Principles and Practice of Pharmaceutical Medicine

amongst different agonists, describing response
size for a standard degree of receptor occupation
(Jenkinsonet al., 1995). When an agonist must
occupy 100% of available receptors to causeEmax,
its efficacy may be said to be unity. If occupation of
all receptors achieves a response that is less than
Emax, then the agonist’s efficacy is less than 1 and
equal to the ratio of observed maximal effect/max-
imal effect for an agonist with efficacy 1 (we call
these partial agonists or agonist–antagonists).
Some agonists need occupy only a subset of the
available receptors, in order to achieveEmax,and
these have efficacy greater than unity. In the latter
case, the concentration–response curve lies to the
left of the concentration–receptor occupancy
curve (e.g. Minnemanet al., 1983). Drugs with
efficacy1 are also calledfull agonists.
Below, we present some model relationships
between observed concentration and effect size,
as examples from a considerable volume of litera-
ture. The reader is referred to key texts for com-
prehensive coverage of this topic (e.g. Smolen,
1971; Gibaldi and Perrier, 1982, Daynekaet al.,
1993; Levy, 1993; Lesko and Williams, 1994;
Colburn, 1995; Derendorf and Hochhaus, 1995;
Gabrielsson and Weiner, 1997; Sharma and
Jusko, 1997).

Pharmacokinetic–pharmacodynamic
(PK/PD) modeling

Single-compartment, time-independent
PK/PD models

The simplest model is where (a) the drug distri-
butes into a single compartment, represented by
plasma, and (b) the effect is an instantaneous,
direct function of the concentration in that com-
partment. In this situation, the relationship
between drug concentration (C) and a pharmaco-
logical effect (E) can be simply described by the
linear function:

E¼SC

whereSis a slope parameter. If the measured effect
has some baseline value (E 0 ), when drug is absent

(e.g. physiological, diastolic blood pressure or rest-

ing tension on the tissue in an organ bath), then the

model may be expressed as:

E¼E 0 þSC

The parameters of this model,SandE 0 , may be

estimated by linear regression. This model does not

contain any information about efficacy and

potency, cannot identify the maximum effect and

thus cannot be used to find EC 50.

When effect can be measured for a wide con-

centration range, the relationship between effect

and concentration is often observed to be curvi-

linear. A semi-logarithmic plot of effect versus log

concentration commonly linearizes these data

within the approximate range 20–80% of maximal

effect. This log transformation of the concentration

axis facilitates a graphical estimation of theslope

of the apparently linear segment of the curve:

E¼mlnðCþC 0 Þ

wheremandC 0 are the slope and the hypothetical

baseline concentration (usually zero, but not for

experiments of add-on therapy or when adminis-

tering molecules that are also present endogen-

ously), respectively. In this equation, the

pharmacological effect may be expressed, when

the drug concentration is zero, as:

E 0 ¼mlnðC 0 Þ

As mentioned earlier, for functional data based on

biophase, plasma or tissue measurements, we often

represent potency as EC 50 ; and when two com-

pounds are compared with respect to potency, the

one with the lowest EC 50 value has the highest

potency. A general expression for observed effect,

by analogy with the Michaelis–Menten equation

(above) is:

E¼

EmaxC

EC 50 þC

There are various forms of this function for agonist

(stimulatory) and antagonist (inhibitory) effects.

For example, if there is a baseline effect (E 0 ),

90 CH8 PHASE I: THE FIRST OPPORTUNITY FOR EXTRAPOLATION FROM ANIMAL DATA