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CPS1201 M. Iftakhar Alam et al.
the best needs very similar numbers of cohorts to the design with = 0. A
similar trend is found when the simple combined criterion is utilised.

4. Discussion and Conclusion
We have looked at three different approaches for dose finding. In the first
approach, the intention is to allocate doses to the patients that are most
efficacious according to the current knowledge while searching for the best
dose, an approach known in the literature as the “best intention”. The second
approach targets the most effective, from the parameter estimation point of
view, gathering of information and consequently should give the best estimate
of the optimum dose. The third approach tries to achieve a trade-off between
the two. Best intention designs are ethically attractive, as they take care of the
patients, but, unlike the one based on the D-optimality criterion, they have
limitations in terms of convergence to the optimum dose. Pronzato (2000) and
Fedorov et al. (2011) report that “best intention” designs may converge to a
sub-optimal dose. Their studies are based on the frequentist approach and
use the least squares or the maximum likelihood estimates of the parameters.
We are using Bayesian parameter estimation, and, to our knowledge, the
convergence properties are not known in this case.
The gains in the combined criteria over the penalised D-criterion or D-
criterion are evident from the presented results. All of the performance
measures are found to be improved. Most importantly, we notice an
appreciable improvement in the quality of treatment allocation, reflected
through the sampling efficiency measure SE and the measure of OD allocation
during the trial, %AD. The quality of optimum dose selection for the next
phase, presented through the DE, is also found to be improved. The combined
criteria also outperform the criterion based on the maximisation of the
probability of success. In general, the combined criteria utilise a reasonable
number of cohorts compared to the other two designs.
All of these results guide us to recommend the proposed combined criteria
as dose-optimisation tools in early phase clinical trials. In terms of
performance, the penalised combined criterion does slightly better than the
simple combined criterion. The choice of values for will solely depend on the
objective. In extreme scenarios like 1, 4, 5 and 6, we have seen that high values
of perform surprisingly well. The middle values are also found to perform
satisfactorily in the majority of the scenarios. Since, in reality, we may not know
the shape of the dose-response relationship in advance of the trial, we suggest
using the middle values. Alternatively, we can have some idea on the optimum
value of during the progress of a trial. Once a trial has come through some
reasonable number of stages, we can locate where the optimum dose may lie
based on the estimates of probability of success and toxicity at hand. If it is
found to be either at the lower end or at the upper end of dose region, we can

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