School of Mathematical Sciences

Covariate-Adjusted Response-Adaptive Designs for Weibull Distributed Survival Responses menu

Covariate-Adjusted Response-Adaptive Designs for Weibull Distributed Survival Responses

Ayon Mukherjee
Tue, 14/03/2017 - 12:00
Laws 2.09

Covariate-adjusted response-adaptive (CARA) designs use available responses to skew the treatment alloca-
tion in an ongoing clinical trial in favour of the treatment arm found at an interim stage to be best for a
patient's covariate pro le. There has recently been extensive research on CARA designs mainly involving
binary responses. Though exponential survival responses have also been considered, the constant hazard
property of the exponential model makes the mean residual life for patients constant, making it too restric-
tive for wide-ranging applicability. To overcome this limitation, designs are developed for Weibull distributed
survival responses by deriving two variants of optimal designs based on an optimality criterion. The optimal
designs are based on the doubly-adaptive biased coin design (DBCD) in one case, and the ecient randomised
adaptive design (ERADE) in the other. The observed treatment allocation proportions for these designs con-
verge to the expected targeted values, which are derived based on constrained optimization problems. The
merits of these two optimal designs are also discussed. Given the treatment allocation history, response his-
tories, previous covariate information and the covariate pro le of the incoming patient, an expression for the
conditional probability of a patient being allocated to a particular treatment has been obtained. To apply
such designs, the treatment allocation probabilities are sequentially modi ed based on the history of previous
patients' treatment assignments, responses, covariates and the covariates of the new patient.

The ERADE is preferable to the DBCD when the main objective is to minimise the variance of the al-
location procedure. However, the former procedure being discrete tends to be slower in converging towards
the expected target allocation proportion. Since the ERADE provides a design with minimum variance,
it is better than the CARA design based on the DBCD as far as the power of the Wald test for testing
treatment di erences is concerned. An extensive simulation study of the operating characteristics of the pro-
posed designs supports these ndings. It is concluded that the proposed CARA procedures can be suitable
alternatives to the traditional balanced randomization designs in survival trials, provided that response data
are available during the recruitment phase to enable adaptations to the designs.