Which is more accurate way to calculate Potency?

Discussions about HPLC, CE, TLC, SFC, and other "liquid phase" separation techniques.

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I found there are two ways to calculate potency when issuing a COA:

1. potency = 100%- total impurities by HPLC-- water content% - residual solvent% - counter ion%

2. potency = (100%- total impurities by HPLC) x (100% - water content% - residual solvent% - counter ion%)

Which way is more accurate to use for issuing a COA? Can anyone tell me where I can find the origins of these two equations?

Thanks~
Apple

The first one; the second formula is not correct.

Two quick comments:

- you may need a term for inorganics: either residue on ignition or a specific metals test, depending on the situation.

- I think the residual organic solvents will usually be too small to have much effect.

neither one is correct, but the second one is closer to the right answer.

yes, a term for inorganic should be added, e.g., ROI%, if the counter ion does not contribute to ROI.

assuming Total Impurities% is deternimed by HPLC-UV, the HPLC method is only seeing organic components with chromophors. of the whole sample, the portion that can be seen by UV is

(100% - water content% - residual solvent% - counter ion% - ROI%)

Out of the portion detected by UV, only the following is the desired compound: (100% - total impuritys by HPLC)

therefore potency = (100% - total impuritys by HPLC) x (100% - water content% - residual solvent% - counter ion% - ROI%)
Regards,

JZT

Just out of curiosity: Why is a purity of a substance called potency here? I know of an activity which is a biological response and is used if the substance is not characterized (so many Units . . . .). Also, why should there be a multiplication factor in this when impurities are obviously additive?

I am not 100% certain why it is called pontency. for a material with 92.5% pontency, it means out of the 100 mg of the material, only 92.5 mg is responsible for the biological activitiy observed.

impurities are additive, if they were calculated based on the same starting point. the percentage of residual solvents, water content, inorganic impurities (ROI) and counter ions are all calculated against the original sample as a whole. while "total impurities by HPLC" is based on the "organic components detectable by HPLC-UV", which is a subportion of the original sample.
Regards,



JZT
This was a very good question. None of the responses were entirely accurate, but by combining them the answer can be revealed. The best answer is that it depends on whether or not the sample you are analyzing is a reference standard or a sample of drug substance. One should see two different equations.

For a reference standard, to determine purity (which is expressed in % usually) necessitates the use of area normalization. Since the HPLC UV detector does not see everything (residual solvents, residue on ignition, counter ion, moisture) this area percent is not on a %w/w basis. However: moisture, ROI, RS, and counter ion are all determined on a %w/w basis. Therefore an equation that just subtracts everything from 100% will not work. The units do not match. See a simplified example below where it is a drug with no counter ion, to simplify the equation:

Assume you have 100 mg reference standard sample. It has 1.0% moisture (%w/w, or 1.0 mg), 0.1% ROI (0.1 mg), and 0.5% RS (0.5 mg). None of the impurities are seen when a solution of the 100 mg is injected onto the HPLC. You are injecting 98.4 mg of visible drug sample. Now let us say you have an organic impurity peak that is 0.2% of the main drug substance peak and assume that the response factor is equivalent to the parent compound. Since this was determined by area normalization, this 0.2% value is of the 98.4 mg. The overall equation you should be using is:

%Purity = (100 - % HPLC impurities)*[(100-%moisture-%ROI-%RS)/100]

In the example above this yields a %purity of 98.2032. You will see that this would give 0.1968 mg for the 0.2% organic impurity value. Once you convert the %organic impurities to mg, you can see that the real value of the purity is 98.2032% via a subtraction equation. For a counter ion example, just subtract this in the numerator where the moisture is. The potency value here is usually expressed in mg/mg, so its answer is 0.982032 mg active/1 mg substance. Notice the difference between potency and purity. Note that using an equation that just subtracts everything would have given an answer of 98.2%: it is close, but since the question was the most accurate way, one can see that there is a difference; An error of -0.00326% in my hypothetical example.

Now, what if you are analyzing a sample? Here, you are comparing the sample to a reference standard which already has a potency determined. Therefore, when you do your calculations to quantify the organic impurity, this potency value goes into the calculation to do so, area normalization is not being used but the sample area compared to the reference standard peak area, and the impurity results is on a %w/w basis. Now the correct equation that is used is just a subtraction:

%Purity = 100-%moisture-%ROI-RS-%organic impurities-%counter ion
I agree with the purity equation posted by jarednathan which addresses HPLC impurities quantitated by area normalization.

But, I am wondering about HPLC impurities that may be quantitated by %w/w using a standard of their own. Would %w/w HPLC impurities be subtracted directly from 100% like ROI, etc? I think the answer is 'yes', but I have never seen anyone do it that way.
If I am understanding your question right, I believe the answer is yes. As long as you have a number that is on a %w/w basis, you can subtract from 100. For example, I have developed a method before that was able to separate acetone, so I used HPLC to quantitate the acetone value instead of GC. I used an external standard and then calculated the %w/w. However, if you are doing area normalization for the rest of the chromatogram, you obviosly do not use this peak area in any of the area norm calculations. Another example is if you had a know refernece material for one of the organic impurities in the HPLC chromatogram. Now that is just like the an assay type calculation I stated before, and you get a %w/w value from the reference standard/material comparison calculation. Does this make sense? Perhaps if you give an exact example we can go through the calculation together.
Yes, I think you understood my intent. The situation I had in mind is one where a reference material is available for a specific HPLC impurity. An example would be quantitating a starting material as an HPLC impurity in a batch of API that is being characterized as a Reference Standard.

In your example above, say Impurity A is an API starting material and and 0.10% is carried over into the final batch. And this batch of API is being characterized as a Reference Standard. Impurity A can be quantitated on a %w/w basis, since a reference material exists.

So, the 0.10%w/w Impurity A would be subtracted from 100% along with the moisture, etc. So, in your example, 100mg reference standard sample would have 98.3mg of the actual drug. Therefore, the 0.2% area% of unknown HPLC impurities would be of the 98.3mg. And the Impurity A area should be excluded from the total area, since in this example, Impurity A is quantitated in the same HPLC run as the unknown impurities.
Yes, in your example where you are actually analyzing a reference standard, the calculation technique is appropriate. Note that if it was a sample, you would be subtracting it from 100 anyway.

The question I have for you, however, it why are you using the reference material for quantitation? If you have that material it would be easy enough to figure out the response factor for the impurity. Then you wouldn't have to make that solution (or synthesize the impurity, recertify it, ect) anymore or waste time making injections of it. It is only necessary to use reference materials ,after this determination has been made, when you need it to establish system suitability. For example, the impurity is a critical pair, so you need the reference material to ensure that the chromatograhpy system is separating this pair correctly. I was just wondering out of curiosity....
I agree with you about using response factors whenever possible.
I chose my example because I was trying to keep the situation straightforward.

The actual situation is where there are two HPLC purity methods. One has unknowns by area % and two specific impurities using RRFs to get %w/w of those. The second method is for a specific impurity. There is a Ref Std for that impurity and that result would be %w/w.

In my case, I am looking at a Reference Standard Characterization document from an API supplier. They combine all the known (%w/w) and unknown (area%) impurities together into one total. Their purity equation follows the example as if all impurities were unknowns by area%. So, they are almost correct.

Mathematically, though, due to rounding, the results are the same for the correct case and "almost correct" case.
And in the real world, it is difficult to justify (certainly to management) making too many waves about a purist argument that has little to no impact - even though we would be correct.
I understand that many times rounding will end up giving you the same number. However, if the calculation is wrong, it is wrong. This refelcts the quality aspect in a companies science. I have never encountered an instance where management would not want it corrected, and I have been in the "real world" for some years. They would not let it hold up a batch release at the time, when project timelines are at stake, but they would definately want it addressed to be correct the next time, in my humble opinion. Additionally, as scientists/former scientists, management loves to get involved with these technical subjects. It gets them away for the normal boring boss things and gets them to use thir minds again.

When it is a supplier it is even more important to raise the issue. First of all, you are the customer. They must address reasonable concerns in scientific accuracy. The question could always come up...if they get this simple thing wrong, what else do they do wrong? Secondly, it is your company that is ultimately responsible for all API characteristics. Thirdly, it is always good to let suppliers know that you look at everthing they are doing. It shows pride and your companies strive for excellence. This is also good for your own customers to know. You pay attention to the smallest details. They ultimately use your products and their safety is your number one concern. If you had a manager that was OK to just let it go, this is definately an issue you would bring to their boss. In pharmaceuticals, we are all trained to do this. Ask your quality department if they are satisfied that something is not scientifically accurate in a document used to release a drug supply...I would hate to be audited by the FDA and have them discover it
I share your opinion and I do feel it should be addressed and not be allowed to delay anything. In this current case, if the API supplier does not change their documentation, then for me to have a memo identifying the issue and showing the same result is probably where this will go.

But, if the result was off by 0.1%, say from 99.4% to 99.3%, I am not sure what the outcome would be. The ideal way would be to recalculate everything done with the incorrect potency. My company has not used the standard for very long, so it wouldn't be much work for us to correct all results. But, if a year or more of data had to be addressed, I wouldn't bet that all senior management would concede the time to correct it. I think a more likely outcome would be some overall review and statement about the 0.1% impact, and a commitment to use the correct value going forward. Thus, accepting a slight inaccuracy in the dta.
The FDA would be content with that. They are always happy when you show improvement. I could also foresee another possibility why a company wpould say, let's do this only moving forward....Imagine if you used an example of the difference between 98.0 and 97.9%, and the specificaiton was 98.0%...OOS would not be fun. Then again, that is why something so small makes that much of a difference. Important to do right the first time. Thank you much for this conversation :)
It was fun. Thanks.
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