Why google is the best search engine out there? In my opinion, it is due to its capability of capturing the least amount of words provided by the user and comes up with the closest answer to your search. The same goes with analytical methods, one of the critical performance characteristics to identify the capability of the method is how much the method can detect and quantify reliably i.e. (with high repeatability and accuracy).
Limit of Blank (LOB), Limit of Detection (LOD), and Limit of Quantitation (LOQ) they’re like three legs of the stool if you short-change any one of them the whole stool is going to fall down. They are generally used to describe the smallest concentration of an analyte that can be detected by the analytical method. An analogy of google search engine helps to distinguish between these terms. LOB is analogous to no typed words in the search bar, just the google search web page; LOD is like typing few words with no key identifiers not enough to get the accurate search results. With the LOQ, the key identifying words are enough to get the correct search results.
Some definitions:
Limit of Detection LoD (Minimum detection limit, Minimum detectable value, EU directive CCa): is defined as the lowest conc. of analyte that can be detected in the test sample with a repeatability and precision.
Limit of Quantitation LoQ (Minimum reporting limit/application limit): is the lowest conc. of analyte that can be quantified in the test sample with accepted accuracy.
There’re several approaches for determining LOD, and LOQ are possible according to the ICH Q2:
- Based on visual evaluation
- Based on the standard deviation of the response and the Slope
- Based on the signal-to-noise ratio
- Based on standard deviation of the blank (not required by ICH)
In this blog we are going to discuss the application of the last 3.
Determination based on standard deviation of the response of the calibration curve and the slope:
The standard deviation of the response curve is a measure of the variability in the instrument response at a given concentration of analyte. It is calculated by analyzing a series of replicate measurements of the instrument response at a fixed concentration of the analyte. The standard deviation of the response is typically used to estimate the noise level of the analytical method and is an important parameter for calculating the limit of detection and quantitation.
On the other hand, the slope of the response curve is a measure of the change in the instrument response with respect to changes in the concentration of the analyte. It is typically determined by constructing a calibration curve using a series of standard solutions of the analyte and measuring the corresponding instrument response. The slope is an important for determining the sensitivity of the analytical method, and is used to calculate the limit of detection and quantitation as well as to quantify the amount of analyte in unknown samples.
In the following example, I will demonstrate how to generate the slope and standard deviation data using a excel spreadsheet. By understanding the underlying concepts, you can effectively apply these methods to your own data sets. Moreover, proper interpretation of the results could lead to valuable insights and pave the way for more advanced statistical analysis.
Determination based on standard deviation of the blank:
Determining LoD and LoQ using the standard deviation of the blank is one of the common approach that are widely recognized. The blank is a measurement of the instrument response in the absence of any analyte, and it provides an estimate of the background noise level of the analytical method.
Figure 1: Regression Analysis Results
The regression function provides three outputs: regression statistics, ANOVA, and coefficients. Regression statistics: provides info on how well the regression equation fits the data. ANOVA: studies the level of variability within the regression model.Coefficient’s table: provides the slope of the curve and the standard deviation of the Y-intercept.
Determination based on the signal to noise ratio: ICH Q2 (R1) doc (1)
In metrology, signal in form of numbers is the language of the instrument where it communicates with us data to extract information. For instance, in the field of nutraceuticals, the main focus is not always the detection and quantification of main compounds, rather residuals, contaminants, heavy metal products in trace levels.
Why SNR is important data parameter?
Contextually, noise is a random small signal that provides information on the heath of the detector, pumping system, and contaminated reagents. It is a key component in determining limit of detection. Conceptually, If the signal of the analyte is smaller than the baseline noise of the analytical method, the analyte is not recognized. However, trying to determine SNR visually could be less accurate as it involves analyst bias. Examine the figure below.
Figure 2: Zoomed in SNR
How to determine LOD / LOQ using the SNR?
Print a copy of the chromatogram and perform a vertical measurement of the baseline noise (N = h), next, measure the signal (S = H) from the middle of the baseline noise vertically to the top of the peak of interest. So, measurements are h= 50 and H = 300.According to the USP formula: S/N = 2H/h, therefore, S/N = [(2*300
) / 50] = 12.
Figure 3: SNR – Blank Vs. Sample
Takeaways:
- LOD and LOQ determination based on the statistical performance of the calibration curve is instrumental from a scientific standpoint.
- Visual evaluation to determine LOD and LOQ is not as accurate as it involves analyst bias.
- SNR technique is better to be used to confirm that the regression technique gives reasonable values.
- ICH requires analyzing minimum of 6 determinations at the LOD and LOQ.
- Acceptable precision between samples of +/- 15%.
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