Investigator choice of standard therapy versus sequential novel therapy arms in the treatment of relapsed follicular lymphoma (REFRACT): study protocol for a multi-centre, open-label, randomised, phase II platform trial.

BACKGROUND: Relapsed or refractory follicular lymphoma (rrFL) is an incurable disease associated with shorter remissions and survival after each line of standard therapy. Many promising novel, chemotherapy-free therapies are in development, but few are licensed as their role in current treatment pathways is poorly defined. METHODS: The REFRACT trial is an investigator-initiated, UK National Cancer Research Institute, open-label, multi-centre, randomised phase II platform trial aimed at accelerating clinical development of novel therapies by addressing evidence gaps. The first of the three sequential novel therapy arms is epcoritamab plus lenalidomide, to be compared with investigator choice standard therapy (ICT). Patients aged 18 years or older with biopsy proven relapsed or refractory CD20 positive, grade 1-3a follicular lymphoma and assessable disease by PET-CT are eligible. The primary outcome is complete metabolic response by PET-CT at 24 weeks using the Deauville 5-point scale and Lugano 2014 criteria. Secondary outcomes include overall metabolic response, progression-free survival, overall survival, duration of response, and quality of life assessed by EQ-5D-5 L and FACT-Lym. The trial employs an innovative Bayesian design with a target sample size of 284 patients: 95 in the ICT arm and 189 in the novel therapy arms. DISCUSSION: Whilst there are many promising novel drugs in early clinical development for rrFL, understanding the relative efficacy and safety of these agents, and their place in modern treatment pathways, is limited by a lack of randomised trials and dearth of published outcomes for standard regimens to act as historic controls. Therefore, the aim of REFRACT is to provide an efficient platform to evaluate novel agents against standard therapies for rrFL. The adaptive Bayesian power prior methodology design will minimise patient numbers and accelerate trial delivery. TRIAL REGISTRATION: ClinicalTrials.gov: NCT05848765; 08-May-2023. EUDRACT: 2022-000677-75; 10-Feb-2022.

Case weighted power priors for hybrid control analyses with time-to-event data.

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.

A Bayesian method to detect drug-drug interaction using external information for spontaneous reporting system.

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.

Prior elicitation for Gaussian spatial process: An application to TMS brain mapping.

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.

Incorporating Prior Beliefs Into Meta-Analyses of Health-State Utility Values Using the Bayesian Power Prior.

OBJECTIVES: Health-state utility values (HSUVs) directly affect estimates of Quality-Adjusted Life-Years and thus the cost-utility estimates. In practice a single preferred value (SPV) is often selected for HSUVs, despite meta-analysis being an option when multiple (credible) HSUVs are available. Nevertheless, the SPV approach is often reasonable because meta-analysis implicitly considers all HSUVs as equally relevant. This article presents a method for the incorporation of weights to HSUV synthesis, allowing more relevant studies to have greater influence. METHODS: Using 4 case studies in lung cancer, hemodialysis, compensated liver cirrhosis, and diabetic retinopathy blindness, a Bayesian Power Prior (BPP) approach is used to incorporate beliefs on study applicability, reflecting the authors' perceived suitability for UK decision making. Older studies, non-UK value sets, and vignette studies are thus downweighted (but not disregarded). BPP HSUV estimates were compared with a SPV, random effects meta-analysis, and fixed effects meta-analysis. Sensitivity analyses were conducted iteratively updating the case studies, using alternative weighting methods, and simulated data. RESULTS: Across all case studies, SPVs did not accord with meta-analyzed values, and fixed effects meta-analysis produced unrealistically narrow CIs. Point estimates from random effects meta-analysis and BPP models were similar in the final models, although BPP reflected additional uncertainty as wider credible intervals, particularly when fewer studies were available. Differences in point estimates were seen in iterative updating, weighting approaches, and simulated data. CONCLUSIONS: The concept of the BPP can be adapted for synthesizing HSUVs, incorporating expert opinion on relevance. Because of the downweighting of studies, the BPP reflected structural uncertainty as wider credible intervals, with all forms of synthesis showing meaningful differences compared with SPVs. These differences would have implications for both cost-utility point estimates and probabilistic analyses.

Utility of propensity score-based Bayesian borrowing of external adult data in pediatric trials: A pragmatic evaluation through a case study in acute lymphoblastic leukemia (ALL).

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.

Utilization of treatment effect on a surrogate endpoint for planning a study to evaluate treatment effect on a final endpoint.

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.

Bayesian borrowing from historical control data in a vaccine efficacy trial.

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

Power priors with entropy balancing weights in data augmentation of partially controlled randomized trials.

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.

Multi-stage dose expansion cohort (MSDEC) design with Bayesian stopping rule.

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.

Propensity score-integrated power prior approach for augmenting the control arm of a randomized controlled trial by incorporating multiple external data sources.

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.

Bayesian sample size determination in a three-arm non-inferiority trial with binary endpoints.

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.

Bayesian Divide-and-Conquer Propensity Score Based Approaches for Leveraging Real World Data in Single Arm Clinical Trials.

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.

The power prior with multiple historical controls for the linear regression model.

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.

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.

Bayesian adaptive randomization design incorporating propensity score-matched historical controls.

Incorporating historical control data to augment the control arm in randomized controlled trials (RCTs) is one way of increasing their efficiency and feasibility when adequate RCTs cannot be conducted. In recent work, a Bayesian adaptive randomization design incorporating historical control data has been proposed to reduce sample size according to the amount of information that could be borrowed, assessed at interim assessment in respect to prior-data conflict. However, the approach does not distinguish between the two sources of prior-data conflict: (1) imbalance in measured covariates, and (2) imbalance in unmeasured covariates. In this paper, we propose an extension of the Bayesian adaptive randomization design to incorporate propensity score-matched historical controls. At interim assessment, historical controls similar to the concurrent controls in terms of measured covariates are selected using propensity score matching. Then, final sample size of the control arm is adjusted according to the extent of borrowing from the matched historical controls quantified by effective historical sample size. The conditional power prior approach and commensurate prior approach are adopted for designing the prior, and addressing prior-data conflict due to unmeasured covariate imbalance. Simulation results show that the proposed method yields reduced bias in treatment effect estimates, type I error at the nominal level, and reduced sample size while maintaining statistical power. Even when residual imbalance exists due to unmeasured covariates, the proposed method borrowed more information without risking substantially inflated type I error and bias, providing meaningful implications for use of historical controls to facilitate the conduct of adequate RCTs.

Incorporating historical models with adaptive Bayesian updates.

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.

On the normalized power prior.

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.

New partition based measures for data compatibility and information gain.

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.

Dynamic borrowing from a single prior data source using the conditional power prior.

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.