LOD and LOC can be calculated from the calibration plot. One of the ways to do it is:
LOD = 3 SD(intercept)/S
LOC = 10 SD(intercept)/S
Where SD is the standard deviation of the intercept and S is the slope.
However, I have seen that standard error (SE) is often used instead of SD. But, SE is not the same that SD:
SD = SE*(N)^1/2
Thus, LOD and LOC from SE should be less than LOD and LOC from SD. However, I used SE for my work because I noticed that when I used SD, LOD and LOC were very high.
What do you think about using SE and SD for LOD and LOC estimation?
SD estimates the variability of the measurement (mean) for a single sample/population.
SE estimates the variability of the measurement (mean) when repeating different samples within the same total population.
As such, and I'm using the exact same LOD/LOQ methodology as you are, my philosophy so far is to use :
- SD when I have run only one "sample" (min five calibration curves, generally) when developing the analytical method : I do my calibrations only when developing.
- SE when I have developed the method and used it for some time : compute SDs for all cumulated calibration intercepts up to now and divide by fixed N (number of accumulated calibrations you chose when developing, e.g. 5 or 10).
Thus, SD provides a very conservative estimation for LOD/LOQ at the start of the project and SE will provide a better estimation when the method has become routiine.
It is important to note that the LOD and LOC are values that are often misused and mistreated. The LOD and LOC are defined by the signal to noise ratio. Unless the sample response curves are run from detectable to undetectable levels, the LOD and LOC are extrapolations to a level where otherwise negligible effects, such as loss of sample due to surface adsorption during sample handling become major drivers. Many non-ideal behaviors become significant at very low concentrations, and most of these behaviors are not well understood and hard to control. I have not even mentioned the other factor in the LOD or LOC yet, which is the noise level. In a typical measurement system, there are numerous sources of noise that are stochastic. It is possible to quantify the noise at a specific time, but it is not possible to truly predict the noise.
LOD and LOC are both inherently instantaneous values due to their dynamic behavior, so both of these values should be treated as a rough estimate rather than a discrete value. The uncertainty of the LOD and LOC are both very limited even for a specific dataset collected at one time.
Hi Javier,
The IUPAC publications remain the fundation stones regarding LOD and LOQ.
http://publications.iupac.org/pac/1997/pdf/6902x0297.pdf
but agree with very much Pierre Caulet approach.
We uses SE for determination of LOD/LOQ by which we get most practical LOD/LOQ values which are easy to establish.
Dear colleagues,
Let me draw attention to some points that were left out in the above discussion.
1. The term standard error itself is objectionable and should be avoided. This term is not explicitly defined in statistical terminology and is often used synonymously for standard deviation. The ISO 3534-1: 2006 Statistics — Vocabulary and symbols — Part 1 (Entry 1.24, Note 2) states that “Standard error can be viewed as an abbreviation for the expression “standard deviation of an estimator”. Commonly, in practice, standard error is implicitly referring to the standard deviation of the sample mean”. If so, why is this term even needed? We know very well that there are two common measures of dispersion (apart from variance itself): standard deviation, s, and standard deviation of the mean, s/(n)^1/2, where n is the number of observations. As applied to calibration statistics, if we have N calibrations performed near zero, each characterized by the residual standard deviation, we can calculate the pooled standard deviation (using corresponding degrees of freedom) and then divide it by N^1/2, thus providing the standard deviation of the mean (of N calibrations). There is no need at all to use the term standard error, which only leads to confusion in terminology.
2. It is surprising to see the expression for LOD (and equally for LOQ) in the form of LOD = 3.3 SD(intercept)/s and the wording “standard error of the intercept”) in the title of the discussion. In actual fact, in the regression approach to LOD, the blank signal standard deviation used in the classical approach is replaced by the regression statistic, the residual standard deviation around the regression line, not the standard deviation of the intercept of the line. As for the intercept itself, this is considered as a point of reference similarly to the mean blank signal in the classical approach. Generally, this reference point should be added to the “3s” value in the expression for LOD unless blank corrected signals are used in the calculation, but in practice, this term is usually omitted.
As I also wrote a blog article about that topic and received a lot questions regarding the SD vs. SE topic, I added an update today. Please check: https://mpl.loesungsfabrik.de/en/english-blog/method-validation/calibration-line-procedure
Janet Thode thank you very much for taking this discussion into account for your interesting and very useful article.
- Badges
- Science topic
- Similar topics
- Analytical Chemistry
- Extraction