Page 57 - Contributed Paper Session (CPS) - Volume 7

CPS2028 Ayon M.
The doubly-adaptive biased coin design (DBCD) or the efficient
randomized adaptive design (ERADE) can be used to allocate the patient and
target these derived allocation proportions. After the allocation of the two
treatments to m patients and observing their responses, let
() and () = − () denote the numbers of patients assigned to

th
each of the two treatments. When the ( + 1) patient enters the clinical
trial with covariate vector +1 , let ̂ = π ( ̂ , ̂ , +1 ) represent the

estimate of ( , , ) based on the responses observed from the m

patients, adjusted for the covariate +1 of the incoming patient. Using the
th
DBCD procedure, the ( + 1) patient can be assigned to treatment A with
probability +1 ( () , ̂ ), where () is the proportion of patients who

have been assigned to treatment A after allocations. Let ̂ =

∑ ( ̂ , ̂ , ) be an estimate of the average target allocation of patients
−1

to treatment A, based on the data for the first m patients. The mathematical
th
form of the allocation rule for the ( + 1) patient entering the clinical trial
with covariate vector +1 ,to be assigned to treatment A is given in
Sverdlov,Rosenberger and Ryzenik (2013), whereas the mathematical form for
the ERADE allocation rule is given by

where 0 ≤ < 1 is a constant that reflects the degree of randomization. This
gives a family of CARA designs that are fully randomized and also
asymptotically efficient. The ERADE can be viewed as a generalisation of
Efron’s biased coin design for any desired allocation function, which may
depend on the unknown parameters. If the response distribution belong to
the exponential family, the ERADE for any ∈ [0,1) is fully efficient. The
parameter controls the degree of randomness of the design. The
performance of the various randomization procedures targeting each of the
derived allocation proportions is discussed in the next section after performing
an extensive simulation study.

4. Simulation Results
The simulation results compare different designs according to three
experimental scenarios, the first being the neutral treatment effect, which
refers to the hypothetical experimental scenario where treatments A and B are
equally effective. In the case of comparing a new treatment with a control, this
scenario refers to the situation where the new treatment is as good as the

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