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The hybrid frequentist-Bayesian approach to sample size determination is based on the expectation of the power function of a test with respect to a design prior for the unknown parameter value. In clinical trials this quantity is often called probability of success (PoS). Determination of the limiting value of PoS as the number of observations tends to infinity, that is crucial for well defined sample size criteria, has been considered in previous articles. Here, we focus on the asymptotic behavior of the whole distribution of the power function induced by the design prior. Under mild conditions, we provide asymptotic results for the three most common classes of hypotheses on a scalar parameter. The impact of the design parameters choice on the distribution of the power function and on its limit is discussed. [ABSTRACT FROM AUTHOR]

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. In this article we consider one‐sided testing for the scale parameter of exponential families and we derive general unifying expressions for cumulative distribution and density functions of the random power. Sample size determination criteria based on alternative summaries of these functions are discussed. The study sheds light on the relevance of the choice of the design prior in order to construct a successful experiment. [ABSTRACT FROM AUTHOR]

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. We examine non-inferiority tests based on credible intervals for the unknown effects-difference between two vaccines on the log odds ratio scale, with an application to new Covid-19 vaccines. We explore the frequentist properties of the method and we address the sample size determination problem. [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]

In Bayesian decision theory, the performance of an action is measured by its posterior expected loss. In some cases it may be convenient/necessary to use a non-optimal decision instead of the optimal one. In these cases it is important to quantify the additional loss we incur and evaluate whether to use the non-optimal decision or not. In this article we study the predictive probability distribution of a relative measure of the additional loss and its use to define sample size determination criteria in a general testing set-up. [ABSTRACT FROM AUTHOR]

In this article, we consider sample size determination for experiments in which estimation and design are performed by multiple parties. This problem has relevant applications in contexts involving adversarial decision makers, such as control theory, marketing, and drug testing. Specifically, we adopt a decision-theoretic perspective, and we assume that a decision on an unknown parameter of a statistical model involves two actors [ABSTRACT FROM AUTHOR]

Abstract: In the presence of prior information on an unknown parameter of a statistical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However, in many standard parametric problems, this difference tends to decrease for growing sample size. In this paper we consider as a measure of discrepancy (D n ) the squared difference between Bayesian and frequentist point estimators of the parameter of a model. We derive the predictive distribution of D n for finite sample sizes in the case of a one-dimensional exponential family and we study its behavior for increasing sample size. Numerical examples are illustrated for normal models. [Copyright &y& Elsevier]

In this article we consider the sample size determination problem in the context of robust Bayesian parameter estimation of the Bernoulli model. Following a robust approach, we consider classes of conjugate Beta prior distributions for the unknown parameter. We assume that inference is robust if posterior quantities of interest (such as point estimates and limits of credible intervals) do not change too much as the prior varies in the selected classes of priors. For the sample size problem, we consider criteria based on predictive distributions of lower bound, upper bound and range of the posterior quantity of interest. The sample size is selected so that, before observing the data, one is confident to observe a small value for the posterior range and, depending on design goals, a large (small) value of the lower (upper) bound of the quantity of interest. We also discuss relationships with and comparison to non robust and non informative Bayesian methods. [ABSTRACT FROM AUTHOR]

We consider the sample size determination (SSD) problem, which is a basic yet extremely important aspect of experimental design. Specifically, we deal with the Bayesian approach to SSD, which gives researchers the possibility of taking into account pre-experimental information and uncertainty on unknown parameters. At the design stage, this fact offers the advantage of removing or mitigating typical drawbacks of classical methods, which might lead to serious miscalculation of the sample size. In this context, the leading idea is to choose the minimal sample size that guarantees a probabilistic control on the performance of quantities that are derived from the posterior distribution and used for inference on parameters of interest. We are concerned with the use of historical data—i.e. observations from previous similar studies—for SSD. We illustrate how the class of power priors can be fruitfully employed to deal with lack of homogeneity between historical data and observations of the upcoming experiment. This problem, in fact, determines the necessity of discounting prior information and of evaluating the effect of heterogeneity on the optimal sample size. Some of the most popular Bayesian SSD methods are reviewed and their use, in concert with power priors, is illustrated in several medical experimental contexts. [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]

The identification of factors that increase the chances of a certain disease is one of the classical and central issues in epidemiology. In this context, a typical measure of the association between a disease and risk factor is the odds ratio. We deal with design problems that arise for Bayesian inference on the odds ratio in the analysis of case–control studies. We consider sample size determination and allocation criteria for both interval estimation and hypothesis testing. These criteria are then employed to determine the sample size and proportions of units to be assigned to cases and controls for planning a study on the association between the incidence of a non-Hodgkin's lymphoma and exposition to pesticides by eliciting prior information from a previous study. [ABSTRACT FROM AUTHOR]

This paper considers the problem of choosing the sample size for testing hypotheses on the parameters of a model using Bayes factors. Extending the evidential approach outlined in Royall (Statistical Evidence: a Likelihood paradigm. Chapman & Hall, London (1997), J. Amer. Statist. Assoc. 95 (2000) 760) to the Bayesian framework, the predictive criterion proposed for determining the sample size is maximizing the probability of obtaining substantial evidence in favor of the true hypotheses, i.e. minimizing the probabilities of having either misleading or weak evidence. The method is developed for the normal model in several testing problems that arise, for instance, when comparing treatments in clinical trials. [Copyright &y& Elsevier]