Chemistry Reference
In-Depth Information
100
4
4
8A
8B
75
3
3
2
50
2
1
25
10B
10A
1
0
0
0
1
2
3
4
Dose (D)
0
0
1
2
3
4
FIGURE 10
Examples of sigmoid models.
Dose (D)
FIGURE 8
Examples of exponential models when b>1. Curve
8A, log
b
E = a(D). Curve 8B, log
b
(E + 1) = a(D).
Two types of sigmoid curves are illustrated in
Figure 10. The nature of the model is that there is an
initial slow increase in effect with increasing dose,
followed by a relatively linear or directly propor-
tional increase in effect with dose, and fi nally another
slow increase in effect with increasing dose, up to the
maximum effect that the system can demonstrate. In
curve l0A, the effect is zero until the value of the dose
becomes greater than 1.5, and the maximum effect of
4 units is observed at a dose of 3.25; further increases
in dose will produce only the same maximum effect
of 4 units.
In contrast, curve l0B has characteristics similar
to curve l0A, except that the curve begins at the ori-
gin (zero dose-zero effect) and is asymptotic to the
maximum effect of 4 units. The graphical representa-
tion of Figure 10 does not provide a clear picture of a
quantifi able value for effect at the lower dose levels,
but the model for curve 10B requires that there is an
extremely small, but fi nite, value for effect at infi nitely
small values for dose. The signifi cance of this feature
and the consequence of this contrast with curve 10A
are discussed in later sections.
One of the most common explanations of the sig-
moid or ogive curve is that a value on the effect scale
includes the summation of all of the effects occur-
ring at dose levels up to and including that dose. This
explanation is particularly appropriate for the dose-
response relationship. It was noted earlier that models
with a maximum effect provide the possibility of con-
verting the effect scale with graded units to a percent
effect scale as illustrated in the right hand margin (Fig-
ure 10). The percent scale may alternately be defi ned
as a percent response scale that would be necessary if
the curves l0A and l0B are to be considered as dose-
4
3
2
1
0
0
1
2
3
4
Dose (D)
FIGURE 9
Example of a power-function model when n>1.
E = KD
n
.
2.2 The Sigmoid Curve
The sigmoid (or ogive) curvilinear relationship is
often observed with dose-effect data and is almost
always observed with dose-response data. This model
as illustrated in Figure 10 has to have an upward swing
(curvature) at the lower dose levels and a downward
swing (curvature) at the higher dose levels. The middle
range seems to be close to linearity and these curves
may or may not be symmetrical.
