A dynamic power prior approach to non-inferiority trials for normal means

Non-inferiority trials compare new experimental therapies to standard ones (active control). In these experiments, historical information on the control treatment is often available. This makes Bayesian methodology appealing since it allows a natural way to exploit information from past studies. In the present paper, we suggest the use of previous data for constructing the prior distribution of the control effect parameter. Specifically, we consider a dynamic power prior that possibly allows to discount the level of borrowing in the presence of heterogeneity between past and current control data. The discount parameter of the prior is based on the Hellinger distance between the posterior distributions of the control parameter based, respectively, on historical and current data. We develop the methodology for comparing normal means and we handle the unknown variance assumption using MCMC. We also provide a simulation study to analyze the proposed test in terms of frequentist size and power, as it is usually requested by regulatory agencies. Finally, we investigate comparisons with some existing methods and we illustrate an application to a real case study.

Decoupling power and type I error rate considerations when incorporating historical control data using a test-then-pool approach

To accelerate a randomized controlled trial, historical control data may be used after ensuring little heterogeneity between the historical and current trials. The test-then-pool approach is a simple frequentist borrowing method that assesses the similarity between historical and current control data using a two-sided test. A limitation of the conventional test-then-pool method is the inability to control the type I error rate and power for the primary hypothesis separately and flexibly for heterogeneity between trials. This is because the two-sided test focuses on the absolute value of the mean difference between the historical and current controls. In this paper, we propose a new test-then-pool method that splits the two-sided hypothesis of the conventional method into two one-sided hypotheses. Testing each one-sided hypothesis with different significance levels allows for the separate control of the type I error rate and power for heterogeneity between trials. We also propose a significance-level selection approach based on the maximum type I error rate and the minimum power. The proposed method prevented a decrease in power even when there was heterogeneity between trials while controlling type I error at a maximum tolerable type I error rate larger than the targeted type I error rate. The application of depression trial data and hypothetical trial data further supported the usefulness of the proposed method.

Composite Likelihoods with Bounded Weights in Extrapolation of Data

Among many efforts to facilitate timely access to safe and effective medicines to children, increased attention has been given to extrapolation. Loosely, it is the leveraging of conclusions or available data from adults or older age groups to draw conclusions for the target pediatric population when it can be assumed that the course of the disease and the expected response to a medicinal product would be sufficiently similar in the pediatric and the reference population. Extrapolation then can be characterized as a statistical mapping of information from the reference (adults or older age groups) to the target pediatric population. The translation, or loosely mapping of information, can be through a composite likelihood approach where the likelihood of the reference population is weighted by exponentiation and that this exponent is related to the value of the mapped information in the target population. The weight is bounded above and below recognizing the fact that similarity (of the disease and the expected response) is still valid despite variability of response between the cohorts. Maximum likelihood approaches are then used for estimation of parameters, and asymptotic theory is used to derive distributions of estimates for use in inference. Hence, the estimation of effects in the target population borrows information from the reference population. In addition, this manuscript also talks about how this method is related to the Bayesian statistical paradigm.

Bayesian borrowing from historical control data in a vaccine efficacy trial

In the context of vaccine efficacy trial where the incidence rate is very low and a very large sample size is usually expected, incorporating historical data into a new trial is extremely attractive to reduce sample size and increase estimation precision. Nevertheless, for some infectious diseases, seasonal change in incidence rates poses a huge challenge in borrowing historical data and a critical question is how to properly take advantage of historical data borrowing with acceptable tolerance to between-trials heterogeneity commonly from seasonal disease transmission. In this article, we extend a probability-based power prior which determines the amount of information to be borrowed based on the agreement between the historical and current data, to make it applicable for either a single or multiple historical trials available, with constraint on the amount of historical information to be borrowed. Simulations are conducted to compare the performance of the proposed method with other methods including modified power prior (MPP), meta-analytic-predictive (MAP) prior and the commensurate prior methods. Furthermore, we illustrate the application of the proposed method for trial design in a practical setting.

On efficient posterior inference in normalized power prior Bayesian analysis

The power prior has been widely used to discount the amount of information borrowed from historical data in the design and analysis of clinical trials. It is realized by raising the likelihood function of the historical data to a power parameterδ ∈ [ 0 , 1 ] $\delta \in [0, 1]$ , which quantifies the heterogeneity between the historical and the new study. In a fully Bayesian approach, a natural extension is to assign a hyperprior to δ such that the posterior of δ can reflect the degree of similarity between the historical and current data. To comply with the likelihood principle, an extra normalizing factor needs to be calculated and such prior is known as the normalized power prior. However, the normalizing factor involves an integral of a prior multiplied by a fractional likelihood and needs to be computed repeatedly over different δ during the posterior sampling. This makes its use prohibitive in practice for most elaborate models. This work provides an efficient framework to implement the normalized power prior in clinical studies. It bypasses the aforementioned efforts by sampling from the power prior withδ = 0 $\delta = 0$ andδ = 1 $\delta = 1$ only. Such a posterior sampling procedure can facilitate the use of a random δ with adaptive borrowing capability in general models. The numerical efficiency of the proposed method is illustrated via extensive simulation studies, a toxicological study, and an oncology study.

Bayesian Dynamic Borrowing of Historical Information with Applications to the Analysis of Large-Scale Assessments

The purpose of this paper is to demonstrate and evaluate the use of Bayesian dynamic borrowing (Viele et al, in Pharm Stat 13:41-54, 2014) as a means of systematically utilizing historical information with specific applications to large-scale educational assessments. Dynamic borrowing via Bayesian hierarchical models is a special case of a general framework of historical borrowing where the degree of borrowing depends on the heterogeneity among historical data and current data. A joint prior distribution over the historical and current data sets is specified with the degree of heterogeneity across the data sets controlled by the variance of the joint distribution. We apply Bayesian dynamic borrowing to both single-level and multilevel models and compare this approach to other historical borrowing methods such as complete pooling, Bayesian synthesis, and power priors. Two case studies using data from the Program for International Student Assessment reveal the utility of Bayesian dynamic borrowing in terms of predictive accuracy. This is followed by two simulation studies that reveal the utility of Bayesian dynamic borrowing over simple pooling and power priors in cases where the historical data is heterogeneous compared to the current data based on bias, mean squared error, and predictive accuracy. In cases of homogeneous historical data, Bayesian dynamic borrowing performs similarly to data pooling, Bayesian synthesis, and power priors. In contrast, for heterogeneous historical data, Bayesian dynamic borrowing performed at least as well, if not better, than other methods of borrowing with respect to mean squared error, percent bias, and leave-one-out cross-validation.

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.

Comparative Study of Bayesian Information Borrowing Methods in Oncology Clinical Trials

With deeper insight into precision medicine, more innovative oncology trial designs have been proposed to contribute to the characteristics of novel antitumor drugs. Bayesian information borrowing is an indispensable part of these designs, which shows great advantages in improving the efficiency of clinical trials. Bayesian methods provide an effective framework when incorporating information. However, the key point lies in how to choose an appropriate method for complex oncology clinical trials.

Power prior for borrowing the real-world data in bioequivalence test with a parallel design

Recently, real-world study has attracted wide attention for drug development. In bioequivalence study, the reference drug often has been marketed for many years and accumulated abundant real-world data. It is therefore appealing to incorporate these data in the design to improve trial efficiency. In this paper, we propose a Bayesian method to include real-world data of the reference drug in a current bioequivalence trial, with the aim to increase the power of analysis and reduce sample size for long half-life drugs. We adopt the power prior method for incorporating real-world data and use the average bioequivalence posterior probability to evaluate the bioequivalence between the test drug and the reference drug. Simulations were conducted to investigate the performance of the proposed method in different scenarios. The simulation results show that the proposed design has higher power than the traditional design without borrowing real-world data, while controlling the type I error. Moreover, the proposed method saves sample size and reduces costs for the trial.

Handling Poor Accrual in Pediatric Trials: A Simulation Study Using a Bayesian Approach

In the conduction of trials, a common situation is related to potential difficulties in recruiting the planned sample size as provided by the study design. A Bayesian analysis of such trials might provide a framework to combine prior evidence with current evidence, and it is an accepted approach by regulatory agencies. However, especially for small trials, the Bayesian inference may be severely conditioned by the prior choices. The Renal Scarring Urinary Infection (RESCUE) trial, a pediatric trial that was a candidate for early termination due to underrecruitment, served as a motivating example to investigate the effects of the prior choices on small trial inference. The trial outcomes were simulated by assuming 50 scenarios combining different sample sizes and true absolute risk reduction (ARR). The simulated data were analyzed via the Bayesian approach using 0%, 50%, and 100% discounting factors on the beta power prior. An informative inference (0% discounting) on small samples could generate data-insensitive results. Instead, the 50% discounting factor ensured that the probability of confirming the trial outcome was higher than 80%, but only for an ARR higher than 0.17. A suitable option to maintain data relevant to the trial inference is to define a discounting factor based on the prior parameters. Nevertheless, a sensitivity analysis of the prior choices is highly recommended.

Summarising salient information on historical controls: A structured assessment of validity and comparability across studies

BACKGROUND

While placebo-controlled randomised controlled trials remain the standard way to evaluate drugs for efficacy, historical data are used extensively across the development cycle. This ranges from supplementing contemporary data to increase the power of trials to cross-trial comparisons in estimating comparative efficacy. In many cases, these approaches are performed without in-depth review of the context of data, which may lead to bias and incorrect conclusions.

METHODS

We discuss the original 'Pocock' criteria for the use of historical data and how the use of historical data has evolved over time. Based on these factors and personal experience, we created a series of questions that may be asked of historical data, prior to their use. Based on the answers to these questions, various statistical approaches are recommended. The strategy is illustrated with a case study in colorectal cancer.

RESULTS

A number of areas need to be considered with historical data, which we split into three categories: outcome measurement, study/patient characteristics (including setting and inclusion/exclusion criteria), and disease process/intervention effects. Each of these areas may introduce issues if not appropriately handled, while some may preclude the use of historical data entirely. We present a tool (in the form of a table) for highlighting any such issues. Application of the tool to a colorectal cancer data set demonstrates under what conditions historical data could be used and what the limitations of such an analysis would be.

CONCLUSION

Historical data can be a powerful tool to augment or compare with contemporary trial data, though caution is required. We present some of the issues that may be considered when involving historical data and what (if any) statistical approaches may account for differences between studies. We recommend that, where historical data are to be used in analyses, potential differences between studies are addressed explicitly.

Critical appraisal of Bayesian dynamic borrowing from an imperfectly commensurate historical control

Bayesian dynamic borrowing designs facilitate borrowing information from historical studies. Historical data, when perfectly commensurate with current data, have been shown to reduce the trial duration and the sample size, while inflation in the type I error and reduction in the power have been reported, when imperfectly commensurate. These results, however, were obtained without considering that Bayesian designs are calibrated to meet regulatory requirements in practice and even no-borrowing designs may use information from historical data in the calibration. The implicit borrowing of historical data suggests that imperfectly commensurate historical data may similarly impact no-borrowing designs negatively. We will provide a fair appraiser of Bayesian dynamic borrowing and no-borrowing designs. We used a published selective adaptive randomization design and real clinical trial setting and conducted simulation studies under varying degrees of imperfectly commensurate historical control scenarios. The type I error was inflated under the null scenario of no intervention effect, while larger inflation was noted with borrowing. The larger inflation in type I error under the null setting can be offset by the greater probability to stop early correctly under the alternative. Response rates were estimated more precisely and the average sample size was smaller with borrowing. The expected increase in bias with borrowing was noted, but was negligible. Using Bayesian dynamic borrowing designs may improve trial efficiency by stopping trials early correctly and reducing trial length at the small cost of inflated type I error.

Revisit of test-then-pool methods and some practical considerations

Test-then-pool is a simple statistical method that borrows historical information to improve efficiency of the drug development process. The original test-then-pool method examines the difference between the historical and current information and then pools the information if there is no significant difference. One drawback of this method is that a nonsignificant difference may not always imply consistency between the historical and current information. As a result, the original test-then-pool method is more likely to incorrectly borrow information from the historical control when the current trial has a small sample size. Statistically, it is more natural to use an equivalence test for examining the consistency. This manuscript develops an equivalence-based test-then-pool method for a continuous endpoint, explains the relationship between the two test-then-pool methods, explores the choice of an equivalence margin through the overlap probability, and proposes an adjustment to the nominal testing level for controlling type I error under the true consistency scenario. Furthermore, the analytical forms of the type I error and power for the two test-then-pool methods are derived, and practical considerations for using them are presented.

An adaptive power prior for sequential clinical trials - Application to bridging studies

During drug evaluation trials, information from clinical trials previously conducted on another population, indications or schedules may be available. In these cases, it might be desirable to share information by efficiently using the available resources. In this work, we developed an adaptive power prior with a commensurability parameter for using historical or external information. It allows, at each stage, full borrowing when the data are not in conflict, no borrowing when the data are in conflict or "tuned" borrowing when the data are in between. We propose to apply our adaptive power prior method to bridging studies between Caucasians and Asians, and we focus on the sequential adaptive allocation design, although other design settings can be used. We weight the prior information in two steps: the effective sample size approach is used to set the maximum desirable amount of information to be shared from historical data at each step of the trial; then, in a sort of Empirical Bayes approach, a commensurability parameter is chosen using a measure of distribution distance. This approach avoids elicitation and computational issues regarding the usual Empirical Bayes approach. We propose several versions of our method, and we conducted an extensive simulation study evaluating the robustness and sensitivity to prior choices.