Power priors based on multiple historical studies for binary outcomes

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.

SAM: Self-adapting mixture prior to dynamically borrow information from historical data in clinical trials

Mixture priors provide an intuitive way to incorporate historical data while accounting for potential prior-data conflict by combining an informative prior with a noninformative prior. However, prespecifying the mixing weight for each component remains a crucial challenge. Ideally, the mixing weight should reflect the degree of prior-data conflict, which is often unknown beforehand, posing a significant obstacle to the application and acceptance of mixture priors. To address this challenge, we introduce self-adapting mixture (SAM) priors that determine the mixing weight using likelihood ratio test statistics or Bayes factors. SAM priors are data-driven and self-adapting, favoring the informative (noninformative) prior component when there is little (substantial) evidence of prior-data conflict. Consequently, SAM priors achieve dynamic information borrowing. We demonstrate that SAM priors exhibit desirable properties in both finite and large samples and achieve information-borrowing consistency. Moreover, SAM priors are easy to compute, data-driven, and calibration-free, mitigating the risk of data dredging. Numerical studies show that SAM priors outperform existing methods in adopting prior-data conflicts effectively. We developed R package "SAMprior" and web application that are freely available at CRAN and www.trialdesign.org to facilitate the use of SAM priors.

Power priors for replication studies

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I 2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

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.

A model-based approach for historical borrowing, with an application to neovascular age-related macular degeneration

Bayesian historical borrowing has recently attracted growing interest due to the increasing availability of historical control data, as well as improved computational methodology and software. In this article, we argue that the statistical models used for borrowing may be suboptimal when they do not adjust for differing factors across historical studies such as covariates, dosing regimen, etc. We propose an alternative approach to address these shortcomings. We start by constructing a historical model based on subject-level historical data to accurately characterize the control treatment by adjusting for known between trials differences. This model is subsequently used to predict the control arm response in the current trial, enabling the derivation of a model-informed prior for the treatment effect parameter of another (potentially simpler) model used to analyze the trial efficacy (i.e. the trial model). Our approach is applied to neovascular age-related macular degeneration trials, employing a cross-sectional regression trial model, and a longitudinal non-linear mixed-effects drug-disease-trial historical model. The latter model characterizes the relationship between clinical response, drug exposure and baseline covariates so that the derived model-informed prior seamlessly adapts to the trial population and can be extrapolated to a different dosing regimen. This approach can yield a more accurate prior for borrowing, thus optimizing gains in efficiency (e.g. increasing power or reducing the sample size) in future trials.

The scale transformed power prior for use with historical data from a different outcome model

We develop the scale transformed power prior for settings where historical and current data involve different data types, such as binary and continuous data. This situation arises often in clinical trials, for example, when historical data involve binary responses and the current data involve some other type of continuous or discrete outcome. The power prior, proposed by Ibrahim and Chen, does not address the issue of different data types. Herein, we develop a new type of power prior, which we call the scale transformed power prior (straPP). The straPP is constructed by transforming the power prior for the historical data by rescaling the parameter using a function of the Fisher information matrices for the historical and current data models, thereby shifting the scale of the parameter vector from that of the historical to that of the current data. Examples are presented to motivate the need for such a transformation, and simulation studies are presented to illustrate the performance advantages of the straPP over the power prior and other informative and noninformative priors. A real dataset from a clinical trial undertaken to study a novel transitional care model for stroke survivors is used to illustrate the methodology.

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.

Using horseshoe prior for incorporating multiple historical control data in randomized controlled trials

Meta-analytic approaches and power priors are often used to incorporate historical controls into the analysis of a current randomized controlled trial. In this study, we propose a method for incorporating multiple historical controls based on a horseshoe prior, which is a type of global-local shrinkage prior. The method assumes that historical controls follow the same distribution as the current control. In the case in which only a few historical controls are heterogeneous, we consider them to follow a potentially biased distribution from the distribution of the current control. We analyze two clinical trial examples with binary and time-to-event endpoints and conduct simulation studies to compare the performance of the proposed and existing methods. In the analysis of the clinical trial example, the posterior standard deviation of the treatment effect is decreased by the proposed method by considering the bias between the current control and heterogeneous historical control. In the scenarios in which the current and historical controls follow the same distribution, the statistical power using the proposed method is higher than that using existing methods. The proposed method is advantageous when few or no heterogeneous historical controls are expected.

Incorporating historical controls in clinical trials with longitudinal outcomes using the modified power prior

Several dynamic borrowing methods, such as the modified power prior (MPP), the commensurate prior, have been proposed to increase statistical power and reduce the required sample size in clinical trials where comparable historical controls are available. Most methods have focused on cross‐sectional endpoints, and appropriate methodology for longitudinal outcomes is lacking. In this study, we extend the MPP to the linear mixed model (LMM). An important question is whether the MPP should use the conditional version of the LMM (given the random effects) or the marginal version (averaged over the distribution of the random effects), which we refer to as the conditional MPP and the marginal MPP, respectively. We evaluated the MPP for one historical control arm via a simulation study and an analysis of the data of Alzheimer's Disease Cooperative Study (ADCS) with the commensurate prior as the comparator. The conditional MPP led to inflated type I error rate when there existed moderate or high between‐study heterogeneity. The marginal MPP and the commensurate prior yielded a power gain (3.6%–10.4% vs. 0.6%–4.6%) with the type I error rates close to 5% (5.2%–6.2% vs. 3.8%–6.2%) when the between‐study heterogeneity is not excessively high. For the ADCS data, all the borrowing methods improved the precision of estimates and provided the same clinical conclusions. The marginal MPP and the commensurate prior are useful for borrowing historical controls in longitudinal data analysis, while the conditional MPP is not recommended due to inflated type I error rates.

Unit information prior for adaptive information borrowing from multiple historical datasets

In clinical trials, there often exist multiple historical studies for the same or related treatment investigated in the current trial. Incorporating historical data in the analysis of the current study is of great importance, as it can help to gain more information, improve efficiency, and provide a more comprehensive evaluation of treatment. Enlightened by the unit information prior (UIP) concept in the reference Bayesian test, we propose a new informative prior called UIP from an information perspective that can adaptively borrow information from multiple historical datasets. We consider both binary and continuous data and also extend the new UIP to linear regression settings. Extensive simulation studies demonstrate that our method is comparable to other commonly used informative priors, while the interpretation of UIP is intuitive and its implementation is relatively easy. One distinctive feature of UIP is that its construction only requires summary statistics commonly reported in the literature rather than the patient-level data. By applying our UIP to phase III clinical trials for investigating the efficacy of memantine in Alzheimer's disease, we illustrate its ability to adaptively borrow information from multiple historical datasets. The Python codes for simulation studies and the real data application are available at https://github.com/JINhuaqing/UIP.

Hi3 + 3: A model-assisted dose-finding design borrowing historical data

BACKGROUND

In phase I clinical trials, historical data may be available through multi-regional programs, reformulation of the same drug, or previous trials for a drug under the same class. Statistical designs that borrow information from historical data can reduce cost, speed up drug development, and maintain safety.

PURPOSE

Based on a hybrid design that partly uses probability models and partly uses algorithmic rules for decision making, we aim to improve the efficiency of the dose-finding trials in the presence of historical data, maintain safety for patients, and achieve a level of simplicity for practical applications.

METHODS

We propose the Hi3 + 3 design, in which the letter "H" represents "historical data". We apply the idea in power prior to borrow historical data and define the effective sample size (ESS) of the prior. Dose-finding decision rules follow the idea in the i3 + 3 design (Liu et al., 2020 [1]) while incorporating the historical data via the power prior and ESS. The proposed Hi3 + 3 design pretabulates the dosing decisions before the trial starts, a desirable feature for ease of application in practice.

RESULTS

In most cases we investigated, the Hi3 + 3 design is superior than the i3 + 3 design due to information borrow from historical data. Even when the historical data is incompatible with the current data, it is capable of maintaining a high level of safety for trial patients and comparable performances without sacrificing the ability to identify the correct MTD too much. Ilustration of this feature are found in the simulation results.

CONCLUSION

With the demonstrated safety, efficiency, and simplicity, the Hi3 + 3 design could be a desirable choice for dose-finding trials borrowing historical data.

A phase I dose-finding design with incorporation of historical information and adaptive shrinking boundaries

Although many novel phase I designs have been developed in recent years, few studies have discussed how to incorporate external information into dose-finding designs. In this paper, we first propose a new method for developing a phase I design, Bayesian optimal interval design (BOIN)[Liu S et al. (2015), Yuan Y et al. (2016)], for formally incorporating historical information. An algorithm to automatically generate parameters for prior set-up is introduced. Second, we propose a method to relax the fixed boundaries of the BOIN design to be adaptive, such that the accumulative information can be used more appropriately. This modified design is called adaptive BOIN (aBOIN). Simulation studies to examine performances of the aBOIN design in small and large sample sizes revealed comparable performances for the aBOIN and original BOIN designs for small sample sizes. However, aBOIN outperformed BOIN in moderate sample sizes. Simulation results also showed that when historical trials are conducted in settings similar to those for the current trial, their performance can be significantly improved. This approach can be applied directly to pediatric cancer trials, since all phase I trials in children are followed by similar efficient adult trials in the current drug development paradigm. However, when information is weak, operating characteristics are compromised.

Power gains by using external information in clinical trials are typically not possible when requiring strict type I error control

In the era of precision medicine, novel designs are developed to deal with flexible clinical trials that incorporate many treatment strategies for multiple diseases in one trial setting. This situation often leads to small sample sizes in disease-treatment combinations and has fostered the discussion about the benefits of borrowing of external or historical information for decision-making in these trials. Several methods have been proposed that dynamically discount the amount of information borrowed from historical data based on the conformity between historical and current data. Specifically, Bayesian methods have been recommended and numerous investigations have been performed to characterize the properties of the various borrowing mechanisms with respect to the gain to be expected in the trials. However, there is common understanding that the risk of type I error inflation exists when information is borrowed and many simulation studies are carried out to quantify this effect. To add transparency to the debate, we show that if prior information is conditioned upon and a uniformly most powerful test exists, strict control of type I error implies that no power gain is possible under any mechanism of incorporation of prior information, including dynamic borrowing. The basis of the argument is to consider the test decision function as a function of the current data even when external information is included. We exemplify this finding in the case of a pediatric arm appended to an adult trial and dichotomous outcome for various methods of dynamic borrowing from adult information to the pediatric arm. In conclusion, if use of relevant external data is desired, the requirement of strict type I error control has to be replaced by more appropriate metrics.

Optimizing the Design and Analysis of Clinical Trials for Antibacterials Against Multidrug-resistant Organisms: A White Paper From COMBACTE's STAT-Net

Innovations are urgently required for clinical development of antibacterials against multidrug-resistant organisms. Therefore, a European, public-private working group (STAT-Net; part of Combatting Bacterial Resistance in Europe [COMBACTE]), has reviewed and tested several innovative trials designs and analytical methods for randomized clinical trials, which has resulted in 8 recommendations. The first 3 focus on pharmacokinetic and pharmacodynamic modeling, emphasizing the pertinence of population-based pharmacokinetic models, regulatory procedures for the reassessment of old antibiotics, and rigorous quality improvement. Recommendations 4 and 5 address the need for more sensitive primary end points through the use of rank-based or time-dependent composite end points. Recommendation 6 relates to the applicability of hierarchical nested-trial designs, and the last 2 recommendations propose the incorporation of historical or concomitant trial data through Bayesian methods and/or platform trials. Although not all of these recommendations are directly applicable, they provide a solid, evidence-based approach to develop new, and established, antibacterials and address this public health challenge.

Quantification of prior impact in terms of effective current sample size

Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual "loss of information" induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.