Page 53 - Contributed Paper Session (CPS) - Volume 7

CPS2028 Ayon M.
Sverdlov (2008) gave an overview of different techniques for handling
covariates in the design of clinical trials and distinguished between two main
approaches. These are covariate-adaptive randomization and covariate-
adjusted response-adaptive (CARA) randomization procedures. CARA
randomization is applicable to clinical trials where nonlinear and
heteroscedastic models determine the relationship among responses,
treatments and covariates, and when multiple experimental objectives are
pursued in the trial. The goals of a CARA procedure may be to skew allocation
in the direction of the treatment that is clinically best given a patient’s
covariate profile, while maintaining the power of a statistical test for treatment
differences. These designs rely on correctly specified parametric models.
Although the exponential model for survival responses has been previously
considered by Sverdlov, Rosenberger and Ryzenik (2013) for developing CARA
designs, to extend the scope of application of such designs in real-life clinical
trials, the survival models that have been considered here relaxes on any
distributional assumption of the patient responses but relies only on a lighter
assumption of proportional hazards of patients between the two treatment
arms.

2. Background
The exponential model used by Sverdlov, Rosenberger and Ryeznik (2013)
to develop CARA randomization procedures for survival trials is useful for its
historical significance and mathematical simplicity, but it is less likely to fit data
in practice. This is because the exponential distribution corresponds to a “lack
of memory” model and that it has only one parameter making the expected
remaining lifetime for a patient at any point in the trial, to be a constant. The
methods discussed in this paper extends the applicability of CARA designs
even further by encompassing situations where the designs are applicable for
survival responses irrespective of its theoretical distribution, provided the
hazards of the event considered at any given time point is proportional and
time-independent for any two patients in the trial.
In a medical context, the hazard rate is also known as the force of mortality
and it represents a continuous version of a death rate per unit time. It is always
convenient in survival analysis to describe the distribution of the survival
responses in various different but inter-related ways. For a continuously
distributed survival time T let f(t) be the density function and F(t) be the
distribution function. The hazard function ℎ() = [()/()] can be
interpreted as the instantaneous failure rate, where S(t) is the survivor function
and gives the probability for a patient to survive beyond a given time point t.
The survivor function can also be written as;

() = (− ∫ ℎ()) = [−()] (1)
0

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