We discuss methods for comparing effects of two treatments A and B. We investigate
the performance of response-adaptive (RA) and covariate-adjusted response-adaptive
(CARA) designs in multi-center clinical trials. First, we discuss applying RA designs
to maximize the well-being of participating patients in multi-center clinical trials. We
assume that the centers are selected from a large population of centers and develop a
generalized linear mixed model (GLMM) to examine the treatment effect. The asymptotic
properties of the maximum likelihood (ML) estimators of model parameters are
derived using the in
uence function method. We verified their theoretical properties
through simulation studies. The techniques are then applied to a real data that were
obtained from a multi-center clinical trial designed to compare two cream preparations
(active drug/control) for treating an infection. Secondly, we investigate the efficiency for estimates of model parameters and ethics for participating patients among
RA, CARA, and completely randomized (CR) designs for a generalized linear model
(GLM). We consider the logit model to measure efficiency and ethics. Furthermore,
we showed that ML estimators of GLM parameters are consistent and asymptotically
follow multivariate normal distribution for adaptive designs. A simulation study was
conducted to verify these theoretical results. Finally, we provide a justification of why
asymptotic results for Wald-type tests for adaptive designs can be used. We proved
that the choice of adaptive designs affects the statistical power of hypothesis testing
via these quantities: the target allocation proportion, the bias of the randomization
procedure from the target, and the variability induced by the randomization process.
Moreover, we showed that the statistical power increases when the design variability
decreases for a covariate in a logit model. Our theoretical findings are verified by
simulation results