Jul 04
Parallelism: Two parallel 4PL models

What is Relative Potency?

Relative potency (RP) refers to the dose of a test sample required to produce the same response in an assay as a dose of a reference sample. Since we (usually) know the potency of the reference sample, this gives us a measure of the potency of the test sample by comparing it to that reference.

Relative potency is often used to determine whether a batch of therapeutic product is suitable for release, as well as in other important phases of the drug development process. There are, therefore, extensive guidances which describe proper procedures to measure and use RP, including the European Pharmacopoeia (Ph.Eur) 8th edition and the United States Pharmacopia (USP) bioassay guidance. Here, we’ll examine some of the basics of what relative potency means, and why it’s so important for bioassay.

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.”

If, instead, we use a relative measure of potency – comparing a test sample of unknown potency to a reference standard of known potency – many of the factors which cause the variability of a biological assay will affect both samples similarly. This means a measurement of relative potency will be far less variable than one of absolute potency – we take a deep dive into this in this blog.

Finney provided an oft quoted definition of relative potency in the 2nd edition of his book Statistical method in biological assay, relased in 1964:

“The ratio of two equally effective doses is an estimate of the potency of the test preparation relative to that of the standard.” 

Relative potency: parallel curves
For two parallel curves, the horizontal shift Δ is the same for all doses

Mathematically, for a dose of reference standard (Dose_S) and test sample (Dose_T) which produce the same response, we can define:


By taking the log of both sides, we can see that this is the same as:

    \[\log(RP)= \log(Dose_S) - \log(Dose_T)\]

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 response of any magnitude.

This relies on the key assumption that the standard and test sample have the same biologically active component, and so behave similarly across the whole range of doses. That is, one can be considered as a simple dilution of the other. This is one of the issues with biosimilars, which are not usually identical in their biological activity across all doses. We cover this in detail here.

Experimental determination of relative potency

How do we determine relative potency is practice? It would, of course, be possible to define an absolute level of response, titrate the standard and test samples to achieve that level of response, and measure the dose of each required.

This would provide the relative potency of the test sample at a single dose, which 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.

In practice, a range of doses are tested, and results plotted as log(dose) against response. We fit a mathematical model to these results, and find the we can find the horizontal shift \Delta between them at a particular response as:

\Delta = \log (Dose_S) - \log(Dose_T)

Notice this is identical to our definition of the log(RP)! This means we can say that:


Relative potency: non-parallel curves
If the curves are non-parallel, the horizontal shift will vary over the dose range, meaning the RP is no longer well-defined

For two samples with the same biologically active component, we would expect that \Delta would be the same at all doses. This means that the RP would be constant with dose – exactly the behaviour we expect! If the test item did not have the same biologically active component as the standard, \Delta, and, therefore, the relative potency would vary over the dose range.

Two lines that are the same distance apart (when measured in a defined way) are said to be 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, i.e. it does contain the same biologically active components.

We cover parallelism in more depth in this blog. And, we cover the  process of mathematically modelling dose – response curves here.

QuBAS Bioassay Software is designed to perform relative potency calculations and more to rigorous GxP standards. Find out more about Qubas here.

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.


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