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The scaled-uniform model has been lately considered to illustrate problems in frequentist point estimation arising when the minimal sufficient statistic is not complete. Here we consider the problem of interval estimation and derive pivotal quantities based on a series of point estimators proposed in the literature. We compare the resulting intervals of given confidence level in terms of expected lengths. Pivotal quantities, confidence intervals and expected lengths are all computed using simulations implemented with R (code is available). Numerical results suggest that the maximum likelihood estimator, regardless of its inefficiency, yields confidence intervals that outperform the other available sets of the same level. [ABSTRACT FROM AUTHOR]

In Bayesian inference, the two most widely used methods for set estimation of an unknown one-dimensional parameter are equal-tails and highest posterior density intervals. The resulting estimates may be quite different for specific observed samples but, at least for standard but relevant models, they tend to become closer and closer as the sample size increases. In this article we propose a pre-posterior method for measuring the progressive alignment between these two classes of intervals and discuss relationships with the skewness of the posterior distribution. We illustrate the implementation of the method using the software R for the Poisson model and for some standard examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article reviews power priors, a class of prior distributions for an unknown parameter that exploits information from results of previous, similar studies, a situation arising often in clinical trials. The article shows that, for independent and identically distributed historical data, a basic formulation of power priors (geometric priors) can be obtained as the result of a prior updating-and-combining process based on training samples of iid historical data. This formulation gives an operational justification to power priors. It also allows us to relate the discount scalar quantity controlling the influence of historical information on final inference to the size of training samples. Properties of power priors and their extension to more complex set-ups are discussed. Then several examples are provided of their use in the analysis of clinical trials data. The approach is shown to be appropriate for handling problems arising when information is combined from different studies, such as lack of exchangeability between preceding and current data, and the risk that prior information overwhelms evidence from the study in question. [ABSTRACT FROM AUTHOR]

This article considers a robust Bayesian approach to the sample size determination problem. We focus on global Bayesian robustness that studies lower bound (Ln), upper bound (Un), and range (Rn) of posterior quantities of interest, obtained as the prior varies in a class of distributions. Specifically, we are interested in the selection of an appropriate sample size that gives guarantees to the researcher of observing a small value of the range and, depending on the problems, either a sufficiently large lower bound or a sufficiently small upper bound. Toward this end, we approach the problem as a design issue and provide new sample size determination criteria based on summaries of the predictive distributions of Ln, Un, and Rn, such as expectations and tail probabilities. Relationships and comparison to standard classical and (nonrobust) Bayesian methods are discussed. The proposed methods are studied for the normal model with conjugate priors and used for choosing the size of a clinical trial. [ABSTRACT FROM AUTHOR]