Bayesian Sample Size Determination Research Articles

Bayesian Sample Size Determination for Causal Discovery

Bayesian Sample Size Determination for Causal Discovery

Bayesian design of clinical trials using the scale transformed power prior

ABSTRACT There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint.

Bayesian sample size determination for detecting heterogeneity in multi-site replication studies

Bayesian sample size determination for detecting heterogeneity in multi-site replication studies

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

Bayesian sample size determination for coefficient of variation of normal distribution

Sample size determination is an active area of research in statistics. Generally, Bayesian methods provide relatively smaller sample sizes than the classical techniques, particularly average length criterion is more conventional and gives relatively small sample sizes under the given constraints. The objective of this study is to utilize major Bayesian sample size determination techniques for the coefficient of variation of normal distribution and assess their performance by comparing the results with the freqentist approach. To this end, we noticed that the average coverage criterion is the one that provides relatively smaller sample sizes than the worst outcome criterion. By comparing with the existing frequentist studies, we show that a smaller sample size is required in Bayesian methods to achieve the same efficiency.

BayesPPD: An R Package for Bayesian Sample Size Determination Using the Power and Normalized Power Prior for Generalized Linear Models

BayesPPD: An R Package for Bayesian Sample Size Determination Using the Power and Normalized Power Prior for Generalized Linear Models

Practical approaches to Bayesian sample size determination in non-inferiority trials with binary outcomes.

Bayesian analysis of a non-inferiority trial is advantageous in allowing direct probability statements to be made about the relative treatment difference rather than relying on an arbitrary and often poorly justified non-inferiority margin. When the primary analysis will be Bayesian, a Bayesian approach to sample size determination will often be appropriate for consistency with the analysis. We demonstrate three Bayesian approaches to choosing sample size for non-inferiority trials with binary outcomes and review their advantages and disadvantages. First, we present a predictive power approach for determining sample size using the probability that the trial will produce a convincing result in the final analysis. Next, we determine sample size by considering the expected posterior probability of non-inferiority in the trial. Finally, we demonstrate a precision-based approach. We apply these methods to a non-inferiority trial in antiretroviral therapy for treatment of HIV-infected children. A predictive power approach would be most accessible in practical settings, because it is analogous to the standard frequentist approach. Sample sizes are larger than with frequentist calculations unless an informative analysis prior is specified, because appropriate allowance is made for uncertainty in the assumed design parameters, ignored in frequentist calculations. An expected posterior probability approach will lead to a smaller sample size and is appropriate when the focus is on estimating posterior probability rather than on testing. A precision-based approach would be useful when sample size is restricted by limits on recruitment or costs, but it would be difficult to decide on sample size using this approach alone.

Bayesian Design of Superiority Trials: Methods and Applications

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.

Optimal sample size determination for single-arm trials in pediatric and rare populations with Bayesian borrowing

ABSTRACT In many therapeutic areas with unmet medical needs, such as pediatric oncology and rare diseases, one of the deterrent factors for clinical trial interpretability is the limited sample size with less-than-ideal operating characteristics. Single arm is usually the only viable design due to feasibility and ethical concerns. For the trial results to be more interpretable and conclusive, the evaluation of operating characteristics, such as type I error rate and power, and the appropriate utilization of prior information for study design, shall be prespecified and fully investigated during the trial planning phase. So far, very few existing literature addressed optimal sample size determination issues for the planning of pediatric and rare population trials, with majority of research focusing on analysis perspective with focus on Bayesian borrowing. In practice, when a single-arm trial is designed for rare population, it is not uncommon that the only information available is from an earlier trial and/or a few clinical publications based on observational studies, often constituting mixed or uncertain conclusions. In light of this, an optimal Bayesian sample size determination method for single-arm trial with binary or continuous endpoint is proposed, where conflicting prior beliefs can be readily incorporated. Prior effective sample size can be calculated to assess the robustness as well as the prior information borrowed. Moreover, due to the lack of closed-form posterior distributions in general, an alternative approach for calculating Bayesian power is described. Simulation studies are provided to demonstrate the utility of the proposed methods. In addition, a case study in pediatric patients with leukemia is included to illustrate the proposed method with the existing approaches.

Remote, real-time expert elicitation to determine the prior probability distribution for Bayesian sample size determination in international randomised controlled trials: Bronchiolitis in Infants Placebo Versus Epinephrine and Dexamethasone (BIPED) study

BackgroundBayesian 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.MethodsWe 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.ResultsFifteen 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%.ConclusionRemote, 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 registrationClinicalTrials.govNCT03567473

Bayesian sample size determination for diagnostic accuracy studies.

The development of a new diagnostic test ideally follows a sequence of stages which, among other aims, evaluate technical performance. This includes an analytical validity study, a diagnostic accuracy study, and an interventional clinical utility study. In this article, we propose a novel Bayesian approach to sample size determination for the diagnostic accuracy study, which takes advantage of information available from the analytical validity stage. We utilize assurance to calculate the required sample size based on the target width of a posterior probability interval and can choose to use or disregard the data from the analytical validity study when subsequently inferring measures of test accuracy. Sensitivity analyses are performed to assess the robustness of the proposed sample size to the choice of prior, and prior‐data conflict is evaluated by comparing the data to the prior predictive distributions. We illustrate the proposed approach using a motivating real‐life application involving a diagnostic test for ventilator associated pneumonia. Finally, we compare the properties of the approach against commonly used alternatives. The results show that, when suitable prior information is available, the assurance‐based approach can reduce the required sample size when compared to alternative approaches.

Bayesian sample size determination using commensurate priors to leverage preexperimental data.

This paper develops Bayesian sample size formulae for experiments comparing two groups, where relevant preexperimental information from multiple sources can be incorporated in a robust prior to support both the design and analysis. We use commensurate predictive priors for borrowing of information and further place Gamma mixture priors on the precisions to account for preliminary belief about the pairwise (in)commensurability between parameters that underpin the historical and new experiments. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria that control certain aspects of the posterior distribution, such as the coverage probability or length of a defined density region. Our Bayesian methodology can be applied to circumstances that compare two normal means, proportions, or event times. When nuisance parameters (such as variance) in the new experiment are unknown, a prior distribution can further be specified based on preexperimental data. Exact solutions are available based on most of the criteria considered for Bayesian sample size determination, while a search procedure is described in cases for which there are no closed-form expressions. We illustrate the application of our sample size formulae in the design of clinical trials, where pretrial information is available to be leveraged. Hypothetical data examples, motivated by a rare-disease trial with an elicited expert prior opinion, and a comprehensive performance evaluation of the proposed methodology are presented.

Bayesian sample size determination using commensurate priors to leverage pre-experimental data.

This paper develops Bayesian sample size formulae for experiments comparing two groups, where relevant pre-experimental information from multiple sources can be incorporated in a robust prior to support both the design and analysis. We use commensurate predictive priors for borrowing of information, and further place Gamma mixture priors on the precisions to account for preliminary belief about the pairwise (in)commensurability between parameters that underpin the historical and new experiments. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria that control certain aspects of the posterior distribution, such as the coverage probability or length of a defined density region. Our Bayesian methodology can be applied to circumstances that compare two normal means, proportions or event times. When nuisance parameters (such as variance) in the new experiment are unknown, a prior distribution can further be specified based on pre-experimental data. Exact solutions are available based on most of the criteria considered for Bayesian sample size determination, while a search procedure is described in cases for which there are no closed-form expressions. We illustrate the application of our sample size formulae in the design of clinical trials, where pre-trial information is available to be leveraged. Hypothetical data examples, motivated by a rare-disease trial with elicited expert prior opinion, and a comprehensive performance evaluation of the proposed methodology are presented.

Bayesian sample size determination in a three-arm non-inferiority trial with binary endpoints

ABSTRACT 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.

Bayesian sample size determination in a single-server deterministic queueing system

Although queueing models in the mathematical field of queueing theory are mainly studied in the steady-state regime and practical applications are interested mostly in queues in transient situations subject to burst arrivals and congestion, their use is still justified as a first step towards a more complex and thorough analysis. In these practical applications, parameters such as the traffic intensity, which is the ratio between the arrival rate and service rate, are unknown and need to be estimated statistically. In this study, a Markovian arrival and deterministic single-server queueing system, known in Kendall notation as an M∕D∕1 queueing model, is considered. This is one of the simplest queueing models with deterministic service time and may be seen as an approximation of a variety of applications in the performance evaluation of production management, telecommunications networks, and other areas. The main goal of this manuscript is to propose a methodology to determine the sample size for an M∕D∕1 queueing system under the Bayesian setup by observing the number of customer arrivals during the service time of a customer. To verify the efficiency and efficacy of the proposed approach, an extensive set of numerical results is presented and discussed.

The variation of the posterior variance and Bayesian sample size determination

We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for bounding the posterior variance below a prescribed limit under the true sampling distribution. Compared with sample size determination based on the average of the posterior variance the proposed criterion leads to an increase in sample size and significantly improved success rates. Generic asymptotic properties are proven, such as an asymptotic expression for the sample size and a sort of phase transition. Our study is illustrated using two real world datasets with Poisson and normally distributed data. Based on our results some recommendations are given.

Bayesian Sample Size Determination for Joint Modeling of Longitudinal Measurements and Survival Data

Bayesian Sample Size Determination for Joint Modeling of Longitudinal Measurements and Survival Data

Bayesian sample size determination for phase IIA clinical trials using historical data and semi-parametric prior's elicitation.

The Simon's two-stage design is the most commonly applied among multi-stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre-trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two-stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B-splines. The motivating example is the planning of the phase IIA two-stage trial on anti-HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.

Bayesian sample size determination for longitudinal studies with continuous response based on different scientific questions of interest

ABSTRACT Longitudinal study designs are commonly applied in much scientific research, especially in the medical, social, and economic sciences. Longitudinal studies allow researchers to measure changes in each individual’s responses over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. In longitudinal studies, because of the complexity of their design, including the selection of the number of individuals and the number of repeated measurements, sample size determination is less studied. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion. We determine the sample size of a longitudinal study based on the scientific question of interest, by the choice of an appropriate model. Most of the methods of determining sample size are based on the definition of a single hypothesis. In this paper, in addition to using this method, we determine the sample size using multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed.

Bayesian Sample size Determination for Longitudinal Studies with Continuous Response using Marginal Models

Bayesian Sample size Determination for Longitudinal Studies with Continuous Response using Marginal Models