Linearity

[syx]

Dear members,
How do we perform the linearity test?
1. Using dilution of a standard stock solution
2. Using separate weighing for each concentration of solution, and then make a series of 3 or more injections for each of them
3. Using separate weighing for each replication for each concentration, and them make a single injection for each of them

Thanks in advance.

[krickos]

Hi Syx

Could you elaborate a bit?

As I see it, it is not one question. Linearity as area vs. Concentration in for instance validation of a procedure is one thing, compared to a "concordance test" or similar where the responsfactors are compared from different injections of different standard preparations(different or same weighing intervall).

Somewhat simplified, in your case 1 the detector linearity is checked, in case 2-3 the accuracy of the analyst/procedure comes into play.
So it is for valadation, calibration or a combination of both?

[syx]

it is linearity in analytical method development.

in case 1, several concentration of the standard solutions are made from one stock solution and then injected to LC system in same volume.

[krickos]

Hi

I usually have to follow the ICH Q2 guideline as I am in the pharma sector. Below I have pasted some info from that guideline and also included info about range.

Given the information below I would at minimum prepare 5 concentrations covering the intended specification limit, due to range/precision requirements I would at minimum make 3-6 injections at the specification limit and at the upper and lower extremes.

Happy Easter

2. LINEARITY
A linear relationship should be evaluated across the range (see section 3) of the analytical procedure. It may be demonstrated directly on the drug substance (by dilution of a standard stock solution) and/or separate weighings of synthetic mixtures of the drug product components, using the proposed procedure. The latter aspect can be studied during investigation of the range.
Linearity should be evaluated by visual inspection of a plot of signals as a function of analyte concentration or content. If there is a linear relationship, test results should be evaluated by appropriate statistical methods, for example, by calculation of a regression line by the method of least squares. In some cases, to obtain linearity between assays and sample concentrations, the test data may need to be subjected to a mathematical transformation prior to the regression analysis. Data from the regression line itself may be helpful to provide mathematical estimates of the degree of linearity.
The correlation coefficient, y-intercept, slope of the regression line and residual sum of squares should be submitted. A plot of the data should be included. In addition, an analysis of the deviation of the actual data points from the regression line may also be helpful for evaluating linearity.
Some analytical procedures, such as immunoassays, do not demonstrate linearity after any transformation. In this case, the analytical response should be described by an appropriate function of the concentration (amount) of an analyte in a sample.
For the establishment of linearity, a minimum of 5 concentrations is recommended. Other approaches should be justified.


3. RANGE
The specified range is normally derived from linearity studies and depends on the intended application of the procedure. It is established by confirming that the analytical procedure provides an acceptable degree of linearity, accuracy and precision when applied to samples containing amounts of analyte within or at the extremes of the specified range of the analytical procedure.The following minimum specified ranges should be considered:
- for the assay of a drug substance or a finished (drug) product: normally from 80 to 120 percent of the test concentration;
- for content uniformity, covering a minimum of 70 to 130 percent of the test concentration, unless a wider more appropriate range, based on the nature of the dosage form (e.g., metered dose inhalers), is justified;
- for dissolution testing: +/-20 % over the specified range;
e.g., if the specifications for a controlled released product cover a region from 20%, after 1 hour, up to 90%, after 24 hours, the validated range would be 0-110% of the label claim.

- for the determination of an impurity: from the reporting level of an impurity1 to 120% of the specification;
- for impurities known to be unusually potent or to produce toxic or unexpected pharmacological effects, the detection/quantitation limit should be commensurate with the level at which the impurities must be controlled;
Note: for validation of impurity test procedures carried out during development, it may be necessary to consider the range around a suggested (probable) limit.
- if assay and purity are performed together as one test and only a 100% standard is used, linearity should cover the range from the reporting level of the impurities1 to 120% of the assay specification.

[DSP007]

Dear members,
How do we perform the linearity test?
1. Using dilution of a standard stock solution
2. Using separate weighing for each concentration of solution, and then make a series of 3 or more injections for each of them
3. Using separate weighing for each replication for each concentration, and them make a single injection for each of them

Thanks in advance.

Any metod, but "dilution of a standard stock solution" minimizated variants of mistakes, and yields large (big)range (daipazone) of concentations .Therefore, the first method used most often

[syx]

Given the information below I would at minimum prepare 5 concentrations covering the intended specification limit, due to range/precision requirements I would at minimum make 3-6 injections at the specification limit and at the upper and lower extremes.

Happy Easter

What I want to know is how we prepare those 5 concentration solutions. I found a document from VAM, Preparation of Calibration Curves - A Guide to Best Practice, which mentions:

It is also useful to make at least duplicate measurements at each concentration level, particularly at the method validation stage, as it allows the precision of the calibration process to be evaluated at each concentration level. The replicates should ideally be independent - making replicate measurements on the same calibration standards gives only partial information about the calibration variability, as it only covers the precision of the instrument used to make the measurements, and does not include the preparation of the standards.

next page said:

Ideally the standards should be independent, i.e., they should not be prepared from a common stock solution. Any error in the preparation of the stock solution will propagate through the other standards leading to a bias in the calibration.

Based on this document, method 1 is not recommended. It is recommended to use method 3, but for us it is difficult to do since we should replicate the exactly same weighing for each concentration point. We need to know good linearity test practice (with any literature).

Happy Easter for you too...

[HW Mueller]

There are commercial controls avaiable (for instance, BIO-Rad) for a whole lot of substances with which you can check systematic errors.

[juddc]

What I usually like to do, if I can at all get away with it, is to dilute from a stock solution that was prepared directly (i.e X mass weighed into volume Y with a precision of 4 significant figures) and have that stock solution actually be my top level standard. That way I can tell if I diluted correctly and I'd have the top standard that was actually prepared by weighing X into Y. I can't always get away with that, but I try.

[lmh]

Since "independence of standards" has come up, a few comments are needed.

If you are preparing a calibration curve to calibrate a method, then of course independent standards are good, because they remove the possibility that the entire calibration curve is systematically wrong because the initial most concentrated standard is wrong.

However, it is better not to have independent standards in two scenarios. One is linearity-testing (because you really don't want any errors except those caused by lack of linearity. Other deviations from the "correct" value merely make it harder to tell if the points aren't on a straight line). The other is limit-of-detection work, where if you are measuring the s.d. of the calibration curve with a view to calculating a LOD, it is utterly essential that you don't use several independent standards at each level. The point about a LOD is that it is based on the uncertainty of integration caused by noise, not on the uncertainty of preparing a standard. Of course if the standard is wrong by, say, 10%, the LOD will also be wrong by 10%. If however the standards differ by 10%, this will artificially increase the LOD when estimated based on the scatter of measurements.

Another point of clarification. Again, do you really need certified standards to check linearity? If you standard is grossly wrong, say 20%, then the range over which you prove linearity will be shifted by 20%. But if you have measured linearity over a range with a suitable safety margin at each end, and you're never using the method right at its proven extremes, this 20% shift really doesn't matter. Of course if you intend to use certified standards for calibration, you might as well use them from the outset, but the point is: if you validated with ordinary stuff from a chemical catalogue, the chances are your method is good.

And a final (personal) point. I really find this fixation on linearity totally artificial. The guidelines acknowledge the artificiality already in allowing methods that do not transform to straight lines to be used with any appropriate smooth curve. Fitting curves used to be hard, so linearity mattered. Now it isn't, and I'm certain more harm is done by people trying to put straight lines through curved data than is done by people accepting assays that aren't perfectly straight. The final test of an assay is, given an independent standard at any concentration in the range of the assay, does it give the right result? If it does, always, consistently, within an acceptable narrow margin, it doesn't matter in the faintest how the calibration works.

Now I'm going into hiding ready for the linear-lynch-mob...

[DR]

For method qualification, we use a single stock and make dilutions.
We leave the multiple injections of multiple dilutions from multiple stocks to the intermediate precision portion of our formal validations. 3 analysts prepare their own stocks and standard series and make multiple injections at each level, covering most of the bases.

[juddc]

No lynch mob here.

My opinion: As long as you can validate your process and demonstrate that it produces accurate results within whatever parameters you set, what you do and how you handle your data is entirely up to you.

Hey, if we kew what we were doing, we wouldn't call it R&D.

Cheers!

CJ

[krickos]

For method qualification, we use a single stock and make dilutions.
We leave the multiple injections of multiple dilutions from multiple stocks to the intermediate precision portion of our formal validations. 3 analysts prepare their own stocks and standard series and make multiple injections at each level, covering most of the bases.

We do something similar as above ie the intermediate precision (within laboratory variation) covers different stock preparations.


Also I think lmh made some good points. For me checking linearity and accuracy of calibration is two different things. Linearty is typically check early in development/validation while calibration accuracy is check in a later stage when you more or less has a set procedure.

Syx, if you are "worried" nothing stops you from letting 2 analysts check the "case 1" to verify that there is nothing out of the ordinary/expected

[HW Mueller]

Well, since we have knowledge about many substances regarding linearity of detection, a linearity test also shows whether the method is working. One better straighten out his act if it produces a crooked line when everybody else gets a very good straight one, rather than fooling around with fudge math.

[lmh]

oh, absolutely; entirely agreed. It's just that non-random residuals, when present, upset me. They should be investigated and understood rather than ignored on the grounds that R-squared still looks "OK".

[juddc]

oh, absolutely; entirely agreed. It's just that non-random residuals, when present, upset me. They should be investigated and understood rather than ignored on the grounds that R-squared still looks "OK".

Agreed...if you went through the trouble of calculating them, perhaps you would do well to make an efort at understanding what they tell you.