Page 56 - Contributed Paper Session (CPS) - Volume 7

CPS2028 Ayon M.
better treatment arm. A critical assumption made here is that the survival times
and the censoring times are independent. Since patients arrive sequentially in
the clinical trial and are observed until the end of the trial, the type of
censoring considered here is the generalized Type I right censoring scheme.
This section discusses the method of derivation of this allocation function
using two optimal allocation approaches which target the derived allocation
proportions.
Since clinical trials are complex experiments with multiple experimental
objectives, a formal optimization procedure can be used to develop the CARA
randomization procedures. Treating the baseline hazard as arbitrary makes the
design more dependent on the observed data as compared to that of the
designs based on parametric models. Such designs therefore increases its
applicability in real-life clinical trials.The hazard function plays an important
role in any survival trials. Let ()be the probability of event before censoring

̂
for a patient with treatment k and with covariate vector z,and √ −1 ( () , be
the principal square root of the inversed weighted variance matrix of the
covariates among the individuals at risk at time .One way to meet most of
()
the multiple experimental objectives in a clinical trial is to minimize the overall
hazard for a patient with a given covariate, subject to the constraint of keeping
the asymptotic variance of the difference between the estimated hazard
functions for the two treatment groups to be constant. This is done by

̂
where () is the observed inforation matrix for the Cox regression
coefficients. The optimal allocation proportion for treatment A is given by:

One can use other metrics of treatment difference and obtain different
optimal allocations. For instance, minimizing the overall trial size, subject to
the constraint of keeping the asymptotic variance of the difference between
the estimated hazard functions for the two treatment groups to be constant,
leads to the Neymann allocation. The Neymann allocation function for
treatment A is given below:

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