Linear Regression in Excel, Detection Limits, and ICH Guidelines.
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- เผยแพร่เมื่อ 5 ต.ค. 2024
- Use of Regression Analysis Tool in Excel to find out the Standard Error of the Y-Intercept. The Standard Error of the Y-Intercept may be use for estimation of Limit of Quantitation (LOQ) and Limit of Detection (LOD) as per ICH Guidelines.
The Standard Error of a regression is a measure of its variability. It can be used in a similar manner to standard deviation, allowing for prediction intervals.
The "Standard Error" of the y-intercept in regression is indeed the "Standard Deviation" of the y-intercept, is a measure of the dispersion or sampling distribution in the coefficients.
one big issue: standard deviation (sigma) is not standard error (SE)! You must correct example with equation sigma = SE* sqrt(N), where N is observations.
In the first table (above ANOVA table) we can see the Standard Error which can be calculated by STEYX function. Then LOD is 3.3*STEYX/Slope and LOQ= 10*STEYX/Slope. In ICH procedure is also written Standard deviation of the Y-Intercept and not Standard Error of the Y-Intercept (which was used here). Another way is to calculate the residual standard deviation of the regression line. There is a column of Residuals (next to Predicted Y). If you calculate the standard deviation of the residuals, you can calculate the LOD and LOQ as well.
Hi Mr. Carlos,
Thank you very much for your demonstration.
I was looking for presentation on Analytical Method Validation and came across your video. It helped me recollect all the calculation required for LOD and LOQ. I am into regulatory Affairs field now and its been 6 years I switched from Analytical Method Development department.
Please keep posting such videos. Thanks again.
Regards,
Sanjay
Guys remember from HS statistics that the standard error (SE) is related to the standard deviation (SD) and total number of samples (N) by the following
SE = SD / sqrt(N)
Therefore we can calculate the SD by multiplying the following
SD = SE*sqrt(N)
so the determination of LOQ and LOD in the video is not valid then?
@@a.h.ismail8691 exactly
@@rj9224 Are you sure?
@@tizianodigiulio3534 yes
@@rj9224 do you know how data processing can change when axis values are transformed? That is, if I use the concentration log for the analyte (log [analyte]) or the reciprocal (1 / [analyte]), how is the LOD calculated? can you help me? Or can you tell me about the literature?
Thank you! I've been struggling with this for hours!
Muchas gracias por tu explicación, me ha sido de gran ayuda.
Excuse me, I'm a postgraduate student right now. It's really useful to watch your video to understand the calculation process. But I still have some questions, may I ask you questions? yeah, there are three ways to calculate LOD/LOQ, but I do not really understand the first one based on the visual evaluation, and I think the most convenient one is that S/N =3/1 or S/N=10/1, so why should we still use the other two ones? I appreciate your reply, thank you so much.
Thank you for the straightforward explanation.
Thank you! It was very helpful
Simple and quick!
Peak areas are dependent on concentration. So the concentration needs to be on the X-axis.
Thank you so much. It really helped me :)
Thank you so much. It helped me a lot.
Hello Carlos,
What's the "residual standard deviation of regression line" in the output of linear regression? Why you use Standard Deviation" of the y-intercept?
Very nice explanation, thank you
thank you !! pretty easy to follow
Hi Carlos,
Why don't you use the Standard Error of the Regression (aka residual standard deviation of a regression line, uncertainty of regression, S est, SD of errors of prediction) of in this case 85555.27031 to calculate the LOD and LOQ?
''7.3.2 Based on the calibration curve'' states that you can also use this residual standard deviation of a regression line. But why do you choose to use the standard deviation of y-intercepts of regression lines?
Why are we able to choose our SD anyway.. this will influence our LOD and LOQ outcome, right?
Hope you can help!
I'm still wondering on what basis a particular standard deviation is chosen... can you help me with that?
Hello, thank you for your gob it sample and clear in 2020 i needed and see it therfore it's useful.. i have a question please what the best analysis technique to gain 0.999 in linearity calculation
Thanks. Nice video for data analysis
Please Tell how to manually calculate the standard error of the coefficients in multiple regression.
The Standard Error of a regression is a measure of its variability. It can be used in a similar manner to standard deviation, allowing for prediction intervals.
The "Standard Error" of the y-intercept in regression is indeed the "Standard Deviation" of the y-intercept, is a measure of the dispersion or sampling distribution in the coefficients.
Surely it isn't the standard error, but rather the standard deviation that should be used to work out LOD and LOQ here?
The Standard Error of a regression is a measure of its variability. It can be used in a similar manner to standard deviation, allowing for prediction intervals.
The "Standard Error" of the y-intercept in regression is indeed the "Standard Deviation" of the y-intercept, is a measure of the dispersion or sampling distribution in the coefficients.
Last thing i heard the "Standard Deviation of the y-intercept" = standard error of the y-intercept x √N
Yes, indeed, that's the relationship between Standard Error and Standard Deviation of the Mean.
SE = s / N^0.5
However, the standard error of a sample mean has nothing to do with the standard errors of the slope or the intercept in a Linear Regression, they are different computations.
The standard error of the sampling distribution of an estimator (e.g. a slope coefficient or intercept) is the standard deviation.
Thanks a lot man!!!
Many calibration curves use weighting ie 1/x. This is vert relevant with a broad measuring range. Could you repeat your calculation using weights
thanks a lot !!
Hi Carlos,
What is the difference between the Standard Error in the Regression Statistics Table (8555.27) and the one used in the video (33986.922?
Is there also a way to calculate the The residual standard deviation?
Thank you
very helpful , thank youuu
Good video, but how do you take into account the baseline noise from the chromatograph?
+Martin Jones The baseline noise of the chromatogram is just one of many aspects that will affect the LOD and LOQ of the particular analytical technique. Keep in mind the actual concepts of LOD and LOQ. For instance, LOQ is the level at which the analyte of interest can be quantitated with acceptable accuracy and precision. Now, "acceptable" is a flexible criteria, depending upon the purpose of the analytical method. So, in some instances, one could use the simplistic approach of Signal-to-Noise ratio (SN) assessment. You know, LOQ = 10 x SN and LOD = 3 x SN. This may be sufficient as long as the signals at those levels exhibit adequate precision and accuracy behavior.
However, one may find instances where even with appropriate Signal-to-Noise ratio estimation, the calculated levels for LOD and LOQ exhibit poor precision and accuracy. That's often observed in LCMSMS applications. A very sensitive detection technique and in many cases almost noiseless chromatograms. Then the source of the "noise" is found somewhere else, beyond just the baseline noise. The analysis of the linearity data, including multiple injections at each level, is a more statistical approach, where all factors that contributes to the quality of the signal for LOQ or LOD purposes are considered. The accuracy and precision at the LOQ and LOD levels is influenced by all sort of instrument performance variations (e.g. autosampler precision, detector response variations, etc.).
So, that's how it works. Baseline noise is not the only parameter to determine the LOQ/LOD levels, sometimes is actually useless.
Thanks a lot
Hello, I have a question.
Instead of signal values like the analyte peak area you used in your example, could I use another form of a variable for y axis like processed signal values? I am talking about sensitivity (I-Ia)/Ia versus concentration variable for X axis.
Thank you!
Thank you man.
What's the unit for all these calculations?
Thanks for my chimometrics works ;)
Dude thanks a lot.
Thank you... It was very helpful :)
hi, so few question, how we can calculate Cons=concentration level of detection and also LOD will stiil be the same if we have blank?
Thank you so much for that!
I learn lowest value of my calibration curve range is LOQ, but I don't know how to calculate highest value in calibration curve range. Can you help me for this one? thank you very much!
Inject more ppm upto what level u got response correctly like linear. That is higher value
thank you
plz
who can i calculate Standard Error and slop for x-variable 2,3
good vid
Hello All,
Please, anyone, explain to me how to find binding constant from UV vis titration experiment using excel or manual calculation
Best
Standard error is NOT the same as standard deviation
The wrong calculation, Standard error is not equal to the standard deviation, You are showing standard deviation that needs to calculate the LOQ or LOD but you are using the standard error during calculation.