Concept of Limit of Detection (LOD)

The limit of detection for trace chemical analysis is always a controversial subject. It is worth discussing.

1. https://consultglp.com 17 September 2020 @ 8.00PM * Virtual Zoom Meeting Concepts of limit of detection (LOD) in chemical analysis by Yeoh Guan Huah GLP Consulting, Singapore 1

2. Learning outcome At the end of this presentation, the participants will : have acquired a basic understanding of the terminologies and concepts of Limit of Detection (LOD) appreciate the inferential statistical reasoning behind these be able to apply various LOD estimation methods depending on the situations faced 2

3. Introduction The limit of detection (LOD) is one of the most controversial subjects in analytical chemistry In trace analysis, it is important during metho d validation process to know what the lowest concentration of an analyte value is which can be confidently detected (e.g. with 95% confidence) by the analytical method. This involves the use of statistical tools to minimize the risk of claiming the presence of a contaminant in a sample analysed when it is actually not. Statistically, it is a Type I error (False Positive). The evaluation of LOD is particularly important for analysis of toxic and pollutant residues in food, air, household wares, soil, water, etc. 3

4. Detection limit and method sensitivity The LOD is often confused with the method sensitivity. In fact, the sensitivity of a test method is the capability of the method to discriminate small differences in concentration or mass of the analyte. For example, the slope of a calibration curve can show the sensitivity of the method. The LOD of an analytical procedure is generally defined as the lowest amount of an analyte that can be reliably detected with a given analytical method, but not necessary quantitated as an exact value. 4

5. LOD is a statistical estimate of concentration T he LOD would be the lowest concentration obtained from the measurement of a sample (containing the component) that we would be able to distinguish from the concentration obtained from the measurement of a reagent blank sample. Reagent Blank : A b lank incorporates all reagents used in the method and is subjected to all sample processing operations. It serves to verify that reagents are analyte free and the equipment used does not interfere with or affect the analytical signal. 5

6. Different official definitions of detection limit ISO 11843-1 (Capability of Detection) Part 1: Terms and Definitions calls the limit of detection as the minimum detectable value of the net state variable , which for chemistry translates as ‘ minimum detectable net concentration ’ VIM 4.18 (JCGM 200:2012) : The limit of detection (LOD) is defined in terms of a measured quantity value which is obtained by a given measurement procedure, for which the probability of falsely claiming the absence of a component in a material is β (Type II error), given a probability α (Type I error) of falsely claiming its presence IUPAC instead refers it as a true quantity value (VIM 2.11) which means true value of a quantity. 6

7. RSC AMC’s definition for Detection Limit (LOD) The Analytical Method Committee of Royal Society of Chemistry states that: “ the concentration or amount corresponding to the measurement level 3  B units above the value for zero analyte, the  B being the standard deviation of responses of reagent blank, which is a sample containing zero concentration of analyte .” 7 i.e., Use (   Mean signal measurement of reagent blank

8. Three basic concepts in the study of LOD Where measurements are made at low concentrations, there are three general concepts to consider. (1) T o establish a value of the result which is considered to indicate an analyte level that is significantly different from zero. Often some action is required at this level, such as declaring a material contaminated. This level is known as the ‘ critical value ’ or ‘ decision limit ’ 8

9. Three basic concepts in the study of LOD (2) It is important to know the lowest concentration of the analyte that can be detected by the method at a specified level of confidence (normally at 95% confidence). That is, at what true concentration will we confidently exceed the critical value described above? For this we use t erms such as ‘ limit of detection ’ ( LOD ), ‘ minimum detectable value ’, or ‘ detection limit ’. 9

10. Three basic concepts in the study of LOD (3) It is also important to establish the lowest level at which the performance in declaring the presence of an analyte is acceptable to the data user or fit for purpose . This third concept is usually referred to as the limit of quantification ( LOQ ) . Other terms are : ' quantification limit ’, ‘ quantitation limit ’, ‘ limit of quantitation ’, ‘ limit of determination ’, ‘ reporting limit ’, ‘ limit of reporting (LOR) ’ and ‘ application limit ’. 10 In method validation, it is the LOD and LOQ that are most commonly determined.

11. Relationship between decision limit and limit of detection (LOD) 11

12. Relationship between decision limit and limit of detection (LOD) 12 Analysis of blank solution several times to get a mean value of y o and std deviation  By taking  = 0.05 z α

13. Relationship between decision limit and limit of detection (LOD) 13 Run a solution with concentration to give y dec response several times, there is a 50% chance failing to detect the analyte

14. Relationship between decision limit and limit of detection (LOD) 14 y det = y o + 2(1.645) s y y det = y o + 3.3s y

15. One-Tailed 10% 5% 2.5% 1% 0.5% Two-Tailed 20% 10% 5% 2% 1% z -critical value 1.282 1.645 1.960 2.326 2.576 Normal Probability Distribution Table 15 Excel Functions for z-values =NORM.INV(0.05,0,1) -1.6449 =NORM.INV(0.95,0,1) 1.6449

16. Relationship between decision limit and limit of detection (LOD) To use y det = y o + 3.3s y , the number of replicates, n > 30 . For smaller n , the Student’s t -factor is to be used instead of z = 1.645 for normal probability distribution at error α = 0.05 (or 95% confidence) For example, If the number of replicates , n = 8 The degree of freedom df = 8-1 = 7 Therefore, at error α = 0.05, t -value = 1.895 Use : detected signal y det = y o + 2(1.895) s y = y o + 3.8s y 16

17. Student’s t-Distribution Table One-Tailed 10% 5% 2.5% 1% 0.5% Two-Tailed 20% 10% 5% 2% 1% Deg of Freedom           1 3.078 6.314 12.71 31.82 63.66 2 1.886 2.920 4.303 6.965 9.925 3 1.638 2.353 3.182 4.541 5.841 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 17 Excel T-Functions at DF = 7 =T.INV(0.05,7) -1.8946 =T.INV(0.95,7) 1.8946     =T.INV.2T(0.1,7) 1.8946

18. It is important to distinguish between: Instrument detection limit (IDL) and Method detection limit (MDL) 18

19. Differences between IDL and MDL The instrument detection limit (IDL) can be based on the analysis of a sample, often a reagent blank sample, presented directly to the instrument (i.e. omitting any sample preparation steps ) to record instrument responses several times, or on the signal-to-noise (S/N) ratio in, e.g. a chromatogram. IDL can also be determined based on instrument response error at estimated zero concentration, obtained from a series of spiked reagent blank solutions at very low concentrations (near to expected LOD) . To obtain a method detection limit (MDL) , the LOD must be based on the analysis of samples that have been taken through the whole measurement procedure using results calculated with the same equation as for the test samples. 19

20. Suitable samples for estimating LOD & LOQ Preferably use either A) blank samples – matrices containing no detectable analyte, or B) test samples with concentrations of analyte close to or below the expected LOD (usually spiked with known amounts in sample matrix examined) Blank samples work well for spectrophotometry and atomic spectroscopy because their signals are measurable 20

21. AMC method for LOD As per AMC recommendations, we can use ( by running a reage nt blank on a spectrometric instrument several times Then, run a series of standard solutions with very low concentrations to obtain a linear calibration curve by the least square method to obtain y = a + bx Read the x -value when y = the IDL signal value   21

22. LOD by Signal-to-noise (S/N) ratio method This method is applied to analytical procedures which exhibit baseline noise. For techniques like chromatography which rely on detecting a peak above the noise, the signal-to-noise ratio is made by comparing measured signals from samples with known low concentrations of analyte with those of blank samples and establishing the minimum concentration at which the analyte can be reliably detected. A signal-to-noise ratio between 3 or 2:1 is generally considered acceptable for estimating the detection limit. 22 Noise baseline LOD

23. Determining LOD by linear calibration model Reference : ISO 11843-2:2000 Capability of detection Part 2: Methodology in the linear calibration case If the reagent blank in the prepared solution does not give any significant noise signals in instrument such as LC/MS or GC/MS, one can prepare and run a series of 5 or 6 spiked reagent blank solutions with very low concentrations of standard analyte of interest. Determine its linearity with a best fit (least square) linear equation of y = a + bx . When x = o for zero analyte, the y o is the response of the instrument. 23

24. X Y ε ε y(obs) y(calc) [(y(calculated) – y(observed)] is defined as ‘residual’ or ‘error ’ 24

25. Determining LOD by linear calibration model Use the equation to determine y (calc) ’s at the various standard concentrations. The experimental values are y( obs ) ’s. [(y(calc) – y( obs )] is defined as ‘residual’ or ‘error ε ’ ∑[(y(calc) – y( obs )] = 0 , and √ ∑[(y(calc) – y( obs )] 2 /(n-2) = SE y * Calculate Standard Error: SE y 25

26. Determining LOD by linear calibration model Use equation: y(detection) = y o + 3* SE y to determine the instrument detectable signal at zero concentration. Then, substitute y(detection) into the equation y = a + bx to determine the instrument detection limit , x o for the analyte concerned . 26

27. Determining LOD by linear calibration model Response y y det = y B + 3  B  B = SE(y) x o Analytical concentration x 27

28. Estimation of LOQ The limit of quantitation (LOQ) is the smallest concentration of analyte that can be determined with an acceptable level of uncertainty to the data user or fit for purpose By most convention, m ultiply LOD with a multiplying factor k The value for the multiplier k is usually 10 as suggested by IUPAC, but other values such as 5 or 6 are commonly used (based on ‘fitness for purpose’ criteria). 28

29. Issues in determining LOD and LOQ (1) Preferably use reagent blanks or samples with analyte close to the expected LOD (2) For methods with a scope covering very different matrices, it may be necessary to determine the LOD for each matrix separately (3) Limits are often at the mercy of instrument performance, which can be checked by use of pure standard compounds. Different analytes in a mixture have different instrumental responses. (4) To ensure representative replication, the standard deviation estimated is best to be a intermediate precision (i.e. carried out by different analysts on different periods within the same laboratory) 29

30. Issues in determining LOD and LOQ (5) The number of replicates for determining detection limit is suggested by Eurachem to be 6-15. 10 replicates are often recommended. (6) Allowance for averaging : For example : Let the standard deviation for calculating detection limit during method validation be s y In routine experiment, the method does not require the test result to make a blank correction and the test is done by duplicate ( n = 2), then, Upon averaging the two test results of the sample, the standard deviation used for detection limit calculation is s o ’ = s o / SQRT (2) 30

31. Issues in determining LOD and LOQ What would you do if you have to make a blank correction as specified in the analytical method? Example: Test sample analyzed once ( n t = 1) Results corrected by single blank result ( n b = 1) The concentration obtained from test sample is corrected by subtracting the blank value, and for corrected standard deviation, use equation =   31

32. Conclusion The limit of detection of an analytical method tells us how low a concentration can be said to be measured confidently. No worry for LOD in measurements made in percentage level. When an analytical method is used for trace or ultra-trace analysis, and in the cases where the legislation requires the absence of certain regulated components or contaminants, the LOD has to be estimated in a rigorous way. The estimation of LOD must include the whole analytical process and consider the probabilities of false positive ( α ) and false negative ( β ) decisions. 32

33. References Eurachem Guide The Fitness for Purpose of Analytical Method (2 nd edition 2014) AOAC Guidelines for Single Laboratory Validation of Chemical Methods for Dietary Supplements and Botanicals (2002) US FDA Guidelines for the Validation of Chemical Methods for the FDDA FVM Program (April 2015) ICH Harmonised Tripartite Guideline for Validation of Analytical Procedures: Text and Methodology Q2(R1) (2005) 33