 | John Dolan is considered to be one of the world’s top experts in HPLC. He has written more than 300 user-oriented articles on HPLC troubleshooting over the last 30 years, in addition to more than 100 peer-reviewed technical articles on HPLC and related techniques. His three books (co-authored with Lloyd Snyder), Troubleshooting HPLC Systems, Introduction to Modern Liquid Chromatography (3rd edn), and High-Performance Gradient Elution, are standard references on thousands of desks around the world. He has taught HPLC training classes around the world to more than 10,000 students. |
Introduction to LOD and LOQ Estimation Methods
As we saw in HPLC Solutions #125, the International Committee on Harmonization (ICH, 1) lists three ways to determine the limit of detection (LOD) or limit of quantification (LOQ):
- based on visual evaluation
- based on signal-to-noise
- based on the standard deviation of the response and the slope
Recall that a simple definition of the LOD is something like, “I’m sure there is a peak there for my compound, but I cannot tell you how much is there.” For the LOQ, we might say, “I’m sure there is a peak there for my compound, and I can tell you how much is there with this much certainty.”
Limit of Detection Formula Based on Calibration Curve
In HPLC Solutions #125 we looked at the first two techniques. Now let’s look at the third one. I’ve summarized some data in Figure 1 that will be useful for the present discussion.
The ICH indicates that LOD (which they call DL, the detection limit) can be calculated as LOD = 3.3σ / S, and the limit of quantification (which they call QL, the quantitation limit) LOQ = 10σ / S.
How to Calculate LOD and LOQ from Regression Data
Here σ is the standard deviation of the response and S is the slope of the calibration curve. S is estimated from the slope of the calibration curve for the analyte. σ can be determined in one of two ways:
- Based on the standard deviation of the blank, where blank samples are run and the standard deviation is determined; this is equivalent to the standard deviation of the noise (or root-mean-square, RMS, of the noise).
- From the standard deviation of the calibration curve that contains samples in the range of the LOQ; this can be measured as the standard error of the calibration curve or the standard deviation of the y-intercept.
I think the standard error (SE) method is the simplest, because it is easily obtained from a regression analysis of the calibration curve.
Example of LOD and LOQ Calculation Using Excel
In Figure 1, I’ve listed a set of concentrations (ng/mL) and signal (area) for a calibration curve. These data can be analyzed by a linear regression algorithm, such as is included in most data system software. I’ve chosen to use the linear regression data that can be obtained in Microsoft Excel.
On the upper right, I have listed some of the key data presented in the regression report. The 4th item down, the standard error, is the standard deviation about the regression line for the entire data set, which I am using as σ for the ICH technique. The slope of the calibration curve is listed at the bottom, labeled as the concentration coefficient.
Using these numbers, we can calculate :
- LOD = 3.3 x 0.4328 / 1.9303 = = 0.74 ng/mL.
In a similar manner:
- LOQ = 10 x 0.4328 / 1.9303 = 2.2 ng/mL.
I would probably round these up to 1 ng/mL and 2.5-3.0 ng/mL.
Validating the Estimated LOD and LOQ
The values calculated above should be considered estimates of the LOD and LOQ, and must be demonstrated by injecting multiple samples (e.g., n = 6) at the LOD and LOQ concentrations. If the results meet performance requirements, the LOD and LOQ have then been shown to be correct.
Here is where the other LOD and LOQ techniques can be useful. Do the proposed LOD and LOQ appear to be visually reasonable? Does the LOD consistently meet the S/N of 2H/h requirements of 3:1 or 2:1? Does the LOQ consistently meet a S/N or 2H/h of 10:1 and have acceptable precision (e.g., ±15%)?
Comparing ICH Methods for LOD and LOQ
I find that the determination of LOD and LOQ based on the calibration curve to be much more satisfying from a scientific standpoint. The visual and S/N techniques seem too arbitrary to me for anything other than confirming that the regression technique gives reasonable values.
Remember, however, no matter which technique you choose, the ICH requires that as part of the validation process you should analyze a suitable number of samples prepared at or near the LOD and LOQ to demonstrate that the proposed method limits are appropriate.
International Committee on Harmonization, “Validation of Analytical Procedures: Text and Methodology, Q2(R1), Nov. 2005.
Frequently Asked Questions (FAQ)
Q: What is the formula for limit of detection (LOD)?
A: According to ICH Q2(R1), the LOD is calculated as LOD = 3.3 × σ / S, where σ is the standard deviation of the response and S is the slope of the calibration curve.
Q: How do I calculate LOD and LOQ using calibration data?
A: Use linear regression on your calibration curve data to obtain the slope (S) and standard error (σ). Then apply the formulas:
- LOD = 3.3 × σ / S
- LOQ = 10 × σ / S
Q: What's the difference between LOD and LOQ?
A: LOD indicates the lowest concentration detectable but not quantifiable with precision. LOQ is the lowest level that can be quantified with acceptable accuracy and precision.
Q: Can I use software like Excel to calculate LOD and LOQ?
A: Yes. Excel's regression output provides both the slope and standard error, which you can use in the ICH formulas for LOD and LOQ calculation.
Q: Why validate calculated LOD and LOQ values?
A: Regulatory guidelines require that proposed LOD and LOQ values be experimentally confirmed by analyzing replicate samples near those limits.
Related HPLC Solutions articles:
- HPLC Solutions #122 – How to Measure Noise. Part 1
Covers baseline noise measurement techniques that underpin S/N and calibration‑curve approaches. - HPLC Solutions #124 – How to Determine Signal‑to‑Noise Ratio. Part 3
Explains practical methods for evaluating S/N. Useful for readers comparing alternative LOD/LOQ techniques. - HPLC Solutions #125 – Determining LOD and LOQ Visually or by S/N
Introduces visual and signal‑to‑noise methods, contrasted with the calibration‑curve technique in Part 5. - HPLC Solutions #127 – Peak Integration, Part 1: How It Is Done
Discusses accurate peak integration, which affects calibration precision and slope calculations. - HPLC Solutions #86 – Measuring Dwell Volume
Although less directly tied to LOD/LOQ, dwell volume impacts chromatographic consistency and baseline stability, key factors in method validation. - Back‑to‑Basics #6: Resolution
Deepens understanding of chromatographic quality metrics, including resolution calculation, which supports method performance evaluation.