Optimal adaptive promising zone designs.

We develop optimal decision rules for sample size re-estimation in two-stage adaptive group sequential clinical trials. It is usual for the initial sample size specification of such trials to be adequate to detect a realistic treatment effect δa with good power, but not sufficient to detect the smallest clinically meaningful treatment effect δmin . Moreover it is difficult for the sponsors of such trials to make the up-front commitment needed to adequately power a study to detect δmin . It is easier to justify increasing the sample size if the interim data enter a so-called "promising zone" that ensures with high probability that the trial will succeed. We have considered promising zone designs that optimize unconditional power and promising zone designs that optimize conditional power and have discussed the tension that exists between these two objectives. Where there is reluctance to base the sample size re-estimation rule on the parameter δmin we propose a Bayesian option whereby a prior distribution is assigned to the unknown treatment effect δ , which is then integrated out of the objective function with respect to its posterior distribution at the interim analysis.

Semiparametric Bayesian latent variable regression for skewed multivariate data.

For many real-life studies with skewed multivariate responses, the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution. We present a novel semiparametric multivariate model and associated Bayesian analysis for multivariate skewed responses. Similar to multivariate Gaussian densities, this multivariate model is closed under marginalization, allows a wide class of multivariate associations, and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density. Other desirable properties of our model include the Markov Chain Monte Carlo computation through available statistical software, and the assurance of consistent Bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions. We illustrate the practical advantages of our methods over existing alternatives via simulation studies and the analysis of a clinical study on periodontal disease.