This chapter is related to one of the aims of Section C(i) from the 2017 CICM Primary Syllabus, which expects the exam candidate to *"define and explain dose-effect relationships of drugs, including dose-response curves with reference to... graded and quantal response**"*. At no stage has this ever appeared in historical primary exam papers, but it is a topic so ubiquitous that one can see the merit of squandering an entire chapter on its discussion, even if there may be no immediate pragmatic benefit from it in terms of exam marks.

The best resource for this topic is probably Mark von Zastrow's chapter for the 14th edition of Katzung's *Basic and Clinical Pharmacology. *The quantal dose response territory is covered there without any sort of references but to a level of detail which would surely satisfy any future exam application of this topic. If one for some reason required something more in-depth, one may instead look at something like B.J.T Morgan's *Analysis of Quantal Response Data *(2013), which is 511 pages of articles from the *Monographs on Statistics and Applied Probability* series (the 46th volume).

In summary:

- A quantal dose response is a defined drug effect which is either present or absent.
- In a population, there is usually some variation of doses required to achieve the defined drug effect
- The distribution of these dose tends to be a normal Gaussian distribution (i.e a bell curve)
- The cumulative percentage of the population responses to increasing doses can be plotted as a curve (which assumes a sigmoid shape)
- These curves can be used to describe the therapeutic index, median effective dose, median lethal dose, and several other parameters useful for determing safe dose recommendations.

## Definition of quantal dose-response data

Birkett (1995), in one of the Australian Prescriber articles which would eventually become *“Pharmacokinetics made easy”*, wrote:

"An alternative way of constructing a concentration effect curve is to determine the percentage of a population of patients showing a defined response at various drug concentrations... These are called quantal (population)concentration responsecurves and have the same shape and parameters as the gradedconcentration responsecurves"

Let's expand on that.

A *quantal* response is either there, or it is not. There is no spectrum of greyscale between "response" and "no response". This is obviously completely arbitrary. Realistically, there may be a *clinically relevant *spectrum for this drug - for example, if your experimental drug is noradrenaline, there is obviously a graded spectrum of clinical responses with increasing dose- but because you have defined an all-or-nothing experimental endpoint (for example, death) the data ignores this graded spectrum. The dose-response curve of an individual experiment would therefore look something like this:

You can't even call that a curve while keeping a straight face. As the graphic above is never seen in serious publications, the intelligent reader would at this stage correctly identify it as a plot device leading to the exploration of population pharmacodynamic data. Indeed, one would perform the experiment on a whole group of animals/volunteers/isolated murine ileum segments and then have data available which would look a little like this:

Looking at these data, there is obviously a great deal of population of subjects is obviously heterogeneous with some small percentage requiring a tiny dose to achieve the end-point effect, and some small percentage still failing to achieve the end-point even at a very high dose. This distribution can be described as a bell curve:

At this point, a maths nerd might point out that these dose-response data appear to be normally distributed, which means we can finally return to the familiar sigmoid-shaped dose-response curve we are all more comfortable with. It can be easily reconstructed from this bunch of rectangular dose relationships (in essence, they are stacked atop each other, and a line connecting them is produced).

Thus, instead of demonstrating a graded effect response to increasing drug concentration, one now has a sigmoidal curve describing the cumulative percentage of a population which can be expected to achieve a response at a given dose. This graph actually has a series of important and interesting anatomical features, which are represented by a single dot-point in the 2017 CICM Syllabus, and therefore somehow an entire chapter in Deranged Physiology.

### References

Birkett, D. J. "Pharmacokinetics made easy 10 Pharmacodynamics-the concentration-effect relationship." *Australian Prescriber* 18.4 (1995).

von Zastrow, M. "Chapter 2: Drug Receptors & Pharmacodynamics ". Basic & Clinical Pharmacology, 14th edition. [*The link points to the 2009 version of the chapter, which comes from the 12th edition of that book - somehow, the entire textbook is available for free*]

Morgan, Byron JT. *Analysis of quantal response data*. Vol. 46. Springer, 2013.