Semiparametric Bayesian Testing Procedure for Noninferiority Trials with Binary Endpoints

Borrowing historical information for non-inferiority trials on Covid-19 vaccines

Non-inferiority vaccine trials compare new candidates to active controls that provide clinically significant protection against a disease. Bayesian statistics allows to exploit pre-experimental information available from previous studies to increase precision and reduce costs. Here, historical knowledge is incorporated into the analysis through a power prior that dynamically regulates the degree of information-borrowing. We examine non-inferiority tests based on credible intervals for the unknown effects-difference between two vaccines on the log odds ratio scale, with an application to new Covid-19 vaccines. We explore the frequentist properties of the method and we address the sample size determination problem.

Bayes factors for superiority, non-inferiority, and equivalence designs

Background

In clinical trials, study designs may focus on assessment of superiority, equivalence, or non-inferiority, of a new medicine or treatment as compared to a control. Typically, evidence in each of these paradigms is quantified with a variant of the null hypothesis significance test. A null hypothesis is assumed (null effect, inferior by a specific amount, inferior by a specific amount and superior by a specific amount, for superiority, non-inferiority, and equivalence respectively), after which the probabilities of obtaining data more extreme than those observed under these null hypotheses are quantified by p-values. Although ubiquitous in clinical testing, the null hypothesis significance test can lead to a number of difficulties in interpretation of the results of the statistical evidence.

Methods

We advocate quantifying evidence instead by means of Bayes factors and highlight how these can be calculated for different types of research design.

Results

We illustrate Bayes factors in practice with reanalyses of data from existing published studies.

Conclusions

Bayes factors for superiority, non-inferiority, and equivalence designs allow for explicit quantification of evidence in favor of the null hypothesis. They also allow for interim testing without the need to employ explicit corrections for multiple testing.

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.

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.

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

Under the classical statistical framework, sample size calculations for a hypothesis test of interest maintain prespecified type I and type II error rates. These methods often suffer from several practical limitations. We propose a framework for hypothesis testing and sample size determination using Bayesian average errors. We consider rejecting the null hypothesis, in favor of the alternative, when a test statistic exceeds a cutoff. We choose the cutoff to minimize a weighted sum of Bayesian average errors and choose the sample size to bound the total error for the hypothesis test. We apply this methodology to several designs common in medical studies.

Bayesian methods for design and analysis of safety trials

Safety assessment is essential throughout medical product development. There has been increased awareness of the importance of safety trials recently, in part due to recent US Food and Drug Administration guidance related to thorough assessment of cardiovascular risk in the treatment of type 2 diabetes. Bayesian methods provide great promise for improving the conduct of safety trials. In this paper, the safety subteam of the Drug Information Association Bayesian Scientific Working Group evaluates challenges associated with current methods for designing and analyzing safety trials and provides an overview of several suggested Bayesian opportunities that may increase efficiency of safety trials along with relevant case examples.