On the distribution of the power function for the scale parameter of exponential families.

The expected value of the standard power function of a test, computed with respect to a design prior distribution, is often used to evaluate the probability of success of an experiment. However, looking only at the expected value might be reductive. Instead, the whole probability distribution of the power function induced by the design prior can be exploited.

A dynamic power prior approach to non-inferiority trials for normal means.

Non-inferiority trials compare new experimental therapies to standard ones (active control). In these experiments, historical information on the control treatment is often available. This makes Bayesian methodology appealing since it allows a natural way to exploit information from past studies.

Borrowing historical information for non-inferiority trials on Covid-19 vaccines.

Non-inferiority vaccine trials compare new candidates to active controls that provide clinically significant protection against a disease. Bayesian statistics allows to exploit pre-experimental information available from previous studies to increase precision and reduce costs. Here, historical knowledge is incorporated into the analysis through a power prior that dynamically regulates the degree of information-borrowing.

Joint control of consensus and evidence in Bayesian design of clinical trials.

In Bayesian inference, prior distributions formalize preexperimental information and uncertainty on model parameters. Sometimes different sources of knowledge are available, possibly leading to divergent posterior distributions and inferences. Research has been recently devoted to the development of sample size criteria that guarantee agreement of posterior information in terms of credible intervals when multiple priors are available.

Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials.

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution.

Continuous endpoints in Bayesian two-stage designs.

Single-arm two-stage designs for phase II of clinical trials typically focus on a binary endpoint obtained by dichotomizing an underlying continuous measure of treatment efficacy. To avoid the resulting loss of information, we propose a two-stage design based on a Bayesian predictive approach that directly uses the original continuous endpoint. Numerical results are provided with reference to phase II cancer trials aimed at assessing tumor shrinking effect of an experimental treatment.

Mixtures of prior distributions for predictive Bayesian sample size calculations in clinical trials.

In this paper we propose a predictive Bayesian approach to sample size determination (SSD) and re-estimation in clinical trials, in the presence of multiple sources of prior information. The method we suggest is based on the use of mixtures of prior distributions for the unknown quantity of interest, typically a treatment effect or an effects-difference. Methodologies are developed using normal models with mixtures of conjugate priors.

Robust Bayesian sample size determination in clinical trials.

This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large.

Accounting for historical information in designing experiments: the Bayesian approach.

Two of the most important statistical problems in human and animal experimentation are the selection of an appropriate number of units to include in a given study and the allocation of these units to the various treatments. Properly addressing these issues allows the units to be used as efficiently as possible, which can contribute to addressing the overall issue of reducing the number of subjects in experimentation. To do so, reliable historical information is of particular importance.