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Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian framework offers a unique advantage over the classical framework, especially when incorporating prior information into a new trial with quality external data, such as historical data or another source of co-data. In recent years, there has been a significant increase in regulatory submissions using Bayesian statistics due to its flexibility and ability to provide valuable insights for decision-making, addressing the modern complexity of clinical trials where frequentist trials are inadequate. For regulatory submissions, companies often need to consider the frequentist operating characteristics of the Bayesian analysis strategy, regardless of the design complexity. In particular, the focus is on the frequentist type I error rate and power for all realistic alternatives. This tutorial review aims to provide a comprehensive overview of the use of Bayesian statistics in sample size determination, control of type I error rate, multiplicity adjustments, external data borrowing, etc., in the regulatory environment of clinical trials. Fundamental concepts of Bayesian sample size determination and illustrative examples are provided to serve as a valuable resource for researchers, clinicians, and statisticians seeking to develop more complex and innovative designs. [ABSTRACT FROM AUTHOR]

In conceptual properties norming studies (CPNs), participants list properties that describe a set of concepts. From CPNs, many different parameters are calculated, such as semantic richness. A generally overlooked issue is that those values are only point estimates of the true unknown population parameters. In the present work, we present an R package that allows us to treat those values as population parameter estimates. Relatedly, a general practice in CPNs is using an equal number of participants who list properties for each concept (i.e., standardizing sample size). As we illustrate through examples, this procedure has negative effects on data's statistical analyses. Here, we argue that a better method is to standardize coverage (i.e., the proportion of sampled properties to the total number of properties that describe a concept), such that a similar coverage is achieved across concepts. When standardizing coverage rather than sample size, it is more likely that the set of concepts in a CPN all exhibit a similar representativeness. Moreover, by computing coverage the researcher can decide whether the CPN reached a sufficiently high coverage, so that its results might be generalizable to other studies. The R package we make available in the current work allows one to compute coverage and to estimate the necessary number of participants to reach a target coverage. We show this sampling procedure by using the R package on real and simulated CPN data. [ABSTRACT FROM AUTHOR]

Many sample size criteria exist. These include power calculations and methods based on confidence interval widths from a frequentist viewpoint, and Bayesian methods based on credible interval widths or decision theory. Bayesian methods account for the inherent uncertainty of inputs to sample size calculations through the use of prior information rather than the point estimates typically used by frequentist methods. However, the choice of prior density can be problematic because there will almost always be different appreciations of the past evidence. Such differences can be accommodated a priori by robust methods for Bayesian design, for example, using mixtures or ϵ-contaminated priors. This would then ensure that the prior class includes divergent opinions. However, one may prefer to report several posterior densities arising from a "community of priors," which cover the range of plausible prior densities, rather than forming a single class of priors. To date, however, there are no corresponding sample size methods that specifically account for a community of prior densities in the sense of ensuring a large-enough sample size for the data to sufficiently overwhelm the priors to ensure consensus across widely divergent prior views. In this paper, we develop methods that account for the variability in prior opinions by providing the sample size required to induce posterior agreement to a prespecified degree. Prototypic examples to one- and two-sample binomial outcomes are included. We compare sample sizes from criteria that consider a family of priors to those that would result from previous interval-based Bayesian criteria. [ABSTRACT FROM AUTHOR]

Multilevel mediation analyses play an essential role in helping researchers develop, probe, and refine theories of action underlying interventions and document how interventions impact outcomes. However, little is known about how to plan studies with sufficient power to detect such multilevel mediation effects. In this study, we describe how to prospectively estimate power and identify sufficient sample sizes for experiments intended to detect multilevel mediation effects. We outline a simple approach to estimate the power to detect mediation effects with individual- or cluster-level mediators using summary statistics easily obtained from empirical literature and the anticipated magnitude of the mediation effect. We draw on a running example to illustrate several different types of mediation and provide an accessible introduction to the design of multilevel mediation studies. The power formulas are implemented in the R package PowerUpR and the PowerUp software ( causalevaluation.org ). [ABSTRACT FROM AUTHOR]

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size. [ABSTRACT FROM AUTHOR]

In ethnic sensitivity studies, it is of interest to know whether the same dose has the same effect over populations in different regions. Glasbrenner and Rosenkranz (2006) proposed a criterion for ethnic sensitivity studies in the context of different dose-exposure models. Their method is liberal in the sense that their sample size will not achieve the target power. We will show that the power function can be easily calculated by numeric integration, and the sample size can be determined by bisection. [ABSTRACT FROM AUTHOR]

In recent years, the use of a two-stage seamless design in clinical trials has attracted much attention. A two-stage seamless trial design is referred to as a study design that combines two separate clinical studies that are normally conducted to achieve separate objectives, such as a phase II study for treatment selection and a phase III study for efficacy confirmation. Furthermore, it is not uncommon to consider study endpoints with different treatment durations at different stages (see, e.g., Chow and Chang, 2006; Maca et al., 2006). Chow et al. (2007) and Lu et al. (2009) considered the cases where the study endpoints are continuous variables and binary responses, respectively. In this article, our attention is placed on the case where the study endpoints are time-to-event data with different treatment durations. For testing equality, superiority, and noninferiority/equivalence of two treatments, test statistics for the analysis of the combined data collected from the two stages are developed for Weibull distributed data. In addition, formulas for sample size calculation and sample size allocation between the two stages for each of the hypotheses are derived. Corresponding results are also derived under Cox's proportional hazards model. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper, Finner and Straßburger [2002. The partitioning principle: a powerful tool in multiple decision theory. Ann. Statist. 30, 1194–1213.] introduced a general, weak and strong partitioning principle (SPP), respectively, for the construction of multiple decision procedures, e.g., multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the well-known closure principle and may yield more powerful decision procedures. In this paper, we are concerned with the construction of a step-down procedure for selecting a subset of treatments containing all good treatments by rigorously applying the weak partitioning principle (WPP). This results in some new least favourable parameter configuration (LFC) problems and an improved set of critical values. The new step-down procedure improves the step-down procedure based on the closure principle considerably and decreases the required sample size with respect to a pre-specified power criterion. Various procedures including a Newman–Keuls-type procedure which is related to the SPP and probably the best possible step-down procedure will be compared with respect to power and sample sizes. Finally, we reanalyse an experiment with 13 treatment means. [Copyright &y& Elsevier]

Case-control studies are among the most commonly used means of assessing association between exposure and outcome. Sample size determination and the optimal control-to-case ratio are vital to the design of such studies. In this article we investigate Bayesian sample size determination and the control-to-case ratio for case-control studies, when interval estimation is the goal of the eventual statistical analysis. In certain cases we are able to derive approximate closed-form sample size formulas. We also describe two Monte Carlo methods, each of which provides a unified approach to the sample size problem, because they may be applied to a wide range of interval-based criteria. We compare the accuracy of the different methods. We also extend our methods to include cross-sectional designs and designs for gene-environment interaction studies. [ABSTRACT FROM AUTHOR]

In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms of a threshold value δ > 0. We reformulate the original selection problem as a multiple testing problem and develop various step-down and step-up procedures by applying the closure principle and partitioning principles. The new step-down procedure is shown to provide a uniform improvement over procedures currently in use. Moreover, we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures. [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]

Important similarities and differences are known to exist between the von Mises and wrapped normal distributions, two of the principal models for circular data. In this paper, we consider likelihood-based approaches to determining the sample size required in order to reliably discriminate between the two models. We make use of three new misclassification probability-based criteria to establish lower and upper bounds for the sample size. [ABSTRACT FROM AUTHOR]

Background: Sample size planning for longitudinal data is crucial when designing mediation studies because sufficient statistical power is not only required in grant applications and peer-reviewed publications, but is essential to reliable research results. However, sample size determination is not straightforward for mediation analysis of longitudinal design.Methods: To facilitate planning the sample size for longitudinal mediation studies with a multilevel mediation model, this article provides the sample size required to achieve 80% power by simulations under various sizes of the mediation effect, within-subject correlations and numbers of repeated measures. The sample size calculation is based on three commonly used mediation tests: Sobel's method, distribution of product method and the bootstrap method.Results: Among the three methods of testing the mediation effects, Sobel's method required the largest sample size to achieve 80% power. Bootstrapping and the distribution of the product method performed similarly and were more powerful than Sobel's method, as reflected by the relatively smaller sample sizes. For all three methods, the sample size required to achieve 80% power depended on the value of the ICC (i.e., within-subject correlation). A larger value of ICC typically required a larger sample size to achieve 80% power. Simulation results also illustrated the advantage of the longitudinal study design. The sample size tables for most encountered scenarios in practice have also been published for convenient use.Conclusions: Extensive simulations study showed that the distribution of the product method and bootstrapping method have superior performance to the Sobel's method, but the product method was recommended to use in practice in terms of less computation time load compared to the bootstrapping method. A R package has been developed for the product method of sample size determination in mediation longitudinal study design. [ABSTRACT FROM AUTHOR]