Comparison of Bayesian Sample Size Criteria: ACC, ALC, and WOC

Bayesian statistics for clinical research

Frequentist and Bayesian statistics represent two differing paradigms for the analysis of data. Frequentism became the dominant mode of statistical thinking in medical practice during the 20th century. The advent of modern computing has made Bayesian analysis increasingly accessible, enabling growing use of Bayesian methods in a range of disciplines, including medical research. Rather than conceiving of probability as the expected frequency of an event (purported to be measurable and objective), Bayesian thinking conceives of probability as a measure of strength of belief (an explicitly subjective concept). Bayesian analysis combines previous information (represented by a mathematical probability distribution, the prior) with information from the study (the likelihood function) to generate an updated probability distribution (the posterior) representing the information available for clinical decision making. Owing to its fundamentally different conception of probability, Bayesian statistics offers an intuitive, flexible, and informative approach that facilitates the design, analysis, and interpretation of clinical trials. In this Review, we provide a brief account of the philosophical and methodological differences between Bayesian and frequentist approaches and survey the use of Bayesian methods for the design and analysis of clinical research.

Developments in the Design, Conduct, and Reporting of Child Health Trials

To identify priority areas to improve the design, conduct, and reporting of pediatric clinical trials, the international expert network, Standards for Research (StaR) in Child Health, was assembled and published the first 6 Standards in Pediatrics in 2012. After a recent review summarizing the 247 publications by StaR Child Health authors that highlight research practices that add value and reduce research "waste," the current review assesses the progress in key child health trial methods areas: consent and recruitment, containing risk of bias, roles of data monitoring committees, appropriate sample size calculations, outcome selection and measurement, and age groups for pediatric trials. Although meaningful change has occurred within the child health research ecosystem, measurable progress is still disappointingly slow. In this context, we identify and review emerging trends that will advance the agenda of increased clinical usefulness of pediatric trials, including patient and public engagement, Bayesian statistical approaches, adaptive designs, and platform trials. We explore how implementation science approaches could be applied to effect measurable improvements in the design, conducted, and reporting of child health research.

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.

A Closed-Form EVSI Expression for a Multinomial Data-Generating Process

This paper derives analytic expressions for the expected value of sample information (EVSI), the expected value of distribution information, and the optimal sample size when data consists of independent draws from a bounded sequence of integers. Because of the challenges of creating tractable EVSI expressions, most existing work valuing data does so in one of three ways: (1) analytically through closed-form expressions on the upper bound of the value of data, (2) calculating the expected value of data using numerical comparisons of decisions made using simulated data to optimal decisions for which the underlying data distribution is known, or (3) using variance reduction as proxy for the uncertainty reduction that accompanies more data. For the very flexible case of modeling integer-valued observations using a multinomial data-generating process with Dirichlet prior, this paper develops expressions that (1) generalize existing beta-binomial computations, (2) do not require prior knowledge of some underlying “true” distribution, and (3) can be computed prior to the collection of any sample data.

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

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.govNCT03567473

Supplementary Information

The online version contains supplementary material available at 10.1186/s13063-022-06240-w.

Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

The intranasal dexmedetomidine plus ketamine for procedural sedation in children, adaptive randomized controlled non-inferiority multicenter trial (Ketodex): a statistical analysis plan

Background

Procedural sedation and analgesia (PSA) is frequently required to perform closed reductions for fractures and dislocations in children. Intravenous (IV) ketamine is the most commonly used sedative agent for closed reductions. However, as children find IV insertion a distressing and painful procedure, there is need to identify a feasible alternative route of administration. There is evidence that a combination of dexmedetomidine and ketamine (ketodex), administered intranasally (IN), could provide adequate sedation for closed reductions while avoiding the need for IV insertion. However, there is uncertainty about the optimal combination dose for the two agents and whether it can provide adequate sedation for closed reductions. The Intranasal Dexmedetomidine Plus Ketamine for Procedural Sedation (Ketodex) study is a Bayesian phase II/III, non-inferiority trial in children undergoing PSA for closed reductions that aims to address both these research questions. This article presents in detail the statistical analysis plan for the Ketodex trial and was submitted before the outcomes of the trial were available for analysis.

Methods/design

The Ketodex trial is a multicenter, four-armed, randomized, double-dummy controlled, Bayesian response adaptive dose finding, non-inferiority, phase II/III trial designed to determine (i) whether IN ketodex is non-inferior to IV ketamine for adequate sedation in children undergoing a closed reduction of a fracture or dislocation in a pediatric emergency department and (ii) the combination dose for IN ketodex that provides optimal sedation. Adequate sedation will be primarily measured using the Pediatric Sedation State Scale. As secondary outcomes, the Ketodex trial will compare the length of stay in the emergency department, time to wakening, and adverse events between study arms.

Discussion

The Ketodex trial will provide evidence on the optimal dose for, and effectiveness of, IN ketodex as an alternative to IV ketamine providing sedation for patients undergoing a closed reduction. The data from the Ketodex trial will be analyzed from a Bayesian perspective according to this statistical analysis plan. This will reduce the risk of producing data-driven results introducing bias in our reported outcomes.

Trial registration

ClinicalTrials.gov NCT04195256. Registered on December 11, 2019.

Efficient and flexible simulation-based sample size determination for clinical trials with multiple design parameters

Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of sample size determination problems, often minimising a single parameter (the overall sample size) subject to power being above a target level. We describe a general framework for solving simulation-based sample size determination problems with several design parameters over which to optimise and several conflicting criteria to be minimised. The method is based on an established global optimisation algorithm widely used in the design and analysis of computer experiments, using a non-parametric regression model as an approximation of the true underlying power function. The method is flexible, can be used for almost any problem for which power can be estimated using simulation, and can be implemented using existing statistical software packages. We illustrate its application to a sample size determination problem involving complex clustering structures, two primary endpoints and small sample considerations.

A Bayesian response-adaptive dose-finding and comparative effectiveness trial

BACKGROUND/AIMS

Combinations of treatments that have already received regulatory approval can offer additional benefit over Each of the treatments individually. However, trials of these combinations are lower priority than those that develop novel therapies, which can restrict funding, timelines and patient availability. This article develops a novel trial design to facilitate the evaluation of New combination therapies. This trial design combines elements of phase II and phase III trials to reduce the burden of evaluating combination therapies, while also maintaining a feasible sample size. This design was developed for a randomised trial that compares the properties of three combination doses of ketamine and dexmedetomidine, given intranasally, to ketamine delivered intravenously for children undergoing a closed reduction for a fracture or dislocation.

METHODS

This trial design uses response-adaptive randomisation to evaluate different dose combinations and increase the information collected for successful novel drug combinations. The design then uses Bayesian dose-response modelling to undertake a comparative effectiveness analysis for the most successful dose combination against a relevant comparator. We used simulation methods determine the thresholds for adapting the trial and making conclusions. We also used simulations to evaluate the probability of selecting the dose combination with the highest true effectiveness the operating characteristics of the design and its Bayesian predictive power.

RESULTS

With 410 participants, five interim updates of the randomisation ratio and a probability of effectiveness of 0.93, 0.88 and 0.83 for the three dose combinations, we have an 83% chance of randomising the largest number of patients to the drug with the highest probability of effectiveness. Based on this adaptive randomisation procedure, the comparative effectiveness analysis has a type I error of less than 5% and a 93% chance of correcting concluding non-inferiority, when the probability of effectiveness for the optimal combination therapy is 0.9. In this case, the trial has a greater than 77% chance of meeting its dual aims of dose-finding and comparative effectiveness. Finally, the Bayesian predictive power of the trial is over 90%.

CONCLUSIONS

By simultaneously determining the optimal dose and collecting data on the relative effectiveness of an intervention, we can minimise administrative burden and recruitment time for a trial. This will minimise the time required to get effective, safe combination therapies to patients quickly. The proposed trial has high potential to meet the dual study objectives within a feasible overall sample size.

Sample size determination for BCI studies: How many subjects and trials?

Sample sizes and, consequently, statistical power have a large influence on the reliability of statistical results, but they are often neglected when planning and reporting studies of brain-computer interfaces (BCIs). This may be in part due to the limitations of classical power calculations, which do not apply to nested experimental designs, that are usually employed in BCI research. In this paper we introduce the methodology of simulation-based sample size determination (SSD) for the planning of BCI studies. We show how the proposed method can be used to determine the necessary number of subjects and trials to obtain a precise estimate of BCI accuracy, when the cost of sampling needs to be constrained by a budget. Furthermore, the method is fully general and can be applied in different experimental designs and in different statistical frameworks.

A Bayesian meta-analysis on prevalence of hepatitis B virus infection among Chinese volunteer blood donors

BACKGROUND

Although transfusion-transmitted infection of hepatitis B virus (HBV) threatens the blood safety of China, the nationwide circumstance of HBV infection among blood donors is still unclear.

OBJECTIVES

To comprehensively estimate the prevalence of HBsAg positive and HBV occult infection (OBI) among Chinese volunteer blood donors through bayesian meta-analysis.

METHODS

We performed an electronic search in Pub-Med, Web of Knowledge, Medline, Wanfang Data and CNKI, complemented by a hand search of relevant reference lists. Two authors independently extracted data from the eligible studies. Then two bayesian random-effect meta-analyses were performed, followed by bayesian meta-regressions.

RESULTS

5957412 and 571227 donors were identified in HBsAg group and OBI group, respectively. The pooled prevalence of HBsAg group and OBI group among donors is 1.085% (95% credible interval [CI] 0.859%~1.398%) and 0.094% (95% CI 0.0578%~0.1655%). For HBsAg group, subgroup analysis shows the more developed area has a lower prevalence than the less developed area; meta-regression indicates there is a significant decreasing trend in HBsAg positive prevalence with sampling year (beta = -0.1202, 95% -0.2081~-0.0312).

CONCLUSION

Blood safety against HBV infection in China is suffering serious threats and the government should take effective measures to improve this situation.