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Jul 04

What is Relative Potency?

Relative potency is a term used in bioassay to refer to the ability of a test sample, of unknown potency, to produce the desired response compared to a reference sample, when tested under the same conditions.


This first blog will deal with relative potency, a concept often misunderstood by those new to the field. The official guidance can be found in the EurPh 8th edition and the USP bioassay guidance.

With small molecule chemical drugs the potency is fairly well related to how much drug is in the preparation, and that can be measured with good accuracy. With a biologic, the potency is related not so much to the amount of stuff in the preparation, but to the biological activity of the preparation, and that has to be measured in a biological system (a bioassay) that is itself variable. So, to quote the United States Pharmacopeia. “Because of the inherent variability in biological test systems…an absolute measure of potency is more variable than a measure of potency relative to a standard. “

This was all described in 1964 by Finney:

Relative Potency refers to “the ratio of two equally effective doses is an estimate of the potency of the test preparation (T) relative to that of the standard (S).” (Finney 1964)

Relative Potency=DoseStandard sample / DoseTest sample  when the 2 doses produce the same effect.

Mathematically this is the same as Log(Relative Potency)= Log(Dosestd) – Log(Dosetest)

Note that the relative potency is NOT dose specific. It is not quoted as the potency for a certain effect, but just as a ratio when the two samples produce the same effect (of any magnitude). This assumes that the standard and test sample have the same biologically active component, and so behave similarly across the whole range of doses. I.e., one can be considered as a simple dilution of the other. (This is one of the issues with biosimilars, which are of course, not usually identical in their biological activity across all doses. This will be the subject of a later advanced content blog.)

Experimental determination of relative potency

It would of course be possible to define an absolute level of response, and then titrate the standard and test samples to achieve that level of response and measure the dose of each required. However, as noted by Finney, this has many practical problems particularly if you are examining the effect of, say, an insecticide on aphids. In addition, a measure of relative potency at a single dose does not allow any assessment of the behaviour / potency of the test sample at other doses. Perhaps the test sample has degraded and is no longer the same biologically.

So in practice a range of doses are tested, and results plotted as Log(dose) against response. From the equation above, Log(Relative Potency) = Log(Dosestd) – Log(Dosetest) = the horizontal shift along the log(dose) axis:

Relative Potency Curve

 

Δ = Log (Dosestd) – Log(Dosetest)

= Log(Relative Potency)

 

 

 

 

 

Notice that the Log(Relative Potency) horizontal shift is the same at all doses. Two lines that are the same distance apart (when measured in a defined way) are said to be parallel. If the test item did not have the same biologically active component as the standard the relative potency would vary over the dose range:

Dose Response Curve

The lines are no longer parallel.
This explains the importance given to parallelism testing by the regulatory authorities – it gives confidence that the test item is acting as a dilution of the reference, ie it does contain the same biologically active components.

Mathematically testing for parallelism will be the subject of blog 3. But before this can be done, the Log(dose) – response curves have to be mathematically modeled. This is the subject of the next blog.

We hope you’ve found our first post informative. You can sign up to receive our further material on this subject below & If there are any particular topics you’d like to see covered in the future then please (let us know/comment below).

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References

  1. Council of Europe. 2013. Statistical analysis of results of biological assays and tests. Pages 551-579 in European Pharmacopoeia, 8th ed. Council of Europe.
  2. The United States Pharmacopeial Convention. 2012a. <1032> Design and development of biological assays. Pages 5160-5174 in First Supplement to USP 35-NF 30.
  3. The United States Pharmacopeial Convention. The United States Pharmacopeial Convention. 2012b. <1033> Biological assay validation. Pages 5174-5185 in First Supplement to USP 35-NF 30.
  4. The United States Pharmacopeial Convention. The United States Pharmacopeial Convention. 2012c. <1034> Analysis of biological assays. Pages 5186-5200 in First Supplement to USP 35-NF 30. The United States Pharmacopeial Convention.

 

 

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About The Author

Senior Statistician – Francis joined Quantics in 2013. With a Masters from Cambridge and DPhil in Theoretical Physics from Oxford University, Francis brings high level mathematical ability and extensive experience in simulation techniques to Quantics. These techniques can be used to explore “what if” scenarios, reducing the need for further experimental data. Francis heads the R&D team.

2 Comments

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