Prospectively Specified Adaptive Bayesian Borrowing: Considerations, Methodologies, and Implementations.

The borrowing of historical control data can be an efficient way to improve the treatment effect estimate of the current control group in a randomized clinical trial. When the historical and current control data are consistent, the borrowing of historical data can increase power and reduce Type I error rate. However, when these 2 sources of data are inconsistent, it may result in a combination of biased estimates, reduced power, and inflation of Type I error rate. In some situations, inconsistency between historical and current control data may be caused by a systematic variation in the measured baseline prognostic factors, which can be appropriately addressed through statistical modeling. In this paper, we propose a Bayesian hierarchical model that can incorporate patient-level baseline covariates to enhance the appropriateness of the exchangeability assumption between current and historical control data. The performance of the proposed method is shown through simulation studies, and its application to a clinical trial design for amyotrophic lateral sclerosis is described. The proposed method is developed for scenarios involving multiple imbalanced prognostic factors and thus has meaningful implications for clinical trials evaluating new treatments for heterogeneous diseases such as amyotrophic lateral sclerosis.

A standard two‐arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down‐weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.

When incorporating historical control data into the analysis of current randomized controlled trial data, it is critical to account for differences between the datasets. When the cause of difference is an unmeasured factor and adjustment for only observed covariates is insufficient, it is desirable to use a dynamic borrowing method that reduces the impact of heterogeneous historical controls. We propose a nonparametric Bayesian approach that addresses between-trial heterogeneity and allows borrowing historical controls homogeneous with the current control. Additionally, to emphasize conflict resolution between historical controls and the current control, we introduce a method based on the dependent Dirichlet process (DP) mixture. The proposed methods can be implemented using the same procedure, regardless of whether the outcome data comprise aggregated study-level data or individual participant data. We also develop a novel index of similarity between the historical and current control data, based on the posterior distribution of the parameter of interest. We conduct a simulation study and analyze clinical trial examples to evaluate the performance of the proposed methods compared to existing methods. The proposed method, based on the dependent DP mixture, can accurately borrow from homogeneous historical controls while reducing the impact of heterogeneous historical controls compared to the typical DP mixture. The proposed methods outperform existing methods in scenarios with heterogeneous historical controls, in which the meta-analytic approach is ineffective.

Bringing historical control information into a new trial appropriately holds the promise of more efficient trial design with more accurate estimates, increased power, and fewer patients allocated to inefficacious control group, provided the historical control data are sufficiently similar to the concurrent control. Interest has been growing over the past few decades in leveraging historical clinical trial on the control arm. However, most of the current historical borrowing methods focus on incorporating patient-level historical control information at only one time point. In this work, we propose a Bayesian hierarchical Mixed effect Models for Repeated Measures to incorporate aggregated study-level longitudinal historical control estimates into the concurrent trial that collected repeated longitudinal data. The simulation study demonstrates that, as compared to one time point data analysis approach, leveraging longitudinal historical control data produces greater power enhancement and mitigates the power loss when the missing data under missing at random mechanism is present. Our work also helps fill the gap of lack of methods borrowing historical longitudinal control data from the published summarized estimates when patient-level control data are not available.

A standard two-arm randomised controlled trial usually compares a novel treatment to a standard of care. Patients are randomised 1:1 to each treatment and the analysis is based only on patients within the current trial. While historical data is often used informally to design trials, in choosing endpoints and forming the basis of sample size calculations, only recently has it been considered for formal use in the design and analysis of trials. Often, one or more trials have been conducted on the standard of care. Incorporating historical control data could potentially lead to more efficient trials. This could allow more patients to be randomised to the novel treatment, reduce the sample size and decrease the study duration when historical and current data are commensurate. However, when the data are inconsistent, there is a potential for bias, inflated type I error and reduced power. We propose an adaptive design. An interim analysis is performed to assess the historical-current data conflict. The randomisation ratio is adapted to allocate more patients to the novel treatment and less to control if there is no conflict. The final analysis uses a weighted combination of the historical and current control data. Two weights are proposed, the percentage of overlap in the two control distributions and a weight based on tail area probabilities. This design increases power when there is no conflict and reverts back to a standard design when the conflict is too great. These methods are illustrated with an example and the operating characteristics are compared to those of historical data methods proposed in the literature.

Compilation and use of genetic toxicity historical control data

In many clinical trials, especially trials in rare diseases or a certain population like paediatric, it is of great interest to incorporate historical data to increase power of evaluating the treatment effect of an experimental drug. In practice, historical data and current data may not be congruent, and borrowing historical data is often associated with bias and Type-1 error rate inflation. It remains a challenge for historical data borrowing methods to control Type-1 error rate inflation at an adequate level and maintain sufficient power at the same time. To address this issue, dynamic historical borrowing methods can borrow historical data more when historical data are similar to current data and less otherwise. This paper proposed to use a weighted average of historical and current control data, with the weight being set as an approximation to the optimal weight that minimizes the mean-squared errors in the treatment effect estimation. Comparing to selected existing methods, the proposed method showed reduced bias, robust gain in power and better control in Type-1 error rate inflation through simulation studies. The proposed method enables the utilization of all possible historical data in the public domain and is readily used by skipping the need for external expert input in some existing approaches.

There has been an increased interest in borrowing information from historical control data to improve the statistical power for hypothesis testing, therefore reducing the required sample sizes in clinical trials. To account for the heterogeneity between the historical and current trials, power priors are often considered to discount the information borrowed from the historical data. However, it can be challenging to choose a fixed power prior parameter in the application. The modified power prior approach, which defines a random power parameter with initial prior to control the amount of historical information borrowed, may not directly account for heterogeneity between the trials. In this paper, we propose a novel approach to pick a power prior based on some direct measures of distributional differences between historical control data and current control data under normal assumptions. Simulations are conducted to investigate the performance of the proposed approach compared with current approaches (e.g. commensurate prior, meta-analytic-predictive, and modified power prior). The results show that the proposed power prior improves the study power while controlling the type I error within a tolerable limit when the distribution of the historical control data is similar to that of the current control data. The method is developed for both superiority and non-inferiority trials and is illustrated with an example from vaccine clinical trials.

Prospective trial design often occurs in the presence of 'acceptable' historical control data. Typically, these data are only utilized for treatment comparison in a posteriori retrospective analysis to estimate population-averaged effects in a random-effects meta-analysis. We propose and investigate an adaptive trial design in the context of an actual randomized controlled colorectal cancer trial. This trial, originally reported by Goldberg et al., succeeded a similar trial reported by Saltz et al., and used a control therapy identical to that tested (and found beneficial) in the Saltz trial. The proposed trial implements an adaptive randomization procedure for allocating patients aimed at balancing total information (concurrent and historical) among the study arms. This is accomplished by assigning more patients to receive the novel therapy in the absence of strong evidence for heterogeneity among the concurrent and historical controls. Allocation probabilities adapt as a function of the effective historical sample size (EHSS), characterizing relative informativeness defined in the context of a piecewise exponential model for evaluating time to disease progression. Commensurate priors are utilized to assess historical and concurrent heterogeneity at interim analyses and to borrow strength from the historical data in the final analysis. The adaptive trial's frequentist properties are simulated using the actual patient-level historical control data from the Saltz trial and the actual enrollment dates for patients enrolled into the Goldberg trial. Assessing concurrent and historical heterogeneity at interim analyses and balancing total information with the adaptive randomization procedure lead to trials that on average assign more new patients to the novel treatment when the historical controls are unbiased or slightly biased compared to the concurrent controls. Large magnitudes of bias lead to approximately equal allocation of patients among the treatment arms. Using the proposed commensurate prior model to borrow strength from the historical data, after balancing total information with the adaptive randomization procedure, provides admissible estimators of the novel treatment effect with desirable bias-variance trade-offs. Adaptive randomization methods in general are sensitive to population drift and more suitable for trials that initiate with gradual enrollment. Balancing information among study arms in time-to-event analyses is difficult in the presence of informative right-censoring. The proposed design could prove important in trials that follow recent evaluations of a control therapy. Efficient use of the historical controls is especially important in contexts where reliance on preexisting information is unavoidable because the control therapy is exceptionally hazardous, expensive, or the disease is rare.

Interest in incorporating historical data in the clinical trial has increased with the rising cost of conducting clinical trials. The intervention arm for the current trial often requires prospective data to assess a novel treatment, and thus borrowing historical control data commensurate in distribution to current control data is motivated in order to increase the allocation ratio to the current intervention arm. Existing historical control borrowing adaptive designs adjust allocation ratios based on the commensurability assessed through study-level summary statistics of the response agnostic of the distributions of the trial subject characteristics in the current and historical trials. This can lead to distributional imbalance of the current trial subject characteristics across the treatment arms as well as between current control data and borrowed historical control data. Such covariate imbalance may threaten the internal validity of the current trial by introducing confounding factors that affect study endpoints. In this article, we propose a Bayesian design which borrows and updates the treatment allocation ratios both covariate-adaptively and commensurate to covariate dependently assessed similarity between the current and historical control data. We employ covariate-dependent discrepancy parameters which are allowed to grow with the sample size and propose a regularized local regression procedure for the estimation of the parameters. The proposed design also permits the current and the historical controls to be similar to varying degree, depending on the subject level characteristics. We evaluate the proposed design extensively under the settings derived from two placebo-controlled randomized trials on vertebral fracture risk in post-menopausal women.

When designing a clinical trial, borrowing historical control information can provide a more efficient approach by reducing the necessary control arm sample size while still yielding increased power. Several Bayesian methods for incorporating historical information via a prior distribution have been proposed, for example, (modified) power prior, (robust) meta-analytic predictive prior. When utilizing historical control borrowing, the prior parameter(s) must be specified to determine the magnitude of borrowing before the current data are observed. Thus, a flexible prior is needed in case of heterogeneity between historic trials or prior data conflict with the current trial. To incorporate the ability to selectively borrow historic information, we propose a Bayesian semiparametric meta-analytic-predictive prior. Using a Dirichlet process mixture prior allows for relaxation of parametric assumptions, and lets the model adaptively learn the relationship between the historic and current control data. Additionally, we generalize a method for estimating the prior effective sample size (ESS) for the proposed prior. This gives an intuitive quantification of the amount of information borrowed from historical trials, and aids in tuning the prior to the specific task at hand. We illustrate the effectiveness of the proposed methodology by comparing performance between existing methods in an extensive simulation study and a phase II proof-of-concept trial in ankylosing spondylitis. In summary, our proposed robustification of the meta-analytic-predictive prior alleviates the need for prespecifying the amount of borrowing, providing a more flexible and robust method to integrate historical data from multiple study sources in the design and analysis of clinical trials.

PurposeIn the context of clinical research, there is an increasing need for new study designs that help to incorporate already available data. With the help of historical controls, the existing information can be utilized to support the new study design, but of course, inclusion also carries the risk of bias in the study results.MethodsTo combine historical and randomized controls we investigate the Fill-it-up-design, which in the first step checks the comparability of the historical and randomized controls performing an equivalence pre-test. If equivalence is confirmed, the historical control data will be included in the new RCT. If equivalence cannot be confirmed, the historical controls will not be considered at all and the randomization of the original study will be extended. We are investigating the performance of this study design in terms of type I error rate and power.ResultsWe demonstrate how many patients need to be recruited in each of the two steps in the Fill-it-up-design and show that the family wise error rate of the design is kept at 5%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. The maximum sample size of the Fill-it-up-design is larger than that of the single-stage design without historical controls and increases as the heterogeneity between the historical controls and the concurrent controls increases.ConclusionThe two-stage Fill-it-up-design represents a frequentist method for including historical control data for various study designs. As the maximum sample size of the design is larger, a robust prior belief is essential for its use. The design should therefore be seen as a way out in exceptional situations where a hybrid design is considered necessary.

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.

This paper proposes randomized controlled clinical trial design to evaluate external cooling as a means to control fever and thereby reduce mortality in patients with septic shock. The trial will include concurrent external cooling and control arms while adaptively incorporating historical control arm data. Bayesian group sequential monitoring will be done using a posterior comparative test based on the 60-day survival distribution in each concurrent arm. Posterior inference will follow from a Bayesian discrete time survival model that facilitates adaptive incorporation of the historical control data through an innovative regression framework with a multivariate spike-and-slab prior distribution on the historical bias parameters. For each interim test, the amount of information borrowed from the historical control data will be determined adaptively in a manner that reflects the degree of agreement between historical and concurrent control arm data. Guidance is provided for selecting Bayesian posterior probability group-sequential monitoring boundaries. Simulation results elucidating how the proposed method borrows strength from the historical control data are reported. In the absence of historical control arm bias, the proposed design controls the type I error rate and provides substantially larger power than reasonable comparators, whereas in the presence bias of varying magnitude, type I error rate inflation is curbed.

Historical control refers to the practice of using data from past studies and administrative databases to estimate potential response to placebo or standard‐of‐care treatment among patients in an ongoing study. The historical control information may come from patient‐specific data or from aggregate published estimates. Studies that project response to a control regimen based on historical data rather than concurrently randomized patients are most common in settings where there are ethical barriers to the use of either placebo or an older treatment widely believed to have little benefit. Historical controlled trials (HCTs) are subject to several potentially important sources of bias. HCTs are examples from a broader class of nonrandomized comparative designs called observational studies. Numerous methods have been developed to reduce bias in observational studies, and these methods are sometimes applicable in HCTs, for example, covariate adjustment and matching [Cochran and Rubin (1)], and propensity score methods [Rosenbaum and Rubin (2)]. Bayesian statistical methods can be used to create hybrid designs that use some historical control data and some concurrently collected randomized control data. Times series are another source of historical control information commonly used in economics and marketing as well as, occasionally, in clinical research.