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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]

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]

Over the past decades, the process of the traditional drug discovery study spent tremendous time and resources. More and more studies have shown that genetic determinants may mediate variability among persons in the response to a drug. In this article, the proposed method is considered for genetic heterogeneity in Simon's two-stage design for a phase II clinical trial. We try to propose the method to employ the phase II clinical trial based on the existence of the epidemiological evidence for genetic heterogeneity. For our proposed method, Simon's two-stage design is conditional on the probability of the genetic heterogeneity. The example is used to illustrate how to calculate sample size in given parameters. [ABSTRACT FROM AUTHOR]

We begin with a discussion of results on the asymptotic properties associated with purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean when the distribution is unspecified, under squared error loss (SEL) plus the cost of sampling. We proceed to show that, given certain moment conditions, such properties can be extended to estimation problems under a broader class of loss functions, namely: first order risk-efficiency under powered absolute error loss (PAEL) plus the powered cost of sampling. In addition to purely sequential strategy, we also prove these asymptotic properties for a more operationally convenient, accelerated sequential procedure. We follow-up with extensive data analyses from simulations under mixture distributions. We conclude with illustrations using data from two cancer studies. [ABSTRACT FROM AUTHOR]

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non‐randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre‐specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In this study we consider the problem of sample size determination for clustered count data based on clustered discrete Weibull regression model. Many papers that deal with sample size calculation for clustered count data have a strong assumption about the dispersion type of the data. Poisson, negative binomial are widely used models however their assumptions are hard to be met in real life. Here we propose to use discrete Weibull regression model which can handle both under and over dispersed type of data for clustered count data when calculating the sample size. We incorporate a random intercept to consider the correlation between the subjects in each cluster. We used the h-likelihood method and Monte Carlo simulation to estimate the required sample size for clustered count data. Extensive simulation study is also performed to examine the effect of the skewness of the data, variance of the random effect and the number of the clusters on calculating the required sample calculation. [ABSTRACT FROM AUTHOR]

We discuss three issues. In the first part, we discuss the criteria emphasized by Maurer, Bretz, and Xun, warning that it modifies the per comparison error rate that does not address the concerns raised by multiple testing. In the second part, we strengthen the optimality results developed in the paper, based on our recent results. In the third part, we highlight the potentially important role that the use of weights may have in practice and discuss the difficulties in assigning weights that convey the importance in the gain and loss functions, especially as it pertains to multiple endpoints. [ABSTRACT FROM AUTHOR]

Abstract Prior research has suggested that clustered regression discontinuity designs are a formidable alternative to cluster randomized designs because they provide targeted treatment assignment while maintaining a high-quality basis for inferences on local treatment effects. However, methods for the design and analysis of clustered regression discontinuity designs have not been fully developed to address the array of core effects (e.g., main, moderation and mediation) typically examined in education studies. In this study, we complement prior design literature by developing principles of estimation, sampling variability, and closed-form expressions to predict the statistical power to detect mediation effects in clustered regression discontinuity designs. The results suggest that sample sizes typically seen in educational intervention studies (e.g., about 50 schools) can be sufficient to detect a mediation effect under some conditions when studies are carefully designed. We implement the results in software and a Shiny App (BLINDED FOR REVIEW). [ABSTRACT FROM AUTHOR]

Sample sizes of Phase 2 dose‐finding studies, usually determined based on a power requirement to detect a significant dose–response relationship, will generally not provide adequate precision for Phase 3 target dose selection. We propose to calculate the sample size of a dose‐finding study based on the probability of successfully identifying the target dose within an acceptable range (e.g., 80%–120% of the target) using the multiple comparison and modeling procedure (MCP‐Mod). With the proposed approach, different design options for the Phase 2 dose‐finding study can also be compared. Due to inherent uncertainty around an assumed true dose–response relationship, sensitivity analyses to assess the robustness of the sample size calculations to deviations from modeling assumptions are recommended. Planning for a hypothetical Phase 2 dose‐finding study is used to illustrate the main points. Codes for the proposed approach is available at https://github.com/happysundae/posMCPMod. [ABSTRACT FROM AUTHOR]

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016). [ABSTRACT FROM AUTHOR]

Pragmatic trials evaluating health care interventions often adopt cluster randomization due to scientific or logistical considerations. Systematic reviews have shown that coprimary endpoints are not uncommon in pragmatic trials but are seldom recognized in sample size or power calculations. While methods for power analysis based on K (K≥2$K\ge 2$) binary coprimary endpoints are available for cluster randomized trials (CRTs), to our knowledge, methods for continuous coprimary endpoints are not yet available. Assuming a multivariate linear mixed model (MLMM) that accounts for multiple types of intraclass correlation coefficients among the observations in each cluster, we derive the closed‐form joint distribution of K treatment effect estimators to facilitate sample size and power determination with different types of null hypotheses under equal cluster sizes. We characterize the relationship between the power of each test and different types of correlation parameters. We further relax the equal cluster size assumption and approximate the joint distribution of the K treatment effect estimators through the mean and coefficient of variation of cluster sizes. Our simulation studies with a finite number of clusters indicate that the predicted power by our method agrees well with the empirical power, when the parameters in the MLMM are estimated via the expectation‐maximization algorithm. An application to a real CRT is presented to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The idea that medical treatment costs and outcomes might be connected is not new. Likewise, as long as researchers have been designing clinical trials and public opinion polls, there has been interest in the sample size necessary to obtain a desired level of precision and certainty before collecting the data. However, researchers continue to adapt cost-effectiveness models for scenarios of ever-increasing complexity, and equally adaptable sample size determination schemes are required. Of interest for the current study are those instances wherein a non-trivial proportion of patients incur zero costs associated with their treatment. We propose a sample size determination scheme for a cost-effectiveness model fit to such a scenario. Furthermore, we display our method's usefulness on multiple parameter configurations derived from applications presented in already published research. [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]

In a sequential hypothesis test, the analyst checks at multiple steps during data collection whether sufficient evidence has accrued to make a decision about the tested hypotheses. As soon as sufficient information has been obtained, data collection is terminated. Here, we compare two sequential hypothesis testing procedures that have recently been proposed for use in psychological research: Sequential Probability Ratio Test (SPRT; Psychological Methods, 25(2), 206–226, 2020) and the Sequential Bayes Factor Test (SBFT; Psychological Methods, 22(2), 322–339, 2017). We show that although the two methods have different philosophical roots, they share many similarities and can even be mathematically regarded as two instances of an overarching hypothesis testing framework. We demonstrate that the two methods use the same mechanisms for evidence monitoring and error control, and that differences in efficiency between the methods depend on the exact specification of the statistical models involved, as well as on the population truth. Our simulations indicate that when deciding on a sequential design within a unified sequential testing framework, researchers need to balance the needs of test efficiency, robustness against model misspecification, and appropriate uncertainty quantification. We provide guidance for navigating these design decisions based on individual preferences and simulation-based design analyses. [ABSTRACT FROM AUTHOR]

In this article, we lay out the basic elements of Bayesian sample size determination (SSD) for the Bayesian design of a two-arm superiority clinical trial. We develop a flowchart of the Bayesian SSD that highlights the critical components of a Bayesian design and provides a practically useful roadmap for designing a Bayesian clinical trial in real world applications. We empirically examine the amount of borrowing, the choice of noninformative priors, and the impact of model misspecification on the Bayesian Type I error and power. A formal and statistically rigorous formulation of conditional borrowing within the decision rule framework is developed. Moreover, by extending the partial borrowing power priors, a new borrowing-by-parts power prior for incorporating historical data is proposed. Computational algorithms are also developed to calculate the Bayesian Type I error and power. Extensive simulation studies are carried out to explore the operating characteristics of the proposed Bayesian design of a superiority trial. [ABSTRACT FROM AUTHOR]

We address sampling design of population pharmacokinetics (popPK) experiments in the context of two phase 2b efficacy trials that evaluate the efficacy of VRC01 (vs. placebo) in reducing the rate of HIV infection among 4625 participants. Blood samples are collected at up to 22 study visits from all participants for immediate HIV diagnosis as the primary trial outcome, and stored for future outcome-dependent marker measurements. A key secondary objective of the trials is to evaluate correlates of prevention efficacy among a subcohort of VRC01 recipients in terms of whether the current value of VRC01 serum concentration is associated with the instantaneous rate of HIV infection. To accomplish this, concentrations on a daily grid are estimated via nonlinear mixed effects popPK modeling of observed 4-weekly concentrations. Given the impracticality of measuring concentrations in all stored blood samples, we devised a simulation-based sampling design framework to evaluate the impact of subcohort sample sizes (m) and sampling schemes of time-points on the accuracy and precision of the popPK model parameters. We accounted for specific study schedules and heterogeneity in participants' characteristics and study adherence patterns. We found that with m = 120, reasonably unbiased and consistent estimates of most fixed and random effect terms could be obtained without complete sampling of all 22 time-points, even under low study adherence (about half of the 4-weekly visits missing per participant). The described simulation framework is not only novel in its application to popPK sampling design for studying correlates of prevention efficacy in a subcohort of the parent trial, but also flexible in accommodating real-life study setup options, and can be generalized to other single- or multiple-dose PK sampling design settings. [ABSTRACT FROM AUTHOR]

A three-arm non-inferiority trial including a test treatment, a reference treatment, and a placebo is recommended to assess the assay sensitivity and internal validity of a trial when applicable. Existing methods for designing and analyzing three-arm trials with binary endpoints are mainly developed from a frequentist viewpoint. However, these methods largely depend on large sample theories. To alleviate this problem, we propose two fully Bayesian approaches, the posterior variance approach and Bayes factor approach, to determine sample size required in a three-arm non-inferiority trial with binary endpoints. Simulation studies are conducted to investigate the performance of the proposed Bayesian methods. An example is illustrated by the proposed methodologies. Bayes factor method always leads to smaller sample sizes than the posterior variance method, utilizing the historical data can reduce the required sample size, simultaneous test requires more sample size to achieve the desired power than the non-inferiority test, the selection of the hyperparameters has a relatively large effect on the required sample size. When only controlling the posterior variance, the posterior variance criterion is a simple and effective option for obtaining a rough outcome. When conducting a previous clinical trial, it is recommended to use the Bayes factor criterion in practical applications. [ABSTRACT FROM AUTHOR]

The criteria used for sample size determination are generally developed based on applying averaging techniques to the possible values a variable can take on. This paper presented new methods for estimation of sample size, in particular for binomial distribution, when an observation on number of successes is available. In this paper, first, the general criteria for the determination of sample size were reviewed. Next, the BDLM process was concisely introduced and fit to the first real-world dataset. Then, based on the model, four new methods for the estimation of the missing total number of trials in binomial time series were developed with the illustrated small dataset, where number of successes at any specific time point was known. In addition, the worst outcome criterion was evaluated based on the highest probability density (HPD) confidence set by using the illustrated data and the results were compared with those of the new methods developed in the present paper. Later, an illustration of COVID-19 trinomial data was presented in which BDLM was fit to the time series of cured cases infected due to COVID-19 disease. Finally, the new methods of estimation of missing total confirmed cases evaluated by the relatively large dataset. [ABSTRACT FROM AUTHOR]

The paper addresses estimating and testing treatment effects with multivariate outcomes in clinical trials where imperfect diagnostic devices are used to assign subjects to treatment groups. The paper focuses on the pre‐post design and proposes two novel methods for estimating and testing treatment effects. In addition, methods for sample size and power calculations are developed. The methods are compared with each other and with a traditional method in a simulation study. The new methods show significant advantages in terms of power, coverage probability, and required sample size. The application of the methods is illustrated with data from electroencephalogram (EEG) recordings of alcoholic and control subjects. [ABSTRACT FROM AUTHOR]

Stepped wedge cluster randomized trials enable rigorous evaluations of health intervention programs in pragmatic settings. In the present study, we aimed to update neurosurgeon scientists on the design of stepped wedge randomized trials. We have presented an overview of recent methodological developments for stepped wedge designs and included an update on the newer associated methodological tools to aid with future study designs. We defined the stepped wedge trial design and reviewed the indications for the design in depth. In addition, key considerations, including mainstream methods of analysis and sample size determination, were discussed. Stepped wedge designs can be attractive for study intervention programs aiming to improve the delivery of patient care, especially when examining a small number of heterogeneous clusters. [ABSTRACT FROM AUTHOR]

Background: Bayesian methods are increasing in popularity in clinical research. The design of Bayesian clinical trials requires a prior distribution, which can be elicited from experts. In diseases with international differences in management, the elicitation exercise should recruit internationally, making a face-to-face elicitation session expensive and more logistically challenging. Thus, we used a remote, real-time elicitation exercise to construct prior distributions. These elicited distributions were then used to determine the sample size of the Bronchiolitis in Infants with Placebo Versus Epinephrine and Dexamethasone (BIPED) study, an international randomised controlled trial in the Pediatric Emergency Research Network (PERN). The BIPED study aims to determine whether the combination of epinephrine and dexamethasone, compared to placebo, is effective in reducing hospital admission for infants presenting with bronchiolitis to the emergency department.Methods: We developed a Web-based tool to support the elicitation of the probability of hospitalisation for infants with bronchiolitis. Experts participated in online workshops to specify their individual prior distributions, which were aggregated using the equal-weighted linear pooling method. Experts were then invited to provide their comments on the aggregated distribution. The average length criterion determined the BIPED sample size.Results: Fifteen paediatric emergency medicine clinicians from Canada, the USA, Australia and New Zealand participated in three workshops to provide their elicited prior distributions. The mean elicited probability of admission for infants with bronchiolitis was slightly lower for those receiving epinephrine and dexamethasone compared to supportive care in the aggregate distribution. There were substantial differences in the individual beliefs but limited differences between North America and Australasia. From this aggregate distribution, a sample size of 410 patients per arm results in an average 95% credible interval length of less than 9% and a relative predictive power of 90%.Conclusion: Remote, real-time expert elicitation is a feasible, useful and practical tool to determine a prior distribution for international randomised controlled trials. Bayesian methods can then determine the trial sample size using these elicited prior distributions. The ease and low cost of remote expert elicitation mean that this approach is suitable for future international randomised controlled trials.Trial Registration: ClinicalTrials.gov NCT03567473. [ABSTRACT FROM AUTHOR]

Abstract–It is common for clinical trials to include strata of patients with different risks of disease. In cancer trial settings, patients with different prior treatment history, tumor stages, metastatic sites may be included in a single trial. This is especially so for early phase studies that are exploratory in nature. In many cases, patient responses from these strata may be ordered. For example, earlier stage patients should have better outcomes than later stage patients. Incorporating such stratum information can lead to increased statistical efficiency and therefore possibly reduce sample sizes. Recent works have begun to deal with this issue for single-arm phase II cancer trials in terms of sample size determination. However, no approaches yet exist to explicitly consider the order constraint. In this article, we propose to use likelihood ratio tests with order constraints for both one-stage and two-stage designs. Our numerical results show that the proposed designs tend to have better power profiles compared with existing methods. A real application of our method to an ongoing phase II study is also included. [ABSTRACT FROM AUTHOR]

The matching problem is known since the beginning of the eighteenth century and Bayesian solutions have been proposed. In this paper, we present a Bayesian analysis of an experiment that also leads to the matching problem. Since in this paper we consider the order in which assignments are made and not only the number of matches, our approach is different from the literature on this problem. Our approach also considers that it is possible to have different abilities for the different objects that will be guessed. Hence, we have a parameter that measures the matching ability for each specific object or assignment. As a consequence, we need to have some replicates of the experiment and a prior distribution for each of the parameters. Conjugate prior distributions for the parameters are discussed. The frequentist solution has a particular Bayesian interpretation under a non-informative prior distribution. A real data set is analyzed using the proposed methodology. [ABSTRACT FROM AUTHOR]

Mediation analyses supply a principal lens to probe the pathways through which a treatment acts upon an outcome because they can dismantle and test the core components of treatments and test how these components function as a coordinated system or theory of action. Experimental evaluation of mediation effects in addition to total effects has become increasingly common but literature has developed only limited guidance on how to plan mediation studies with multi-tiered hierarchical or clustered structures. In this study, we provide methods for computing the power to detect mediation effects in three-level cluster-randomized designs that examine individual- (level one), intermediate- (level two) or cluster-level (level three) mediators. We assess the methods using a simulation and provide examples of a three-level clinic-randomized study (individuals nested within therapists nested within clinics) probing an individual-, intermediate- or cluster-level mediator using the R package PowerUpR and its Shiny application. [ABSTRACT FROM AUTHOR]

Bayesian statistics has been widely utilized as an approach that can incorporate prior knowledge into statistical inference. Tolerance intervals (TI) are the most commonly used statistical methods for product quality assurance. There are two main Bayesian approaches for calculating statistical tolerance intervals: Hamada and Wolfinger. A simulation-based approach was implemented to compare two-sided Wolfinger, Hamada, and frequentist tolerance intervals which control the probability content at a specified level of confidence. As sample sizes increase, compared to frequentist, Hamada TI become more conservative while Wolfinger TI are more liberal. To address this issue, we propose an empirical weighted Bayesian TI approach that is a compromise between Hamada and Wolfinger approaches. The proposed Bayesian TI result in narrower limits in certain scenarios while ensuring the confidence content coverage remains comparable to frequentist. [ABSTRACT FROM AUTHOR]

Conceptual properties norming studies (CPNs) ask participants to produce properties that describe concepts. From that data, different metrics may be computed (e.g., semantic richness, similarity measures), which are then used in studying concepts and as a source of carefully controlled stimuli for experimentation. Notwithstanding those metrics' demonstrated usefulness, researchers have customarily overlooked that they are only point estimates of the true unknown population values, and therefore, only rough approximations. Thus, though research based on CPN data may produce reliable results, those results are likely to be general and coarse-grained. In contrast, we suggest viewing CPNs as parameter estimation procedures, where researchers obtain only estimates of the unknown population parameters. Thus, more specific and fine-grained analyses must consider those parameters' variability. To this end, we introduce a probabilistic model from the field of ecology. Its related statistical expressions can be applied to compute estimates of CPNs' parameters and their corresponding variances. Furthermore, those expressions can be used to guide the sampling process. The traditional practice in CPN studies is to use the same number of participants across concepts, intuitively believing that practice will render the computed metrics comparable across concepts and CPNs. In contrast, the current work shows why an equal number of participants per concept is generally not desirable. Using CPN data, we show how to use the equations and discuss how they may allow more reasonable analyses and comparisons of parameter values among different concepts in a CPN, and across different CPNs. [ABSTRACT FROM AUTHOR]

Summary: In assessing biosimilarity between two products, the question to ask is always "How similar is similar?" Traditionally, the equivalence of the means between products is the primary consideration in a clinical trial. This study suggests an alternative assessment for testing a certain percentage of the population of differences lying within a prespecified interval. In doing so, the accuracy and precision are assessed simultaneously by judging whether a two‐sided tolerance interval falls within a prespecified acceptance range. We further derive an asymptotic distribution of the tolerance limits to determine the sample size for achieving a targeted level of power. Our numerical study shows that the proposed two‐sided tolerance interval test controls the type I error rate and provides sufficient power. A real example is presented to illustrate our proposed approach. [ABSTRACT FROM AUTHOR]

This article investigates the homogeneity testing problem of binomial proportions for stratified partially validated data obtained by double-sampling method with two fallible classifiers. Several test procedures, including the weighted-least-squares test with/without log-transformation, logit-transformation and double log-transformation, and likelihood ratio test and score test, are developed to test the homogeneity under two models, distinguished by conditional independence assumption of two classifiers. Simulation results show that score test performs better than other tests in the sense that the empirical size is generally controlled around the nominal level, and hence be recommended to practical applications. Other tests also perform well when both binomial proportions and sample sizes are not small. Approximate sample sizes based on score test, likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the estimated sample sizes, and hence be recommended. An example from the malaria study is illustrated by the proposed methodologies. [ABSTRACT FROM AUTHOR]

SUMMARY: The feasibility of a new clinical trial may be increased by incorporating historical data of previous trials. In the particular case where only data from a single historical trial are available, there exists no clear recommendation in the literature regarding the most favorable approach. A main problem of the incorporation of historical data is the possible inflation of the type I error rate. A way to control this type of error is the so‐called power prior approach. This Bayesian method does not "borrow" the full historical information but uses a parameter 0 ≤ δ ≤ 1 to determine the amount of borrowed data. Based on the methodology of the power prior, we propose a frequentist framework that allows incorporation of historical data from both arms of two‐armed trials with binary outcome, while simultaneously controlling the type I error rate. It is shown that for any specific trial scenario a value δ > 0 can be determined such that the type I error rate falls below the prespecified significance level. The magnitude of this value of δ depends on the characteristics of the data observed in the historical trial. Conditionally on these characteristics, an increase in power as compared to a trial without borrowing may result. Similarly, we propose methods how the required sample size can be reduced. The results are discussed and compared to those obtained in a Bayesian framework. Application is illustrated by a clinical trial example. [ABSTRACT FROM AUTHOR]

A disease prevalence can be estimated by classifying subjects according to whether they have the disease. When gold-standard tests are too expensive to be applied to all subjects, partially validated data can be obtained by double-sampling in which all individuals are classified by a fallible classifier, and some of individuals are validated by the gold-standard classifier. However, it could happen in practice that such infallible classifier does not available. In this article, we consider two models in which both classifiers are fallible and propose four asymptotic test procedures for comparing disease prevalence in two groups. Corresponding sample size formulae and validated ratio given the total sample sizes are also derived and evaluated. Simulation results show that (i) Score test performs well and the corresponding sample size formula is also accurate in terms of the empirical power and size in two models; (ii) the Wald test based on the variance estimator with parameters estimated under the null hypothesis outperforms the others even under small sample sizes in Model II, and the sample size estimated by this test is also accurate; (iii) the estimated validated ratios based on all tests are accurate. The malarial data are used to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data. [ABSTRACT FROM AUTHOR]

Now we develop a tolerance interval considering multiple components in the variance from the measurements to deal with the environment or ethnic factor in the multi-regional trial. The idea is to construct a tolerance interval for a multi-regional trial under a sampling plan. Assuming that the environmental or ethnic effect exists, a sampling plan is derived to ensure that there is a desired probability for the tolerance interval. In this paper, we address the issue that the environmental or ethnic effect exists among regions to design a multi-regional trial. [ABSTRACT FROM AUTHOR]

As described in the ICH E5 guidelines, a bridging study is an additional study executed in a new geographical region or subpopulation to link or "build a bridge" from global clinical trial outcomes to the new region. The regulatory and scientific goals of a bridging study is to evaluate potential subpopulation differences while minimizing duplication of studies and meeting unmet medical needs expeditiously. Use of historical data (borrowing) from global studies is an attractive approach to meet these conflicting goals. Here, we propose a practical and relevant approach to guide the optimal borrowing rate (percent of subjects in earlier studies) and the number of subjects in the new regional bridging study. We address the limitations in global/regional exchangeability through use of a Bayesian power prior method and then optimize bridging study design with a return on investment viewpoint. The method is demonstrated using clinical data from global and Japanese trials in dapagliflozin for type 2 diabetes. [ABSTRACT FROM AUTHOR]

Correlated bilateral data arise from stratified studies involving paired body organs in a subject. When it is desirable to conduct inference on the scale of risk difference, one needs first to assess the assumption of homogeneity in risk differences across strata. For testing homogeneity of risk differences, we herein propose eight methods derived respectively from weighted-least-squares (WLS), the Mantel-Haenszel (MH) estimator, the WLS method in combination with inverse hyperbolic tangent transformation, and the test statistics based on their log-transformation, the modified Score test statistic and Likelihood ratio test statistic. Simulation results showed that four of the tests perform well in general, with the tests based on the WLS method and inverse hyperbolic tangent transformation always performing satisfactorily even under small sample size designs. The methods are illustrated with a dataset. [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]

Aims: Bioequivalence (BE) trials aim to demonstrate that the 90% confidence interval of the T/R‐ratio of the pharmacokinetic metrics between two formulations (test [T] and reference [R]) of a drug is fully included in the acceptance interval [0.80, 1.25]. Traditionally, the sample size of BE trials is based on a power calculation based on the intrasubject variability coefficient of variation (CV) and the T/R‐ratio of the metrics. Since the exact value of the T/R‐ratio is not known prior to the trial, it is often assumed that the difference between the treatments does not exceed 5%. Hence, uncertainty about the T/R‐ratio is expressed by using a fixed value for the sample size calculation. We propose to characterise the uncertainty about the T/R‐ratio by a (normal) distribution for the log(T/R‐ratio), with an assumed mean of  log θ = 0.00 (i.e. θ = 1.00) and a standard deviation σu, which quantifies the uncertainty. Evaluating this distribution leads to the statistical assurance of the BE trial. Methods: The assurance of a clinical trial can be derived by integrating the power over the distribution of the input parameters, in this case, the assumed distribution of the log(T/R)‐ratio. Because it is an average power, the assurance can be interpreted as a measure of the probability of success that does not depend on a specific assumed value for the log(T/R)‐ratio. The relationship between power and assurance will be analysed by comparing the numerical outcomes. Results: Using the assurance concept, values of the standard deviation for the distribution of potential log(T/R)‐ratios can be chosen to reflect the magnitude of uncertainty. For most practical cases (i.e. when 0.95 ≤ θ ≤ 1.05), the sample size is not, or only slightly, changed when σ = |log(θ)|. Conclusion: The advantage of deriving the assurance for BE trials is that uncertainty is directly expressed as a parameter of variability. [ABSTRACT FROM AUTHOR]

Reliability experiments determine which factors drive product reliability. Often, the reliability or lifetime data collected in these experiments tend to follow distinctly non‐normal distributions and typically include censored observations. The experimental design should accommodate the skewed nature of the response and allow for censored observations, which occur when products do not fail within the allotted test time. To account for these design and analysis considerations, Monte‐Carlo simulations are frequently used to evaluate experimental design properties. Simulation provides accurate power calculations as a function of sample size, allowing researchers to determine adequate sample sizes at each level of the treatment. However, simulation may be inefficient for comparing multiple experiments of various sizes. We present a closed‐form approach for calculating power, based on the noncentral chi‐squared approximation to the distribution of the likelihood ratio statistic for large samples. The solution can be used to rapidly compare multiple designs and accommodate trade‐space analyses between power, effect size, model formulation, sample size, censoring rates, and design type. To demonstrate the efficiency of our approach, we provide a comparison to estimates from simulation. [ABSTRACT FROM AUTHOR]

We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma. [ABSTRACT FROM AUTHOR]

Multiregional clinical trials have been accepted in recent years as a useful means of accelerating the development of new drugs and abridging their approval time. The statistical properties of multiregional clinical trials are being widely discussed. In practice, variance of a continuous response may be different from region to region, but it leads to the assessment of the efficacy response falling into a Behrens-Fisher problem-there is no exact testing or interval estimator for mean difference with unequal variances. As a solution, this study applies interval estimations of the efficacy response based on Howe's, Cochran-Cox's, and Satterthwaite's approximations, which have been shown to have well-controlled type I error rates. However, the traditional sample size determination cannot be applied to the interval estimators. The sample size determination to achieve a desired power based on these interval estimators is then presented. Moreover, the consistency criteria suggested by the Japanese Ministry of Health, Labour and Welfare guidance to decide whether the overall results from the multiregional clinical trial obtained via the proposed interval estimation were also applied. A real example is used to illustrate the proposed method. The results of simulation studies indicate that the proposed method can correctly determine the required sample size and evaluate the assurance probability of the consistency criteria. [ABSTRACT FROM AUTHOR]

In pediatric drug development, large amounts of adult data are often available before the start of a pediatric study. It is believed that borrowing this information will improve the efficiency. However, when adult information is not sufficiently similar to that of pediatrics, incorporating adult data will introduce bias and consequently result in efficiency loss. A Bayesian alternative—namely, commensurate prior approach where the level of information borrowing is based on the concordance of adult and pediatric data—was investigated. Simulation results indicate that the commensurate prior approach, in general, provides a balanced and robust trade‐off between bias and efficiency gain. The benefit of this approach was quantified in terms of sample size savings, and recommended sample sizes are provided. [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]

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example. [ABSTRACT FROM AUTHOR]

In this paper, we develop a general Bayesian clinical trial design methodology, tailored for time-to-event trials with a cured fraction in scenarios where a previously completed clinical trial is available to inform the design and analysis of the new trial. Our methodology provides a conceptually appealing and computationally feasible framework that allows one to construct a fixed, maximally informative prior a priori while simultaneously identifying the minimum sample size required for the new trial so that the design has high power and reasonable type I error control from a Bayesian perspective. This strategy is particularly well suited for scenarios where adaptive borrowing approaches are not practical due to the nature of the trial, complexity of the model, or the source of the prior information. Control of a Bayesian type I error rate offers a sensible balance between wanting to use high-quality information in the design and analysis of future trials while still controlling type I errors in an equitable way. Moreover, sample size determination based on our Bayesian view of power can lead to a more adequately sized trial by virtue of taking into account all the uncertainty in the treatment effect. We demonstrate our methodology by designing a cancer clinical trial in high-risk melanoma. [ABSTRACT FROM AUTHOR]

When there are more than two treatments under comparison, we may consider the use of the incomplete block crossover design (IBCD) to save the number of patients needed for a parallel groups design and reduce the duration of a crossover trial. We develop an asymptotic procedure for simultaneously testing equality of two treatments versus a control treatment (or placebo) in frequency data under the IBCD with two periods. We derive a sample size calculation procedure for the desired power of detecting the given treatment effects at a nominal-level and suggest a simple ad hoc adjustment procedure to improve the accuracy of the sample size determination when the resulting minimum required number of patients is not large. We employ Monte Carlo simulation to evaluate the finitesample performance of the proposed test, the accuracy of the sample size calculation procedure, and that with the simple ad hoc adjustment suggested here. We use the data taken as a part of a crossover trial comparing the number of exacerbations between using salbutamol or salmeterol and a placebo in asthma patients to illustrate the sample size calculation procedure. [ABSTRACT FROM AUTHOR]

In this article, we evaluate the relative cost of a targeted design to an untargeted design for a randomized clinical trial comparing a new treatment to a control. We observed that when the ratio of screen cost per person and drug cost per person is very small, say 0.008, the trial cost for conducting a targeted design might be fewer than that for conducting an untargeted design. When the difference between the treatment effect for the targeted patients and the treatment effect for the untargeted patients is increased, the savings in trial cost for the targeted design would be increased significantly. The greater sensitivity and specificity for the screen tool will lead to greater savings in trial cost for the targeted design. The relative cost of a targeted design to an untargeted design is associated with the treatment effect difference between targeted and untargeted patients, the proportion of targeted patients in the population, the screen tool performance, and the ratio of drug cost per person and screen cost per person. [ABSTRACT FROM PUBLISHER]

A well-designed clinical trial requires an appropriate sample size with adequate statistical power to address trial objectives. The statistical power is traditionally defined as the probability of rejecting the null hypothesis with a pre-specified true clinical treatment effect. This power is a conditional probability conditioned on the true but actually unknown effect. In practice, however, this true effect is never a fixed value. Thus, we discuss a newly proposed alternative to this conventional statistical power:statistical assurance, defined as the unconditional probability of rejecting the null hypothesis. This kind of assurance can then be obtained as an expected power where the expectation is based on the prior probability distribution of the unknown treatment effect, which leads to the Bayesian paradigm. In this article, we outline the transition from conventional statistical power to the newly developed assurance and discuss the computations of assurance using Monte Carlo simulation-based approach. [ABSTRACT FROM AUTHOR]

For the archaeobotanical analysis of waterlogged sediments, which are usually very rich in organic remains, subsampling is often necessary. Subsampling strategies for this kind of material are mostly based on non-empirical experience and have rarely been tested. In this paper, we compare results from small-volume subsamples with those from the large-volume residue of the master sample subsamples were drawn from. The extra-variability caused by lumpiness of the unprocessed waterlogged sediment was quantified in order to find out how much the necessary sample sizes need to increase for this type of sediment. We found that subsampling of unprocessed waterlogged material in general should only be done if it is indispensable, as it can introduce a bias. We propose methods to adapt sample sizes based on random sampling for unprocessed waterlogged sediment (where random sampling is impossible) so that the proportions or also the diversity of plant species can be estimated with sufficient precision in these sediments. However, it would be best to use an appropriate sieving method first and then subsample the processed residues of the material. We also think that it is important to clearly present the methods used for subsampling in publications and that more detailed tests about subsampling should be performed. [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 1992, the US Food and Drug Administration declared that two drugs demonstrate average bioequivalence (ABE) if the log-transformed mean difference of pharmacokinetic responses lies in (-0.223, 0.223). The most widely used approach for assessing ABE is the two one-sided tests procedure. More specifically, ABE is concluded when a 100(1 - 2α) % confidence interval for mean difference falls within (-0.223, 0.223). As known, bioequivalent studies are usually conducted by crossover design. However, in the case that the half-life of a drug is long, a parallel design for the bioequivalent study may be preferred. In this study, a two-sided interval estimation - such as Satterthwaite's, Cochran-Cox's, or Howe's approximations - is used for assessing parallel ABE. We show that the asymptotic joint distribution of the lower and upper confidence limits is bivariate normal, and thus the sample size can be calculated based on the asymptotic power so that the confidence interval falls within (-0.223, 0.223). Simulation studies also show that the proposed method achieves sufficient empirical power. A real example is provided to illustrate the proposed method. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Cross-sectional prevalent cohort design has drawn considerable interests in the studies of association between risk factors and time-to-event outcome. The sampling scheme in such design gives rise to length-biased data that require specialized analysis strategy but can improve study efficiency. The power and sample size calculation methods are however lacking for studies with prevalent cohort design, and using the formula developed for traditional survival data may overestimate sample size. We derive the sample size formulas that are appropriate for the design of cross-sectional prevalent cohort studies, under the assumptions of exponentially distributed event time and uniform follow-up for cross-sectional prevalent cohort design. We perform numerical and simulation studies to compare the sample size requirements for achieving the same power between prevalent cohort and incident cohort designs. We also use a large prospective prevalent cohort study to demonstrate the procedure. Using rigorous designs and proper analysis tools, the prospective prevalent cohort design can be more efficient than the incident cohort design with the same total sample sizes and study durations. [ABSTRACT FROM AUTHOR]