Abstract: Mady
[3] introduced two simple procedures for dealing with patients who arrive during
the waiting period, caused by the lag, between the trial and treatment stages
for designing an optimal clinical trial when a total of N
patients with a disease are to be treated with one of medical
treatments. The relative performance of the procedures in the Bayesian framework
is discussed when the responses to treatments
are
normally distributed with unknown means and
a common known variance We notice that when the formulae for the expected
regret function for Procedures 1 and 2 performed by Mady are not equivalent with
those of Langenberg and Srinivasan [2]. We found that the reason for this
situation is as fallows. Mady expressed the expected regret function in terms of
the true difference while Langenberg and Srinivasan
expressed the same function in terms of the absolute difference That is, we must differentiate
between two cases: (i) (ii) as the probability of selecting the
inferior population has a different formual in each case.
This paper will express the expected regret function using Procedures 1 and 2 in
terms of the absolute value of the true difference between the treatments instead
of where
and
are
the unknown means of treatments and
respectively.
The consideration of this modification leads to major changes in the results.
Keywords and phrases: Bayesian approach, decision theory, delayed observations.
