Statistical inference for adaptive designs in multi-center clinical trials

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

Wavelet designs for nonparametric regression models with autocorrelated errors

We consider minimax designs for estimation of nonparametric regression models using wavelet approximations of the mean response function. We assume that the error terms are autocorrelated. Since the method of estimation depends on the choice of design, we argue that using ordinary least squares method (OLS) for estimation may lead to designs that are less efficient than designs constructed based on generalized least squares (GLS) or weighted least squares (WLS). A simulated annealing algorithm is developed to carry out the minimization problems to search for minimax designs. In this thesis we considered AR(1) model for example. We found that the GLS method is good for the moderate level correlation and WLS or OLS is preferred for highly correlated data