Counting People, Not Effects: Quantal Curves, ED50, TD50, LD50

Two ways to read a dose

The previous guide measured how much effect one subject shows — a graded response. But many of the questions that matter clinically are all-or-none: a person either does or does not respond. Did the anaesthetic make this patient lose consciousness? Did this dose abolish the arrhythmia? You cannot be 'half asleep' in any useful clinical sense. For these we use a quantal response.

A quantal curve does not plot how strong the effect is. It plots, at each dose, what fraction of a population crosses the yes/no line. At a low dose, only the most sensitive few respond; at a high dose, almost everyone does. The reason it is a smooth curve rather than a sharp step is biological variability — people are not identical, so they tip over at different doses.

The three 50% doses

Once you have a quantal curve, the most stable, easiest-to-read landmark is the dose at which exactly half the population responds. We give it a name depending on which response we are counting.

1. ED50 — the median effective dose: the dose that produces the desired effect in 50% of the population.
2. TD50 — the median toxic dose: the dose that produces a defined toxic effect in 50% of the population.
3. LD50 — the median lethal dose: the dose that is fatal to 50% of test animals. It is an animal/toxicology measure, never a target in patients.

Reading it on a log scale

Quantal data are almost always plotted as a log dose plot, with the dose on a logarithmic axis. This stretches out the low doses and compresses the high ones, turning a skewed curve into a near-perfect S that crosses the 50% line cleanly. On the same axes you can lay the effective curve and the toxic (or lethal) curve side by side and simply read off the ED50, TD50, and LD50 where each crosses 50%.

Quantal log-dose plot (% of population responding)

100% |               ........----  desired effect
     |          .--''                  .....----  toxic effect
 50% |- - - - .x- - - - - - - - - - .x- - - - - -
     |      .'                    .'
  0% |...--'________________..--'________________
        ED50 (e.g. 10 mg)      TD50 (e.g. 100 mg)   log dose -->

Read ED50 where the desired-effect curve crosses 50%.
Read TD50 (or LD50) where the toxic curve crosses 50%.
The gap between the two curves is what keeps patients safe.