Graded, quantal and ordered drug responses

This chapter is related to one of the aims of Section C(ii) from the 2023 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".  It is another central keystone topic which has never been examined, probably because it is so fundamental that all trainees entering into a career of intensive care medicine are expected to have an intuitive understanding of it ab initio

There is nothing regarding quantal and graded responses in Birkett (2011). Katzung has a small section related to it in Chapter 2, which probably represents the minimum expected knowledge. An excellent article by Ashauer et al (2011) is also available. 

In summary:

Dose-response relationships may be graded or quantal.

  • Graded dose-response relationships:
    • Graded dose-response relationship describes a drug effect which increases in proportion to increasing drug dose.
    • A graded response to a drug is seen in an individual, and increases with dose.
    • Graded dose-response graphs plot the response to a drug against its concentration
  • Quantal dose-response relationships:
    • a Quantal dose-response relationship describes a drug effect which is binary (either present or absent).
    • A quantal response to a drug is observed in a population, and is either present or absent in any single individual.
    • Quantal dose-response graphs plot the rate of an outcome occurrence in a population against the drug dose.
  • Ordered dose-response relationships:
    • an Ordered dose-response relationship is a sequence of quantal dose-response relationships which represent several quantal response end-points which are seen when dose is increased.

Occasionally, some ancient source has done a better job of explaining a topic than any of the more recent authors.  The excellent 1981 article by Doug Waud is a good example of this. It's not available as free full text, but the main element is quoted here:

" If the response can be measured on a continuous scale the dose-response curve is said to be 'graded'.  This group represents the common or garden variety of curve, for example, acetylcholine on arterial pressure, histamine on an isolated ileum,  streptomycin on protein synthesis. etc. The next category is the 'quantal' dose-response curve. This is characterized by a response which is all-or-none. The lethal effect is a classical example. The animal is either dead or alive following the dose of the drug."

The rest of the article is also excellent. Waud takes a relaxed conversational style, with just the tiniest element of curmudgeonly sarcasm. For instance, of quantal dose-response relationships, he says that "Fundamentally, the dose-response curve consists of points only at the top or bottom of the graph, i.e. 1 or 0 on the scale of ordinates". However, if this were true, why does nobody ever see mortality statistics reported in this fashion? Well; "apparently editors object to all that empty space in the middle or pharmacologists feel insecure if an S-shaped array is not visible".  It's gold, people.


One does not see writing like Waud in modern pharmacological literature. For instance, for graded dose-response relationships, Mark von Zastrow of Katzung (Chapter 2, Pharmacodynamics) had this to say:

"When the response of a particular receptor-effector system is measured against increasing concentrations of a drug, the graph of the response versus the drug concentration or dose is called a graded dose-response curve"

Whereas, for quantal dose-response curves, from the same author:

"When the minimum dose required to produce a specified response is determined in each member of a population, the quantal dose-response relationship is defined"

This is somewhat cumbersome and insufficiently hilarious but nonetheless accurate. Others have attempted better definitions, and instead mainly succeeded in making them shorter. For instance, Ashauer et al (2011) describe a quantal dose response as "on or off". This does explain the concept in the smallest possible number of words, but is insufficiently enlightening for the CICM primary exam candidate trying to grasp what the main difference is between the two concepts. The best explanation of this probably comes from Goodman and Gilman (Ch.4, Drug Toxicity and Poisoning):

"There is a graded dose-response relationship in an individual and a quantal dose-response relationship in the population. Graded doses of a drug given to an individual usually result in a greater magnitude of response as the dose increases. In a quantal dose-response relationship, the percentage of the population affected increases as the dose is increased; the relationship is quantal in that the effect is judged to be either present or absent in a given individual."

Thus, from all these definitions, we can surmise that graded and quantal dose-response relationships demonstrate very different things. Graded dose-response graphs plot the response to a drug against its concentration, whereas quantal dose-response graphs plot the rate of an outcome occurring in a population against the drug dose.

Additionally, the third form of dose-response is occasionally mentioned, which is the "ordered" dose-response relationship. This is really just a series of quantal relationships which are displayed on the same graph. It is used where the increase in the dose of a drug produces a progression of effects which can each be set as the end-point of a quantal relationship. Stages of anaesthesia are usually used to explain this concept.  Let's say as the patient receives more and more gas they progress through sedation (let's call that "Response 1"), unconsciousness (Response 2), respiratory depression (Response 3), and ultimately death (depending on the anaesthetist), which we will call Response 4. There is no ordinal relationship between these quantal end-points: for example, one cannot say that, when one is dead from the anaesthetic at Response 4, one is exactly twice as anaesthetised as they were at Response 2. All that can be said is that Response 4 is seen at a higher concentration than Response 2, i.e. there is an ordered progression of responses with increasing dose.

This is all beginning to sound like it would be explained better with some diagrams. Unfortunately, the process of developing these diagrams tends to lead one into a deep rabbit hole. Consequently, two separate chapters had developed out of what would anywhere else be a fairly straightforward exercise in writing revision notes.


"Basic & Clinical Pharmacology" 14th ed. (Katzung)

Waud, D. R. "Analysis of Dose—Response Curves." Smooth Muscle. Springer, Boston, MA, 1975. 471-506.

Ashauer, Roman, et al. "Toxicokinetic‐toxicodynamic modeling of quantal and graded sublethal endpoints: A brief discussion of concepts." Environmental Toxicology and Chemistry 30.11 (2011): 2519-2524.

Hewlett, P. S., and R. L. Plackett. "The relation between quantal and graded responses to drugs." Biometrics 12.1 (1956): 72-78.