Page 136 - Contributed Paper Session (CPS) - Volume 1

CPS1201 M. Iftakhar Alam et al.
exposes few cohorts in a trial to either subtherapeutic or toxic doses and that
can also find the optimum dose accurately.

2. Methodology
Although the penalised D-criterion in Dragalin and Fedorov (2006)
introduces a penalty function to improve the quality of treatment during dose
escalation, we have found it not to be improved as expected. Therefore, further
effort has been taken with the combined criterion defined below. Also,
clinicians may be interested in achieving several objectives, such as efficient
estimation of the model parameters and allocation of the most efficacious
doses to the cohorts during a clinical trial. The combined criteria in (1) and (2)
balance these two objectives.
The penalised combined criterion is a linear combination of the
determinant of the Fisher information matrix for the dose-response model,
penalised for inefficacy and toxicity, and the probability of success. On the
other hand, the simple combined criterion does not penalise for inefficacy and
toxicity. At each stage of the adaptive trial, we select that dose for which the
criterion is maximised.

To implement the penalised criterion, we initially determine the doses +1
and that maximise the probability of success and the determinant of the
+1
penalised Fisher information matrix (FIM), respectively. Since the determinant
and the probability of success may have quite different magnitudes, we scale
them at the dose as
̂
Φ {(| , )} (, ̂

() = and () = .

̂
{( | , )} ( , ̂ )

+1
+

The penalised combined criterion then selects the dose +1 for the next
cohort of patients so that
+1 = argmax{ () + (1 − ) ()}. (1)

∈

where is some weight such that 0 ≤ ≤ 1.
D
If the D-optimum dose + 1 and ()are chosen instead, then the simple

combined criterion takes the form

+1 = argmax{ () + (1 − ) ()}. (2)

∈

This is a special case of the penalised combined criterion if CS = CT = C =
0 in the penalty function. This is due to the fact that, when C = 0, the penalised
D-criterion reduces to the D-criterion. Obviously, the results will depend on
the choice of . It is clear that, when = 1, the combined criterion is simply
the penalised D-criterion or D-criterion. Similarly, for = 0, we have dose
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