curve and lowest conc. on the calibration curve should be accepted as LLOQ if it satisfies following condition. Response at LLOQ=5×Response by blank Analyte peak should be identifiable discrete and reproducible with precision of 20% and accuracy of 80%– 120%

The limit of quantitation is the lowest amount of analyte in a sample, which can be quantitatively determined with precision and accuracy appropriate to analyte and matrix considered
Not specified

Limit should be validated by analysis of suitable no. of samples known to be near or prepared at quantitation limit.
Limits of quantitation and method used for determining should be presented. Expressed as analyte concentration

Not specified Not specified

Not specified

Not specified

Not specified
Mean value of the matrix blank reading plus 10 standard deviations of the mean, expressed in analyte concentration. Not specified

Lowest amount of analyte in a sample, which can be quantitatively determined with suitable precision and accuracy

Not defined

1. By visual evaluation 2. Based on S/N ratio
Applicable to procedure, which exhibits base line noise. Low concentration of analyte is compared with blank 3. Based on S.D. of response and slope LOQ=10σ/s s – Slope of calibration curve σ – S.D. of response; can be obtained by Standard deviation of blank response Residual standard deviation of the regression line Standard deviation of the y-intercept of the regression line Sy/x, i.e. standard error of estimate
Not specified

Not recommended; only recommends expressing uncertainty of measurement as function of concentration
Not specified

Expressed as analyte concentration Not specified (% or ppb)

Not specified

Not specified

ICH – International Conference on Harmonisation, US FDA – United states food and drug administration; AOAC – Association of Analytical

Communities; USP – United States Pharmacopoeia; IUPAC – International Union of Pure and Applied Chemistry

• Calculation from the standard deviation of the blank • Calculation from the calibration line at low
concentrations
F×SD DL/QL =
b
Where F: Factor of 3.3 and 10 for DL and QL, respectively

SD: Standard deviation of the blank, standard deviation of the ordinate intercept, or residual standard deviation of the linear regression
b: Slope of the regression line
The estimated limits should be verified by analyzing a suitable number of samples containing the analyte at the corresponding concentrations. The DL or QL and the

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procedure used for determination, as well as relevant chromatograms, should be reported.

Signal- to-noise By using the signal-to-noise method, the peak-to-peak noise around the analyte retention time is measured, and subsequently, the concentration of the analyte that would yield a signal equal to certain value of noise to signal ratio is estimated. The noise magnitude can be measured either manually on the chromatogram printout or by autointegrator of the instrument. A signal-to-noise ratio (S/N) of three is generally accepted for estimating LOD and signal-to-noise ratio of ten is used for estimating LOQ. This method is commonly applied to analytical methods that exhibit baseline noise.[11]

For chromatography a test sample with the analyte at the level at which detection is required or determined is chromatographed over a period of time equivalent to 20 times the peak width at half-height [Figure 1]. The signalto-noise ratio is calculated from Equation (1).

2H

S/D =

(1)

h

where H is the height of the peak, corresponding to the component concerned, in the chromatogram obtained with the prescribed reference solution, and measured from the maximum of the peak to the extrapolated baseline of the signal observed over a distance equal to 20 times the width at half-height h is the peak-to-peak background noise in a chromatogram obtained after injection or application of a blank, observed over a distance equal to 20 times the width at half-height of the peak in the chromatogram obtained.

This approach is specified in the European Pharmacopoeia.[5] It is important that the system is free from significant baseline drift and/or shifts during this determination.

Figure 1 shows examples of S/N ratios of 10:1 and 3:1 which approximate the requirements for the QL and DL, respectively. This approach works only for peak height measurements.

Blank determination It is assumed that they both have the same variance and are normally distributed. As the curves overlap there is a probability that we could conclude that we have detected the analyte when this is in fact due to the blank signal (false positive, α error or type 1 error). Alternatively, we can conclude that the analyte is not detected when it is in fact present (false negative, β error or type 2 error). When addressing the issue about when an analyte has been detected it is always a matter of risk.[11]

The blank determination is applied when the blank analysis gives results with a nonzero standard deviation. LOD is

Figure 1: Signal-to-noise examples of 10:1 (top) and 3:1 (bottom), using the method of the EP
expressed as the analyte concentration corresponding to the sample blank value plus three standard deviation and LOQ is the analyte concentration corresponding to the sample blank value plus ten standard deviations as shown in the following equations: LOD=Xb1 +3Sb1, LOQ=Xb1+10Sb1,
where Xb1 is the mean concentration of the blank and Sb1 is the standard deviation of the blank. This is a simple and quick method. The weakness is that there is no objective evidence to prove that a low concentration of analyte will indeed produce a signal distinguishable from a blank (zero concentration) sample.[9]
Linear regression For a linear calibration curve, it is assumed that the instrument response y is linearly related to the standard concentration x for a limited range of concentration.[9] It can be expressed in a model such as y=a+bx.
This model is used to compute the sensitivity b and the LOD and LOQ. Therefore, the LOD and LOQ can be expressed as LOD=3Sa/b, LOQ=10Sa/b,
where Sa is the standard deviation of the response and b is the slope of the calibration curve. The standard deviation of the response can be estimated by the standard deviation of either y-residuals, or y-intercepts, of regression lines. This method can be applied in all cases, and it is most applicable when the analysis method does not involve background noise. It uses a range of low values close to zero for calibration curve, and with a more homogeneous distribution will result in a more relevant assessment.

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Limit of blank LoB as the highest apparent analyte concentration expected to be found when replicates of a sample containing no analyte are tested. Note that although the samples tested to define LoB are devoid of analyte, a blank (zero) sample can produce an analytical signal that might otherwise be consistent with a low concentration of analyte. LoB is estimated by measuring replicates of a blank sample and calculating the mean result and the standard deviation (SD).[2] LoB=meanblank+1.645(SDblank)
After calculating this value LOD can be calculated according to LOD=LOB+1.645(SDlow concentration sample).
Precision-based approaches The quantitation limit can also be obtained from precision studies.[10,11] For this approach, decreasing analyte concentrations are analyzed repeatedly and the relative standard deviation is plotted against the corresponding concentration (precision function). If a predefined limit is exceeded (such as 10% or 20%), the corresponding concentration is established as the quantitation limit However, in practice, due to the high variability of standard deviations the true precision function is much more difficult to draw unless a large number of concentrations is included.
The QL can be specifically calculated[11] using the actual precision of the analytical procedure at this concentration. The calculation is based on the compatibility between analytical variability and specification acceptance limits. QL can be regarded as the maximum true impurity content of the manufactured batch, i.e., as the basic limit
QL=AL- (stdf,95%)validation √nassay
AL Acceptance limit of the specification for the impurity. s Precision standard deviation at QL, preferably under
intermediate or reproducibility conditions. AL and s must have the same unit (e.g., percentage with respect to active, mg, mg/ml, etc.). nassay Number of repeated, independent determinations in routine analyses, as far as the mean is the reportable result, i.e., is compared with the acceptance limits. If each individual determination is defined as the reportable result, n=1 has to be used. tdf Student t-factor for the degrees of freedom during

determination of the precision, usually at 95% level of statistical confidence.
Conclusion
In this review, the authors have tried to give information to the researchers engaged in establishing analytical profiles of the drug substances or products. Data are adequate and sufficient to meet the laboratory’s method requirements. The laboratory must be able to match the performance data as described in the standard and to establish these parameters a manufacturer would test a large number of sample replicates to increase the robustness and the statistical confidence of the estimate. Comparison of all of the validation parameters in different regulatory agencies is summarized by Chandran and Singh[1] and is a better option for curious readers.
References
1. Chandran S, Singh RS. Comparison of various international guidelines for analytical method validation. Pharmazie 2007;62:4-14.
2. David A, Armbruster TP. Limit of Blank, Limit of Detection and Limit of Quantitation. Clin Biochem Rev 2008;29:S49-52.
3. Sanagi MM, Ling SL, Nasir Z, Hermawan D, Ibrahim WA, Abu Naim A. Comparison of Signal-to-noise, Blank Determination, and Linear Regression Methods for the Estimation of Detection and Quantification Limits for Volatile Organic Compounds by Gas Chromatography. J AOAC Int 2009;92:1833-8.
4. Putheti RR, Okigbo RN, Patil SC, Advanapu MS, Leburu R. Method Development and Validations: Characterization of Critical Elements in the Development of Pharmaceuticals. Int J Health Res 2008;1:5-14.
5. European Pharmacopoeia. European Directorate for the Quality of Medicines. Strasbourg; 2007.
6. Ermer J, Miller JH, McB. Method Validation in Pharmaceutical Analysis. KGaA, Weinheim: Wiley-Vch Verlag GmbH and Co.; 2005.
7. United States Pharmacopeia. Validation of compendial methods, TwentySixth Revision, National Formulary, 21st ed. Rockville, MD: The United States Pharmacopeial Convention Inc.; 2003.
8. AOAC International. Method Validation Programs. Peer Verified Programs. Gaithersburg, Maryland, USA; 2002
9. Analytical Procedures and Methods Validation: Chemistry, Manufacturing, and Controls, Federal Register (Notices). 2000;65:776-7.
10. Thompson M, Ellison SL, Wood R. Harmonized guidelines for single laboratory Validation of methods of Analysis. Pure Appl Chem 2002;74: 835-55.
11. International Conference on Harmonization (ICH) of Technical Requirements for the Registration of Pharmaceuticals for Human Use, Validation of analytical procedures: Text and Methodology. ICH-Q2B, Geneva; 1996.
How to cite this article: Shrivastava A, Gupta VB. Methods for the determination of limit of detection and limit of quantitation of the analytical methods. Chron Young Sci 2011;2:21-5.
Source of Support: Nil, Conflict of Interest: None declared

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