Graded dose response

Graded dose response describes how the magnitude of a defined biological effect changes with dose or concentration under a specified protocol. The observable can be an activity, force, concentration or other quantitative endpoint. It differs from quantal dose response, which records whether a specified criterion is met. The EPA’s primary terminology explicitly separates degree of response from incidence or probability.^[ref]

For an original saturating concentration-response model, writeThe plateau $E_{\mathrm{top}}$ is an absolute response level, while $E_{\mathrm{top}}-E_0$ is the maximum change above baseline. At $c=K$, the response is halfway between baseline and plateau. If they are $20$ and $100$ response units, that midpoint is $60$, not $50$. Stating the baseline convention is essential when comparing midpoint parameters.

The graded mean also does not determine a binary responder fraction. Two original four-observation examples, $(20,20,20,20)$ and $(0,0,40,40)$, both have mean $20$. With a response criterion of at least $30$, their responder fractions are $0$ and $1/2$. Converting a continuous measurement into a binary outcome discards information about response magnitude.

A controlled assay measures matched concentrations at stated observation times with suitable baseline and reference conditions. Pharmacokinetics can make an administered dose produce different concentration histories, and biological time dependence can change the effect even at the same nominal concentration. ICH-E4 discusses concentration-response information and the interaction of response with time.^[ref]

A fitted curve is a model for the observed endpoint, not proof of a particular receptor mechanism. An apparent plateau may instead reflect an instrument limit or the tested range. Graded dose response is most useful when the measured quantity, normalization, exposure definition and uncertainties are all explicit.