In the conduct of sequential clinical trials, primary statistical issues include design , monitoring and reporting. Currently, approaches built upon frequentist inference methodology predominate. Focusing on the design aspect, our objective is the development of a very general Bayesian framework permitting multiple arms with multiple patient endpoints and multiple stopping criteria. It is impor...

We consider the problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes. All of the processes may be observed simultaneously as long as desired before a final choice between hypotheses is made. The objective is to find a decision rule that identifies the correct hypothesis and strikes the optimal balance...

We consider a buying–selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

A Markov process is registered. At random moment θ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is obtained.

This paper focuses on linear classification using a fast and simple algorithm known as the Ho–Kashyap learning rule (HK). In order to avoid overfitting and instead of adding a regularization parameter in the criterion, early stopping is introduced as a regularization method for HK learning, which becomes HKES (Ho–Kashyap with Early Stopping). Furthermore, an automatic procedure, based on genera...

In this paper, we propose a methodology essentially based on the Central Limit Theorem for Markov chains to monitor convergence of MCMC algorithms using actual outputs. Our methods are grounded on the fact that normality is a testable implication of suucient mixing. The rst control tool tests the normality hypothesis for normalized averages of functions of the Markov chain over independent para...

In this paper we consider a method for monitoring a clinical trial whose patients are sequentially evaluated for response. We focus on a parameter representing treatment effect. Adopting a Bayesian approach we suggest to update progressively prior information on this unknown quantity: in particular, we monitor the trend of the posterior probability that the parameter is larger than a minimally ...

A standard Bayesian stopping rule for sequential trials is based on the posterior probability that a treatment effect exceeds a minimum relevant clinical threshold. In this paper we consider a robust version of this criterion by replacing the single prior distribution with a class of prior distributions. We compare the average sample sizes of the robust sequential approach both with the sample ...

An iterative univariate minimizer (line search) is often used to generate a steplength in each step of a descent method for minimizing a multivariate function. The line search performance strongly depends on the choice of the stopping rule enforced. This termination criterion and other algorithmic details also affect the overall efficiency of the multivariate minimization procedure. Here we pro...