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AbstractIn basket trials a treatment is investigated in several subgroups. They are primarily used in oncology in early clinical phases as single-arm trials with a binary endpoint. For their analysis primarily Bayesian methods have been suggested, as they allow partial sharing of information based on the observed similarity between subgroups. Fujikawa et al. (2020) suggested an approach using empirical Bayes methods that allows flexible sharing based on easily interpretable weights derived from the Jensen-Shannon divergence between the subgroup-wise posterior distributions. We show that this design is closely related to the method of power priors and investigate several modifications of Fujikawa’s design using methods from the power prior literature. While in Fujikawa’s design, the amount of information that is shared between two baskets is only determined by their pairwise similarity, we also discuss extensions where the outcomes of all baskets are considered in the computation of the sharing weights. The results of our comparison study show that the power prior design has comparable performance to fully Bayesian designs in a range of different scenarios. At the same time, the power prior design is computationally cheap and even allows analytical computation of operating characteristics in some settings. [ABSTRACT FROM AUTHOR]

Due to the insufficiency of safety assessments of clinical trials for drugs, further assessments are required for post‐marketed drugs. In addition to adverse drug reactions (ADRs) induced by one drug, drug‐drug interaction (DDI)‐induced ADR should also be investigated. The spontaneous reporting system (SRS) is a powerful tool for evaluating the safety of drugs continually. In this study, we propose a novel Bayesian method for detecting potential DDIs in a database collected by the SRS. By applying a power prior, the proposed method can borrow information from similar drugs for a drug assessed DDI to increase sensitivity of detection. The proposed method can also adjust the amount of the information borrowed by tuning the parameters in power prior. In the simulation study, we demonstrate the aforementioned increase in sensitivity. Depending on the scenarios, approximately 20 points of sensitivity of the proposed method increase from an existing method to a maximum. We also indicate the possibility of early detection of potential DDIs by the proposed method through analysis of the database shared by the Food and Drug Administration. In conclusion, the proposed method has a higher sensitivity and a novel criterion to detect potential DDIs early, provided similar drugs have similar observed‐expected ratios to the drug under assessment. [ABSTRACT FROM AUTHOR]

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCTs) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g., unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted power prior provides robust inference under various forms of incompatibility between the external controls and RCT population. [ABSTRACT FROM AUTHOR]

United States law bars using peremptory strikes during jury selection because of prospective juror race, ethnicity, sex, or membership in certain other cognizable classes. Here, we extend a Bayesian approach for detecting such illegal strike bias by showing how to incorporate historical data on an attorney's use of peremptory strikes in past cases. In so doing, we use the power prior to adjust the weight of such historical information in the analysis. Using simulations, we show how the choice of the power prior's discounting parameter influences bias detection (how likely the credible interval for the bias parameter excludes zero), depending on the degree of incompatibility between current and historical trial data. Finally, we extend this approach with a prototype software application that lawyers could use to detect strike bias in real time during jury-selection. We illustrate this application's use with real historical strike data from a convenience sample of cases from one court. [ABSTRACT FROM AUTHOR]

Use of historical control data to augment a small internal control arm in a randomized control trial (RCT) can lead to significant improvement of the efficiency of the trial. It introduces the risk of potential bias, since the historical control population is often rather different from the RCT. Power prior approaches have been introduced to discount the historical data to mitigate the impact of the population difference. However, even with a Bayesian dynamic borrowing which can discount the historical data based on the outcome similarity of the two populations, a considerable population difference may still lead to a moderate bias. Hence, a robust adjustment for the population difference using approaches such as the inverse probability weighting ormatching, canmake the borrowingmore efficient and robust. In this article,we propose a novel approach integrating the propensity score for the covariate adjustment and Bayesian dynamic borrowing using power prior. The proposed approach uses Bayesian bootstrap in combination with the empirical Bayes (EB) method using quasi-likelihood for determining the power prior. The performance of our approach is examined by a simulation study. We apply the approach to two Acute Myeloid Leukemia (AML) studies for illustration. [ABSTRACT FROM AUTHOR]

The development process of medical devices can be streamlined by combining different study phases. Here, for a diagnostic medical device, we present the combination of confirmation of diagnostic accuracy (phase III) and evaluation of clinical effectiveness regarding patient-relevant endpoints (phase IV) using a seamless design. This approach is used in the Thyroid HEmorrhage DetectOr Study (HEDOS & HEDOS II) investigating a post-operative hemorrhage detector named ISAR-M THYRO® in patients after thyroid surgery. Data from the phase III trial are reused as external controls in the control group of the phase IV trial. An unblinded interim analysis is planned between the two study stages which includes a recalculation of the sample size for the phase IV part after completion of the first stage of the seamless design. The study concept presented here is the first seamless design proposed in the field of diagnostic studies. Hence, the aim of this work is to emphasize the statistical methodology as well as feasibility of the proposed design in relation to the planning and implementation of the seamless design. Seamless designs can accelerate the overall trial duration and increase its efficiency in terms of sample size and recruitment. However, careful planning addressing numerous methodological and procedural challenges is necessary for successful implementation as well as agreement with regulatory bodies. [ABSTRACT FROM AUTHOR]

We examine the performance of the power prior and the meta-analytic-predictive (MAP) prior for the analysis of (overdispersed) count data when multiple historical control data are incorporated into the analysis of the current data. To this end, we explore the Poisson and the negative binomial distribution. We propose a computational approach based on path sampling for the calculation of the scaling constant of the Modified Power Prior (MPP). We illustrate the methods through a motivating example of a clinical trial evaluating the effect of an experimental treatment to reduce the number of incontinence events for patients with an overactive bladder. Furthermore, we assess the performance of these methods via a simulation study in case of heterogeneity of the control arms. For similar current and historical control arms, the MPP approach offers greater statistical power than the MAP prior approach. When the means are different across the control arms, the MPP yields a slightly inflated Type I error rate, whereas the MAP prior does not. When the dispersion parameters are different across the control arms, the results are reversed. In conclusion, the MPP approach outperforms the MAP prior approach for count data. [ABSTRACT FROM AUTHOR]

A fully powered randomized controlled cancer trial can be challenging to conduct in children because of difficulties in enrollment of pediatric patients due to low disease incidence. One way to improve the feasibility of trials in pediatric patients, when clinically appropriate, is through borrowing information from comparable external adult trials in the same disease. Bayesian analysis of a pediatric trial provides a way of seamlessly augmenting pediatric trial efficacy data with data from external adult trials. However, not all external adult trial subjects may be equally clinically relevant with respect to the baseline disease severity, prognostic factors, co-morbidities, and prior therapy observed in the pediatric trial of interest. The propensity score matching method provides a way of matching the external adult subjects to the pediatric trial subjects on a set of clinically determined baseline covariates, such as baseline disease severity, prognostic factors and prior therapy. The matching then allows Bayesian information borrowing from only the most clinically relevant external adult subjects. Through a case study in pediatric acute lymphoblastic leukemia (ALL), we examine the utility of propensity score matched mixture and power priors in bringing appropriate external adult efficacy information into pediatric trial efficacy assessment, and present considerations for scaling fixed borrowing from external adult data. [ABSTRACT FROM AUTHOR]

Summary: The power and commensurate prior distributions are informative prior distributions that incorporate historical data as prior knowledge in Bayesian analysis to improve inference about a phenomenon under study. Although these distributions have been developed for analyzing non‐spatial data, little or no attention has been given to spatial geostatistical data. In this study, we extend these informative prior distributions to a Gaussian spatial process, which enables the elicitation of prior knowledge from historical geostatistical data for Bayesian analysis. Three informative prior distributions were developed for spatial modeling, and an efficient Markov Chain Monte Carlo algorithm was developed for performing Bayesian analysis. Simulation studies were used to assess the adequacy of the informative prior distributions. Hierarchical models combined with the developed informative prior distributions were applied to analyze transcranial magnetic stimulation (TMS) brain mapping data to gain insights into the spatial pattern of a patient's response to motor cortex stimulation. The study quantified the uncertainty in motor response and found that the primary motor cortex of the hand is responsible for most of the movement of the right first dorsal interosseous muscle. The findings provide a deeper understanding of the neural mechanisms underlying motor function and ultimately aid the improvement of treatment options for individuals with health issues. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To design a phase III study with a final endpoint and calculate the required sample size for the desired probability of success, we need a good estimate of the treatment effect on the endpoint. It is prudent to fully utilize all available information including the historical and phase II information of the treatment as well as external data of the other treatments. It is not uncommon that a phase II study may use a surrogate endpoint as the primary endpoint and has no or limited data for the final endpoint. On the other hand, external information from the other studies for the other treatments on the surrogate and final endpoints may be available to establish a relationship between the treatment effects on the two endpoints. Through this relationship, making full use of the surrogate information may enhance the estimate of the treatment effect on the final endpoint. In this research, we propose a bivariate Bayesian analysis approach to comprehensively deal with the problem. A dynamic borrowing approach is considered to regulate the amount of historical data and surrogate information borrowing based on the level of consistency. A much simpler frequentist method is also discussed. Simulations are conducted to compare the performances of different approaches. An example is used to illustrate the applications of the methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power δ. The derivation of the marginal likelihood based on the original power prior, and its variation, the normalized power prior, introduces a scaling factor C (δ) in the form of a prior predictive distribution with powered likelihood. In this article, we show that the scaling factor might be infinite for some positive δ with conventionally used initial priors, which would change the admissible set of the power parameter. This result seems to have been almost completely ignored in the literature. We then illustrate that such a phenomenon may jeopardize the posterior inference under the power priors when the initial prior of the model parameters is improper. The main findings of this article suggest that special attention should be paid when the suggested level of borrowing is close to 0, while the actual optimum might be below the suggested value. We use a normal linear model as an example for illustrative purposes. [ABSTRACT FROM AUTHOR]

A validated method is used to measure quality attributes of manufactured lots to support the production of active ingredient or drug product for a regulatory filing or product release. Various regulatory guidelines provide expectations on how to validate a method, including accuracy and precision. Validation studies are not typically designed to have the size or scope needed to fully characterize a method. We can and should, however, capitalize on the historical data that is generated from method development, transfer, and clinical trial lot release to facilitate the characterization. Using prior information from these sources affords a more confident characterization of the method's accuracy and precision. This article focuses on Bayesian methods for using the stream of available method data. Considerations are given for prior distributions, including methods to control the influence of prior data. Two case studies are presented to illustrate the continuous validation approach. This is a joint effort of the DIA Bayesian Scientific Working Group and the American Statistical Association Biopharmaceutical Nonclinical Working Group. [ABSTRACT FROM AUTHOR]

Estimates of county-level disease prevalence have a variety of applications. Such estimation is often done via model-based small-area estimation using survey data. However, for conditions with low prevalence (i.e., rare diseases or newly diagnosed diseases), counties with a high fraction of zero counts in surveys are common. They are often more common than the model used would lead one to expect; such zeros are called 'excess zeros'. The excess zeros can be structural (there are no cases to find) or sampling (there are cases, but none were selected for sampling). These issues are often addressed by combining multiple years of data. However, this approach can obscure trends in annual estimates and prevent estimates from being timely. Using single-year survey data, we proposed a Bayesian weighted Binomial Zero-inflated (BBZ) model to estimate county-level rare diseases prevalence. The BBZ model accounts for excess zero counts, the sampling weights and uses a power prior. We evaluated BBZ with American Community Survey results and simulated data. We showed that BBZ yielded less bias and smaller variance than estimates based on the binomial distribution, a common approach to this problem. Since BBZ uses only a single year of survey data, BBZ produces more timely county-level incidence estimates. These timely estimates help pinpoint the special areas of county-level needs and help medical researchers and public health practitioners promptly evaluate rare diseases trends and associations with other health conditions. [ABSTRACT FROM AUTHOR]

In this article, 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. [ABSTRACT FROM AUTHOR]

A three-arm non-inferiority trial including a test treatment, a reference treatment, and a placebo is recommended to assess the assay sensitivity and internal validity of a trial when applicable. Existing methods for designing and analyzing three-arm trials with binary endpoints are mainly developed from a frequentist viewpoint. However, these methods largely depend on large sample theories. To alleviate this problem, we propose two fully Bayesian approaches, the posterior variance approach and Bayes factor approach, to determine sample size required in a three-arm non-inferiority trial with binary endpoints. Simulation studies are conducted to investigate the performance of the proposed Bayesian methods. An example is illustrated by the proposed methodologies. Bayes factor method always leads to smaller sample sizes than the posterior variance method, utilizing the historical data can reduce the required sample size, simultaneous test requires more sample size to achieve the desired power than the non-inferiority test, the selection of the hyperparameters has a relatively large effect on the required sample size. When only controlling the posterior variance, the posterior variance criterion is a simple and effective option for obtaining a rough outcome. When conducting a previous clinical trial, it is recommended to use the Bayes factor criterion in practical applications. [ABSTRACT FROM AUTHOR]

We propose two new classes of Bayesian measure to investigate conflict among data sets from multiple studies. The first ("concentration ratio") is used to quantify the amount of information provided by a single data set through the comparison of the prior and its posterior distribution, or two data sets according to their corresponding posterior distributions. The second class ("dissonance") quantifies the extent of contradiction between two data sets. Both classes are based on volumes of highest density regions. They are well calibrated, supported by simulation, and computational algorithms are provided for their calculation. We illustrate these two classes in three real data applications: a benchmark dose toxicology study, a missing data study related to health effects of pollution, and a pediatric cancer study leveraging adult data. [ABSTRACT FROM AUTHOR]

This article introduces the R package BayesCTDesign for two-arm randomized Bayesian trial design using historical control data when available, and simple two-arm randomized Bayesian trial design when historical control data is not available. The package BayesCTDesign, which is available from the Comprehensive R Archive Network, has two simulation functions, historic_sim() and simple_sim() for studying trial characteristics under user-defined scenarios, and two methods print() and plot() for displaying summaries of the simulated trial characteristics. The package BayesCTDesign works with two-arm trials with equal sample sizes per arm. The package BayesCTDesign allows a user to study Gaussian, Poisson, Bernoulli, Weibull, lognormal, and piecewise exponential outcomes. Power for two-sided hypothesis tests at a user-defined α is estimated via simulation using a test within each simulation replication that involves comparing a 95% credible interval for the outcome specific treatment effect measure to the null case value. If the 95% credible interval excludes the null case value, then the null hypothesis is rejected, else the null hypothesis is accepted. In the article, the idea of including historical control data in a Bayesian analysis is reviewed, the estimation process of BayesCTDesign is explained, and the user interface is described. Finally, the BayesCTDesign is illustrated via several examples.

Phase I trial designs generally fall into three categories: algorithm-based (e.g., the classic 3 + 3 design), model-based (e.g., the continual reassessment method, CRM), and model-assisted designs that combine features of the first two (e.g., the Bayesian Optimal Interval, BOIN, design). The classic '3 + 3' design continues to be the most frequently used design in phase I trials in finding maximum tolerated dose (MTD) due to its simplicity and feasibility, though many other model-based designs such as the Continual Reassessment Method (CRM) have also been proposed and used in various such as immunotherapies trials. The MTD based on three or six patients is not accurate, and dose-expansion cohorts (DEC) are increasingly used to better characterize the toxicity profiles of experimental agents. This article proposes a multi-stage dose-expansion cohort (MSDEC) hybrid frequentist-Bayesian design combining the power prior and the sequential conditional probability ratio test. In this design, results from the dose-escalation part are viewed and treated as historical data, and then are weighted and modeled through power prior. For safety monitoring, the Bayesian stopping rule is developed and the maximum sample size is calculated by a fixed-sample-size test with exact binomial computation. Simulation studies showed that MSDEC reduces the chance that a patient experiences a toxic dose. Power prior provides a reasonable prior for the Bayesian model because the degree of informativeness of the prior can be driven by the ("objective") historical data rather than from expert opinion elicited on parameters in the model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Bayesian design of a randomized, double-blind, placebo-controlled superiority clinical trial. To leverage multiple historical datasets to augment the placebo-controlled arm, we develop three conditional borrowing approaches built upon the borrowing-by-parts prior, the hierarchical prior, and the robust mixture prior. The operating characteristics of the conditional borrowing approaches are examined. Extensive simulation studies are carried out to empirically demonstrate the superiority of the conditional borrowing approaches over the unconditional borrowing or no-borrowing approaches in terms of controlling type I error, maintaining good power, having a large "sweet-spot" region, minimizing bias, and reducing the mean-squared error of the posterior estimate of the mean parameter of the placebo-controlled arm. Computational algorithms are also developed for calculating the Bayesian type I error and power as well as the corresponding simulation errors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Leveraging external data is a topic that have recently received much attention. The propensity score-integrated approaches are a methodological innovation for this purpose. In this paper we adapt these approaches, originally introduced to augment single-arm studies with external data, for the augmentation of both arms of a randomized controlled trial (RCT) with external data. After recapitulating the basic ideas, we provide a step-by-step tutorial of how to implement the propensity score-integrated approaches, from study design to outcome analysis, in the RCT setting in such a way that the study integrity and objectively are maintained. Both the Bayesian (power prior) approach and the frequentist (composite likelihood) approach are included. Some extensions and variations of these approaches are also outlined at the end of this paper. [ABSTRACT FROM AUTHOR]

Combining historical control data with current control data may reduce the necessary study size of a clinical trial. However, this only applies when the historical control data are similar enough to the current control data. Several Bayesian approaches for incorporating historical data in a dynamic way have been proposed, such as the meta‐analytic‐predictive (MAP) prior and the modified power prior (MPP). Here we discuss the generalization of the MPP approach for multiple historical control groups for the linear regression model. This approach is useful when the controls differ more than in a random way, but become again (approximately) exchangeable conditional on covariates. The proposed approach builds on the approach previously developed for binary outcomes by some of the current authors. Two MPP approaches have been developed with multiple controls. The first approach assumes independent powers, while in the second approach the powers have a hierarchical structure. We conducted several simulation studies to investigate the frequentist characteristics of borrowing methods and analyze a real‐life data set. When there is between‐study variation in the slopes of the model or in the covariate distributions, the MPP approach achieves approximately nominal type I error rates and greater power than the MAP prior, provided that the covariates are included in the model. When the intercepts vary, the MPP yields a slightly inflated type I error rate, whereas the MAP does not. We conclude that our approach is a worthy competitor to the MAP approach for the linear regression case. [ABSTRACT FROM AUTHOR]

In pediatric or orphan diseases, there are many instances where it is unfeasible to conduct randomized and controlled clinical trials. This is due in part to the difficulty of enrolling a sufficient number of patients over a reasonable time period to meet adequate statistical power to demonstrate the treatment efficacy. One solution to reduce the sample size or expedite the trial timeline is to complement the current trial with real-world data. To this end, several propensity score-based methods have been developed to create defined groups of patients that are controlled for confounding based on a set of measured covariates at baseline. However, balance checking on the measured covariates and tweaks to the propensity score models is usually inevitable to achieve the joint balance across all covariates. To mitigate this iterative procedure, we utilize the entropy balancing weighting technique which focuses on balancing the covariates of subjects between the experimental and control groups directly and augments the current trial with the external control data via a power prior. The finite-sample properties of the proposed method are assessed via simulations in the context of asymmetrically randomized controlled trials where only a small portion of patients are randomized to the control group. Other methods such as covariate-balancing propensity score (CBPS) and propensity score matching (PSM) and weighting (PSW) are also compared to provide context on the operating characteristics of the proposed method. [ABSTRACT FROM AUTHOR]

There has been a substantial rise in the usage of real-world data (RWD) to supplement trial data in the medical and statistical literature. Propensity score methods such as stratification have been used to balance baseline characteristics and prognostic factors between external patients and current trial patients to improve the estimation of the current trial's parameter of interest. This paper merges propensity score methodology and Bayesian inference to estimate a current trial's parameter of interest as follows: (i) match current patients and external patients by strata using the percentiles of the current patients' propensity scores, (ii) apply a prior within each stratum to leverage RWD to estimate the stratum-specific parameter of interest, and (iii) then use a weighted average scheme to combine the stratum-specific parameters to estimate the overall current trial's parameter of interest. In stage (ii), the three priors used are a double hierarchical prior, an extension of the robust mixture prior, and an extension of the power prior. An extensive simulation study is carried out to evaluate the performance of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, a propensity score-integrated power prior approach is developed to augment the control arm of a two-arm randomized controlled trial (RCT) with subjects from multiple external data sources such as real-world data (RWD) and historical clinical studies containing subject-level outcomes and covariates. The propensity scores for the subjects in the external data sources versus the subjects in the RCT are first estimated, and then subjects are placed in different strata based on their estimated propensity scores. Within each propensity score stratum, a power prior is formulated with the information contributed by the external data sources, and Bayesian inference on the treatment effect is obtained. The proposed approach is implemented under the two-stage study design framework utilizing the outcome-free principle to ensure the integrity of a study. An illustrative example is provided to demonstrate the implementation of the proposed approach. [ABSTRACT FROM AUTHOR]

The power prior is a popular tool for constructing informative prior distributions based on historical data. The method consists of raising the likelihood to a discounting factor in order to control the amount of information borrowed from the historical data. However, one often wishes to assign this discounting factor a prior distribution and estimate it jointly with the parameters, which in turn necessitates the computation of a normalizing constant. In this article, we are concerned with how to approximately sample from joint posterior of the parameters and the discounting factor. We first show a few important properties of the normalizing constant and then use these results to motivate a bisection‐type algorithm for computing it on a fixed budget of evaluations. We give a large array of illustrations and discuss cases where the normalizing constant is known in closed‐form and where it is not. We show that the proposed method produces approximate posteriors that are very close to the exact distributions and also produces posteriors that cover the data‐generating parameters with higher probability in the intractable case. Our results suggest that the proposed method is an accurate and easy to implement technique to include this normalization, being applicable to a large class of models. They also reinforce the notion that proper inclusion of the normalizing constant is crucial to the drawing of correct inferences and appropriate quantification of uncertainty. [ABSTRACT FROM AUTHOR]

The hierarchical Dirichlet processes (HDP) topic model is a Bayesian nonparametric model that provides a flexible mixed-membership to documents through topic allocation to each word. In this paper, we consider dynamic HDP topic models, in which the generative model changes in time, and develop a novel algorithm to update the posterior distribution dynamically by combining the variational inference algorithm and the power prior approach. An important advantage of the proposed algorithm is that it updates the posterior distribution by reusing a given batch algorithm without specifying a complicated dynamic generative model. Thus the proposed algorithm is conceptually and computationally simpler. By analyzing real datasets, we show that the proposed algorithm is a useful alternative approach to dynamic HDP topic identification. [ABSTRACT FROM AUTHOR]

We propose a Bayesian hierarchical method for combining in silico and in vivo data onto an augmented clinical trial with binary end points. The joint posterior distribution from the in silico experiment is treated as a prior, weighted by a measure of compatibility of the shared characteristics with the in vivo data. We also formalise the contribution and impact of in silico information in the augmented trial. We illustrate our approach to inference with in silico data from the UISS-TB simulator, a bespoke simulator of virtual patients with tuberculosis infection, and synthetic physical patients from a clinical trial.

It is of great practical importance to compare and combine data from different studies in order to carry out appropriate and more powerful statistical inference. We propose a partition based measure to quantify the compatibility of two datasets using their respective posterior distributions. We further propose an information gain measure to quantify the information increase (or decrease) in combining two datasets. These measures are well calibrated and efficient computational algorithms are provided for their calculations. We use examples in a benchmark dose toxicology study, a six cities pollution data and a melanoma clinical trial to illustrate how these two measures are useful in combining current data with historical data and missing data. [ABSTRACT FROM AUTHOR]

Benefit-risk assessment plays an important role in the evaluation of medical devices. Unlike the therapeutic devices, the diagnostic tests usually affect patient life indirectly since subsequent therapeutic treatment interventions (such as proper treatment in time, further examination or test, no action, etc.) will depend on correct diagnosis and monitoring of the disease status. A benefit-risk score using statistical models by integrating the information from benefit (true positive and true negative) and risk (false positive and false negative) for diagnostic tests with binary outcomes (i.e., positive and negative) will help evaluation of the utility and the uncertainty of a particular diagnostic device. In this paper, we develop two types of Bayesian models with conjugate priors for constructing the benefit-risk (BR) measures with corresponding credible intervals, one based on a Multinomial model with Dirichlet prior, and the other based on independent Binomial models with independent Beta priors. We then propose a Bayesian power prior model to incorporate the historical data or the real-world data (RWD). Both the fixed and random power prior parameters are considered for Bayesian borrowing. We evaluate the performance of the methods by simulations and illustrate their implementation using a real example. [ABSTRACT FROM AUTHOR]

The conditional power prior is a popular method to borrow information from a single prior data source. The amount of borrowing is controlled by the power parameter which is fixed before running the new study. However, fixing this parameter before running a new study is often difficult and may be unwise because if the outcomes in the current study are much different from the prior data outcomes, the power parameter cannot be changed to reflect a more appropriate degree of borrowing. On the other hand, treating the power parameter as a random variable to be updated via Bayes theorem may relinquish control over how much to borrow in cases where regulatory oversight recommends a conservative approach.Previous authors have determined the power parameter at the end of the current study based on "stochastic" similarity in the outcomes between the current study and the prior data. In this paper, we introduce some modifications to those methods. First, we determine the power parameter based on similarity between a percentage of the current study outcome data available at an interim look and the prior outcome data. This may limit potential for operational bias resulting from the determination of the power parameter after the current study is complete. Next, we introduce a new measure of similarity between the current (interim) and prior data that limits similarity by a pre-specified clinical margin. The proposed clinical similarity region may be readily understood by clinicians who need to assess when such borrowing is clinically appropriate. Through simulations, we show that our approach has low bias and good power, while reducing type I error rate in areas outside of the "similarity region". An example of a hypothetical medical device study illustrates its potential use in practice. [ABSTRACT FROM AUTHOR]

Abstract Background Performing well-powered randomised controlled trials (RCTs) of new treatments for rare diseases is often infeasible. However, with the increasing availability of historical data, incorporating existing information into trials with small sample sizes is appealing in order to increase the power. Bayesian approaches enable one to incorporate historical data into a trial’s analysis through a prior distribution. Methods Motivated by a RCT intended to evaluate the impact on event-free survival of mifamurtide in patients with osteosarcoma, we performed a simulation study to evaluate the impact on trial operating characteristics of incorporating historical individual control data and aggregate treatment effect estimates. We used power priors derived from historical individual control data for baseline parameters of Weibull and piecewise exponential models, while we used a mixture prior to summarise aggregate information obtained on the relative treatment effect. The impact of prior-data conflicts, both with respect to the parameters and survival models, was evaluated for a set of pre-specified weights assigned to the historical information in the prior distributions. Results The operating characteristics varied according to the weights assigned to each source of historical information, the variance of the informative and vague component of the mixture prior and the level of commensurability between the historical and new data. When historical and new controls follow different survival distributions, we did not observe any advantage of choosing a piecewise exponential model compared to a Weibull model for the new trial analysis. However, we think that it remains appealing given the uncertainty that will often surround the shape of the survival distribution of the new data. Conclusion In the setting of Sarcome-13 trial, and other similar studies in rare diseases, the gains in power and accuracy made possible by incorporating different types of historical information commensurate with the new trial data have to be balanced against the risk of biased estimates and a possible loss in power if data are not commensurate. The weights allocated to the historical data have to be carefully chosen based on this trade-off. Further simulation studies investigating methods for incorporating historical data are required to generalise the findings.

The evaluation of diagnostic tests usually involves statistical inference for its sensitivity. As sensitivity is defined as the probability that the test result will be positive when the target condition is present, the key study design consideration of sample size is the determination of the number of subjects with the target condition such that the estimation has adequate precision, or the hypothesis testing has adequate power. Traditionally, one may rely on prospective screening of subjects to obtain the required sample size, which means that if the prevalence of the disease is very low, a large number of subjects would need to be screened, increasing the study duration and cost. In this paper, we consider the possibility of substantially reducing the length and cost of a clinical study by leveraging subjects from a real-world data (RWD) source, focusing specifically on the diagnostic test for the cancer of interest. Using the propensity score methodology, we developed a procedure which ensures that the real-world subjects being leveraged are similar to their prospectively enrolled counterparts, thereby making the leveraging more justified. The procedure allows the down-weighting of the real-world subjects, which can be achieved by either using a Frequentist's method based on the composite likelihood or a Bayesian method based on the power prior. The proposed approach can be applied to the evaluation of any diagnostic test and it is not limited to the current clinical study regarding a cancer diagnostic test. Notably, this paper is in close alignment with a recently released draft framework by the Medical Device Innovation Consortium (MDIC) on real-world clinical evidence and in vitro diagnostics, being a showcase of appropriately leveraging real-world data in diagnostic test evaluation for diseases with low prevalence to support regulatory decision-making. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

SUMMARY: The feasibility of a new clinical trial may be increased by incorporating historical data of previous trials. In the particular case where only data from a single historical trial are available, there exists no clear recommendation in the literature regarding the most favorable approach. A main problem of the incorporation of historical data is the possible inflation of the type I error rate. A way to control this type of error is the so‐called power prior approach. This Bayesian method does not "borrow" the full historical information but uses a parameter 0 ≤ δ ≤ 1 to determine the amount of borrowed data. Based on the methodology of the power prior, we propose a frequentist framework that allows incorporation of historical data from both arms of two‐armed trials with binary outcome, while simultaneously controlling the type I error rate. It is shown that for any specific trial scenario a value δ > 0 can be determined such that the type I error rate falls below the prespecified significance level. The magnitude of this value of δ depends on the characteristics of the data observed in the historical trial. Conditionally on these characteristics, an increase in power as compared to a trial without borrowing may result. Similarly, we propose methods how the required sample size can be reduced. The results are discussed and compared to those obtained in a Bayesian framework. Application is illustrated by a clinical trial example. [ABSTRACT FROM AUTHOR]

Abstract–To evaluate a novel vaccine, randomized clinical trials are often conducted to assess how much the infection or disease rate is reduced in the vaccinated group as compared to the unvaccinated group. Because of low incidence rate for the clinical endpoint, the sample size based on exact conditional binomial test is often very large for vaccine efficacy trials, which poses big challenge for study conduct and enrollment, especially in studies with very low incidence rates. Bayesian framework provides a natural avenue to use historical information, if there is evidence to suggest similarity of the responses between the historical and current studies. In this article, we first propose a hierarchical conditional binomial model to provide a Bayesian framework to use historical information for assessing vaccine efficacy. Secondly, we propose a beta prior distribution which is equivalent to the power prior to borrow partial historical information quantitatively. Simulations are conducted to evaluate the power and Type I error for vaccine efficacy study by borrowing historical information with the proposed analytic approaches. The proposed methods are demonstrated by an example to show the improved efficacy estimation through borrowing information from a historical study. [ABSTRACT FROM AUTHOR]

Chuang-Stein et al. proposed a method for benefit–risk assessment by formulating a five-category multinomial random variable with the first four categories as a combination of benefit and risk, and the fifth category to include subjects who withdraw from study. In this article, we subdivide the single withdrawal category into four sub-categories to consider withdrawal for different reasons. To analyze eight-category data, we propose a two-level multivariate-Dirichlet Model to identify benefit–risk measures at the population level. For individual benefit–risk, we use a log-odds ratio model with Dirichlet process prior. Two methods are applied to a hypothetical clinical trial data for illustration. [ABSTRACT FROM AUTHOR]

This article considers Bayesian approaches for incorporating information from a historical model into a current analysis when the historical model includes only a subset of covariates currently of interest. The statistical challenge is 2-fold. First, the parameters in the nested historical model are not generally equal to their counterparts in the larger current model, neither in value nor interpretation. Second, because the historical information will not be equally informative for all parameters in the current analysis, additional regularization may be required beyond that provided by the historical information. We propose several novel extensions of the so-called power prior that adaptively combine a prior based upon the historical information with a variance-reducing prior that shrinks parameter values toward zero. The ideas are directly motivated by our work building mortality risk prediction models for pediatric patients receiving extracorporeal membrane oxygenation (ECMO). We have developed a model on a registry-based cohort of ECMO patients and now seek to expand this model with additional biometric measurements, not available in the registry, collected on a small auxiliary cohort. Our adaptive priors are able to use the information in the original model and identify novel mortality risk factors. We support this with a simulation study, which demonstrates the potential for efficiency gains in estimation under a variety of scenarios. [ABSTRACT FROM AUTHOR]

As described in the ICH E5 guidelines, a bridging study is an additional study executed in a new geographical region or subpopulation to link or "build a bridge" from global clinical trial outcomes to the new region. The regulatory and scientific goals of a bridging study is to evaluate potential subpopulation differences while minimizing duplication of studies and meeting unmet medical needs expeditiously. Use of historical data (borrowing) from global studies is an attractive approach to meet these conflicting goals. Here, we propose a practical and relevant approach to guide the optimal borrowing rate (percent of subjects in earlier studies) and the number of subjects in the new regional bridging study. We address the limitations in global/regional exchangeability through use of a Bayesian power prior method and then optimize bridging study design with a return on investment viewpoint. The method is demonstrated using clinical data from global and Japanese trials in dapagliflozin for type 2 diabetes. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical regression (BHR) is often used in small area estimation (SAE). BHR conditions on the samples. Therefore, when data are from a complex sample survey, neither survey sampling design nor survey weights are used. This can introduce bias and/or cause large variance. Further, if non-informative priors are used, BHR often requires the combination of multiple years of data to produce sample sizes that yield adequate precision; this can result in poor timeliness and can obscure trends. To address bias and variance, we propose a design assisted model-based approach for SAE by integrating adjusted sample weights. To address timeliness, we use historical data to define informative priors (power prior); this allows estimates to be derived from a single year of data. Using American Community Survey data for validation, we applied the proposed method to Behavioral Risk Factor Surveillance System data. We estimated the prevalence of disability for all U.S. counties. We show that our method can produce estimates that are both more timely than those arising from widely-used alternatives and are closer to ACS' direct estimates, particularly for low-data counties. Our method can be generalized to estimate the county-level prevalence of other health related measurements. [ABSTRACT FROM AUTHOR]

We are now at an amazing time for medical product development in drugs, biological products and medical devices. As a result of dramatic recent advances in biomedical science, information technology and engineering, ''big data" from health care in the real-world have become available. Although big data may not necessarily be attuned to provide the preponderance of evidence to a clinical study, high-quality real-world data can be transformed into scientific evidence for regulatory and healthcare decision-making using proven analytical methods and techniques, such as propensity score methodology and Bayesian inference. In this paper, we extend the Bayesian power prior approach for a single-arm study (the current study) to leverage external real-world data. We use propensity score methodology to pre-select a subset of real-world data containing patients that are similar to those in the current study in terms of covariates, and to stratify the selected patients together with those in the current study into more homogeneous strata. The power prior approach is then applied in each stratum to obtain stratum-specific posterior distributions, which are combined to complete the Bayesian inference for the parameters of interest. We evaluate the performance of the proposed method as compared to that of the ordinary power prior approach by simulation and illustrate its implementation using a hypothetical example, based on our regulatory review experience. [ABSTRACT FROM AUTHOR]