Abstract: The
problem of selecting the better of two exponential distributions is considered.
It is assumed that there are two treatments available. A patient is given one of
these treatments at a point in time, after which his remaining life length has
an exponential distribution. The death ratesanddepend
upon the treatments. One wants as few patients as possible to participate so
that the number of patients receiving the inferior treatment during the trial is
minimized, the trial is brought to as speedy a conclusion as possible and the
results are quickly made available to aid in the treatment of other patients
with the disease in question.
A
two stage procedure, similar to the one considered by
Colton
[2], is given. When a choice has to be made in favor of one of two populations,
the cost of sampling (experimenting) in order to obtain information on which to
base the decision may be balanced against the cost of making the wrong choice.
The cost of sampling is assumed to be the cost of an incorrect choice for half
the sample (which is divided between the two treatments).
Fixed sample size and sequential trials are considered.
Bayesian approach is used for determining the optimal size of a fixed sample
trial. Minimax, maximin and Bayesian approaches are used for determining the
optimal position of the boundaries of a sequential trial. Comparisons of the
results for the fixed and sequential trials are considered.
