Bayesian average error-based approach to sample size calculations for hypothesis testing

Bayesian Design of Superiority Trials: Methods and Applications

In this paper, 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.

Bayesian sample-size determination methods considering both worthwhileness and unpromisingness for exploratory two-arm randomized clinical trials with binary endpoints

A randomized exploratory clinical trial comparing an experimental treatment with a control treatment on a binary endpoint is often conducted to make a go or no-go decision. Such an exploratory trial needs to have an adequate sample size such that it will provide convincing evidence that the experimental treatment is either worthwhile or unpromising relative to the control treatment. In this paper, we propose three new sample-size determination methods for an exploratory trial, which utilize the posterior probabilities calculated from predefined efficacy and inefficacy criteria leading to a declaration of the worthwhileness or unpromisingness of the experimental treatment. Simulation studies, including numerical investigation, showed that all three methods could declare the experimental treatment as worthwhile or unpromising with a high probability when the true response probability of the experimental treatment group is higher or lower, respectively, than that of the control treatment group.

Approaches for testing noninferiority in two-arm trials for risk ratio and odds ratio

For an existing established drug regimen, active control trials are defacto standard due to ethical reason as well as for clinical equipoise. However, when superiority claim of a new drug against the active control is unlikely to be successful, researchers often address the issue in terms of noninferiority (NI), provided the experimental drug demonstrates the evidence of other benefits beyond efficacy. Such trials aim to demonstrate that an experimental treatment is non-inferior to an existing comparator by not more than a pre-specified margin. The issue of choosing such a margin is complex. In this article, two-arm NI trials with binary outcomes are considered when margin is defined in terms of relative risk or odds ratio. A Frequentist test based on proposed NI margin is developed first. Since two-arm NI trials without placebo arm are dependent upon historical information, in order to make accurate and meaningful interpretation of their results, a Bayesian approach is developed next. Bayesian approach is flexible to incorporate the available information from the historical trial. The operating characteristics of the proposed methods are studied in terms of power and sample size for varying design factors. A clinical trial data is reanalyzed to study the properties of the proposed approach.

Hierarchical Bayes approach for subgroup analysis

In clinical data analysis, both treatment effect estimation and consistency assessment are important for a better understanding of the drug efficacy for the benefit of subjects in individual subgroups. The linear mixed-effects model has been used for subgroup analysis to describe treatment differences among subgroups with great flexibility. The hierarchical Bayes approach has been applied to linear mixed-effects model to derive the posterior distributions of overall and subgroup treatment effects. In this article, we discuss the prior selection for variance components in hierarchical Bayes, estimation and decision making of the overall treatment effect, as well as consistency assessment of the treatment effects across the subgroups based on the posterior predictive p-value. Decision procedures are suggested using either the posterior probability or the Bayes factor. These decision procedures and their properties are illustrated using a simulated example with normally distributed response and repeated measurements.

Bayesian Design of Non-Inferiority Clinical Trials via the Bayes Factor

We developed a Bayes factor based approach for the design of non-inferiority clinical trials with a focus on controlling type I error and power. Historical data are incorporated in the Bayesian design via the power prior discussed in Ibrahim and Chen (2000). The properties of the proposed method are examined in detail. An efficient simulation-based computational algorithm is developed to calculate the Bayes factor, type I error and power. The proposed methodology is applied to the design of a non-inferiority medical device clinical trial.

Reporting of core items in hierarchical Bayesian analysis for aggregating N-of-1 trials to estimate population treatment effects is suboptimal

OBJECTIVES

N-of-1 trials can be aggregated to estimate population treatment effects using hierarchical Bayesian models. It is very important to report core items in hierarchical Bayesian analysis. In this study, we assessed reporting of items in hierarchical Bayesian analysis for aggregating N-of-1 trials to estimate population treatment effects.

STUDY DESIGN AND SETTING

This was a systematic literature review of aggregating N-of-1 trials by hierarchical Bayesian models to estimate population treatment effects. A comprehensive search was performed to collect eligible articles. Pilot studies, formal N-of-1 trials and reports in which the data were reanalyzed using hierarchical Bayesian methods, were included. The information of reported items related with hierarchical Bayesian analysis was extracted by two independent reviewers. The guideline "ROBUST," developed for reporting Bayesian analysis of clinical studies, was published in Journal of Clinical Epidemiology in 2005. We assessed the included reports using ROBUST criteria and 18 other important items.

RESULTS

After careful screening, 11 studies were identified to be eligible for inclusion. There were three pilot studies, four formal trials, and four reports in which the data were reanalyzed using hierarchical Bayesian methods. The number of reported items in ROBUST criteria ranged from six to seven, with a median number of six. Five of eleven included articles reported all items of the ROBUST criteria. But for justification and sensitivity analysis in prior distribution items, other items were reported in all of the included articles. Software and analysis data set items were reported the most frequently in additional items excluded from the ROBUST criteria. Less than half of the studies reported the other additional items.

CONCLUSION

Reporting of core items in hierarchical Bayesian analysis for aggregating N-of-1 trials to estimate population treatment effects is suboptimal. A PRISMA-like guidance on reviews of Bayesian N-of-1 trials may be required in the future.

Bayesian methods for the design and analysis of noninferiority trials

The gold standard for evaluating treatment efficacy of a medical product is a placebo-controlled trial. However, when the use of placebo is considered to be unethical or impractical, a viable alternative for evaluating treatment efficacy is through a noninferiority (NI) study where a test treatment is compared to an active control treatment. The minimal objective of such a study is to determine whether the test treatment is superior to placebo. An assumption is made that if the active control treatment remains efficacious, as was observed when it was compared against placebo, then a test treatment that has comparable efficacy with the active control, within a certain range, must also be superior to placebo. Because of this assumption, the design, implementation, and analysis of NI trials present challenges for sponsors and regulators. In designing and analyzing NI trials, substantial historical data are often required on the active control treatment and placebo. Bayesian approaches provide a natural framework for synthesizing the historical data in the form of prior distributions that can effectively be used in design and analysis of a NI clinical trial. Despite a flurry of recent research activities in the area of Bayesian approaches in medical product development, there are still substantial gaps in recognition and acceptance of Bayesian approaches in NI trial design and analysis. The Bayesian Scientific Working Group of the Drug Information Association provides a coordinated effort to target the education and implementation issues on Bayesian approaches for NI trials. In this article, we provide a review of both frequentist and Bayesian approaches in NI trials, and elaborate on the implementation for two common Bayesian methods including hierarchical prior method and meta-analytic-predictive approach. Simulations are conducted to investigate the properties of the Bayesian methods, and some real clinical trial examples are presented for illustration.