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Special Issue "Bayesian Design in Clinical Trials"

A special issue of International Journal of Environmental Research and Public Health (ISSN 1660-4601).

Deadline for manuscript submissions: closed (30 September 2021) | Viewed by 16238

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A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Ileana Baldi
E-Mail Website
Guest Editor
Department of Cardiac, Thoracic, Vascular Sciences and Public Health, University of Padova, 35122 Padova, PD, Italy
Interests: clinical trials; adaptive design; population-based studies; machine Learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the last decade, the number of clinical trials using Bayesian methods has grown dramatically. Nowadays, regulatory authorities appear to be more receptive to Bayesian methods than ever.
The Bayesian methodology is well-suited to address the issues arising in the planning, the analysis, and the conduct of clinical trials. Due of their flexibility, Bayesian design methods based on the accrued data of on-going trials have been recommended by both the US Food and Drug Administration (FDA) and the European Medicines Agency for dose–response trials in early clinical development. More generally, since the inherent adaptive nature of Phase I and Phase II designs, the Bayesian approach tends to be more efficient.
A recent development for oncology clinical trials is represented by the basket studies or multi-disease trials, which enroll patients that have a common genetic mutation but include different tumor types. A Bayesian approach through the Bayesian hierarchical model has the appeal of being able to improve the efficiency of such trials by properly borrowing information.
Another distinctive feature of the Bayesian approach is that it naturally allows for dealing with external information, such as historical data, findings from previous studies, and expert opinions through prior elicitation. In fact, it provides a framework for embedding and handling the variability of such auxiliary information within the planning and analysis of the study. A growing body of literature examines the use of historical data to augment newly collected data, especially in clinical trials where patients are difficult to recruit, which is the case for rare disease, for example. Many works describe the importance of using the available data in clinical trials and how this can be done properly. Using historical data has been recognized as less controversial than eliciting prior information from experts’ opinion also by the FDA in its guidance on the use of Bayesian Statistics in Medical Device Clinical Trials.
Papers addressing these topics are invited for submission to this Special Issue. Novel applications of Bayesian modeling to data from clinical trials, Bayesian designs for early phase trials, seamless phase II/III and phase III clinical trials, the Bayesian approach for monitoring, and hybrid Bayesian–frequentist designs are welcome, as well as papers addressing the advantages and limitations of the Bayesian approach carrying out virtual re-executions of published trials.

Dr. Paola Berchialla
Dr. Ileana Baldi
Guest Editors

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Keywords

  • Bayesian design
  • Interim analyses
  • Bayesian hierarchical models
  • Treatment response adaptive randomization
  • Bayesian sequential design
  • Bayesian monitoring
  • Power priors
  • Dynamic treatment regimes
  • Historical controls

Published Papers (12 papers)

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Research

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Article
Bayesian Design for Identifying Cohort-Specific Optimal Dose Combinations Based on Multiple Endpoints: Application to a Phase I Trial in Non-Small Cell Lung Cancer
Int. J. Environ. Res. Public Health 2021, 18(21), 11452; https://doi.org/10.3390/ijerph182111452 - 30 Oct 2021
Viewed by 907
Abstract
Immunotherapy and chemotherapy combinations have proven to be a safe and efficacious treatment approach in multiple settings. However, it is not clear whether approved doses of chemotherapy developed to achieve a maximum tolerated dose are the ideal dose when combining cytotoxic chemotherapy with [...] Read more.
Immunotherapy and chemotherapy combinations have proven to be a safe and efficacious treatment approach in multiple settings. However, it is not clear whether approved doses of chemotherapy developed to achieve a maximum tolerated dose are the ideal dose when combining cytotoxic chemotherapy with immunotherapy to induce immune responses. This trial of a modulated dose chemotherapy and Pembrolizumab, with or without a second immunomodulatory agent, uses a Bayesian design to select the optimal treatment combination by balancing both safety and efficacy of the chemotherapy and immunotherapy agents within each of two cohorts. The simulation study provides evidence that the proposed Bayesian design successfully addresses the primary study aim to identify the optimal dose combination for each of the two independent patient cohorts. This conclusion is supported by the high percentage of simulated trials which select a treatment combination that is both safe and highly efficacious. The proposed trial was funded and was being finalized when the sponsoring company decided not to proceed due to negative findings in another patient population. The proposed trial design will continue to be relevant as multiple chemotherapy and immunotherapy combinations become the standard of care and future research will require evaluating the appropriate doses of various components of multiple drug regimens. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
Article
Bayesian Sequential Monitoring of Single-Arm Trials: A Comparison of Futility Rules Based on Binary Data
Int. J. Environ. Res. Public Health 2021, 18(16), 8816; https://doi.org/10.3390/ijerph18168816 - 20 Aug 2021
Viewed by 816
Abstract
In clinical trials, futility rules are widely used to monitor the study while it is in progress, with the aim of ensuring early termination if the experimental treatment is unlikely to provide the desired level of efficacy. In this paper, we focus on [...] Read more.
In clinical trials, futility rules are widely used to monitor the study while it is in progress, with the aim of ensuring early termination if the experimental treatment is unlikely to provide the desired level of efficacy. In this paper, we focus on Bayesian strategies to perform interim analyses in single-arm trials based on a binary response variable. Designs that exploit both posterior and predictive probabilities are described and a slight modification of the futility rules is introduced when a fixed historical response rate is used, in order to add uncertainty in the efficacy probability of the standard treatment through the use of prior distributions. The stopping boundaries of the designs are compared under the same trial settings and simulation studies are performed to evaluate the operating characteristics when analogous procedures are used to calibrate the probability cut-offs of the different decision rules. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Adjustment for Baseline Covariates to Increase Efficiency in RCTs with Binary Endpoint: A Comparison of Bayesian and Frequentist Approaches
Int. J. Environ. Res. Public Health 2021, 18(15), 7758; https://doi.org/10.3390/ijerph18157758 - 22 Jul 2021
Viewed by 876
Abstract
Background: In a randomized controlled trial (RCT) with binary outcome the estimate of the marginal treatment effect can be biased by prognostic baseline covariates adjustment. Methods that target the marginal odds ratio, allowing for improved precision and power, have been developed. Methods: The [...] Read more.
Background: In a randomized controlled trial (RCT) with binary outcome the estimate of the marginal treatment effect can be biased by prognostic baseline covariates adjustment. Methods that target the marginal odds ratio, allowing for improved precision and power, have been developed. Methods: The performance of different estimators for the treatment effect in the frequentist (targeted maximum likelihood estimator, inverse-probability-of-treatment weighting, parametric G-computation, and the semiparametric locally efficient estimator) and Bayesian (model averaging), adjustment for confounding, and generalized Bayesian causal effect estimation frameworks are assessed and compared in a simulation study under different scenarios. The use of these estimators is illustrated on an RCT in type II diabetes. Results: Model mis-specification does not increase the bias. The approaches that are not doubly robust have increased standard error (SE) under the scenario of mis-specification of the treatment model. The Bayesian estimators showed a higher type II error than frequentist estimators if noisy covariates are included in the treatment model. Conclusions: Adjusting for prognostic baseline covariates in the analysis of RCTs can have more power than intention-to-treat based tests. However, for some classes of model, when the regression model is mis-specified, inflated type I error and potential bias on treatment effect estimate may arise. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Study Protocol: Phase I Dose Escalation Study of Oxaliplatin, Cisplatin and Doxorubicin Applied as PIPAC in Patients with Peritoneal Metastases
Int. J. Environ. Res. Public Health 2021, 18(11), 5656; https://doi.org/10.3390/ijerph18115656 - 25 May 2021
Viewed by 1278
Abstract
Pressurized Intra-Peritoneal Aerosol Chemotherapy (PIPAC) is a novel laparoscopic intraperitoneal chemotherapy approach offered in selected patients affected by non-resectable peritoneal carcinomatosis. Drugs doses currently established for nebulization are very low: oxaliplatin (OXA) 120 mg/sm, cisplatin (CDDP) 10.5 mg/sm and doxorubicin (DXR) 2.1 mg/sm. [...] Read more.
Pressurized Intra-Peritoneal Aerosol Chemotherapy (PIPAC) is a novel laparoscopic intraperitoneal chemotherapy approach offered in selected patients affected by non-resectable peritoneal carcinomatosis. Drugs doses currently established for nebulization are very low: oxaliplatin (OXA) 120 mg/sm, cisplatin (CDDP) 10.5 mg/sm and doxorubicin (DXR) 2.1 mg/sm. A model-based approach for dose-escalation design in a single PIPAC procedure and subsequent dose escalation steps is planned. The starting dose of oxaliplatin is 100 mg/sm with a maximum estimated dose of 300 mg/sm; an escalation with overdose and under-dose control (for probability of toxicity less than 16% in case of under-dosing and probability of toxicity greater than 33% in case of overdosing) will be further applied. Cisplatin is used in association with doxorubicin: A two-dimensional dose-finding design is applied on the basis of the estimated dose limiting toxicity (DLT) at all combinations. The starting doses are 15 mg/sm for cisplatin and 3 mg/sm for doxorubicin. Safety is assessed according to Common Terminology Criteria for Adverse Events (CTCAE version 4.03). Secondary endpoints include radiological response according to Response Evaluation Criteria in Solid Tumor (version 1.1) and pharmacokinetic analyses. This phase I study can provide the scientific basis to maximize the optimal dose of cisplatin, doxorubicin and oxaliplatin applied as PIPAC. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Handling Poor Accrual in Pediatric Trials: A Simulation Study Using a Bayesian Approach
Int. J. Environ. Res. Public Health 2021, 18(4), 2095; https://doi.org/10.3390/ijerph18042095 - 21 Feb 2021
Cited by 1 | Viewed by 1053
Abstract
In the conduction of trials, a common situation is related to potential difficulties in recruiting the planned sample size as provided by the study design. A Bayesian analysis of such trials might provide a framework to combine prior evidence with current evidence, and [...] Read more.
In the conduction of trials, a common situation is related to potential difficulties in recruiting the planned sample size as provided by the study design. A Bayesian analysis of such trials might provide a framework to combine prior evidence with current evidence, and it is an accepted approach by regulatory agencies. However, especially for small trials, the Bayesian inference may be severely conditioned by the prior choices. The Renal Scarring Urinary Infection (RESCUE) trial, a pediatric trial that was a candidate for early termination due to underrecruitment, served as a motivating example to investigate the effects of the prior choices on small trial inference. The trial outcomes were simulated by assuming 50 scenarios combining different sample sizes and true absolute risk reduction (ARR). The simulated data were analyzed via the Bayesian approach using 0%, 50%, and 100% discounting factors on the beta power prior. An informative inference (0% discounting) on small samples could generate data-insensitive results. Instead, the 50% discounting factor ensured that the probability of confirming the trial outcome was higher than 80%, but only for an ARR higher than 0.17. A suitable option to maintain data relevant to the trial inference is to define a discounting factor based on the prior parameters. Nevertheless, a sensitivity analysis of the prior choices is highly recommended. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Estimating Similarity of Dose–Response Relationships in Phase I Clinical Trials—Case Study in Bridging Data Package
Int. J. Environ. Res. Public Health 2021, 18(4), 1639; https://doi.org/10.3390/ijerph18041639 - 09 Feb 2021
Cited by 1 | Viewed by 1276
Abstract
Bridging studies are designed to fill the gap between two populations in terms of clinical trial data, such as toxicity, efficacy, comorbidities and doses. According to ICH-E5 guidelines, clinical data can be extrapolated from one region to another if dose–reponse curves are similar [...] Read more.
Bridging studies are designed to fill the gap between two populations in terms of clinical trial data, such as toxicity, efficacy, comorbidities and doses. According to ICH-E5 guidelines, clinical data can be extrapolated from one region to another if dose–reponse curves are similar between two populations. For instance, in Japan, Phase I clinical trials are often repeated due to this physiological/metabolic paradigm: the maximum tolerated dose (MTD) for Japanese patients is assumed to be lower than that for Caucasian patients, but not necessarily for all molecules. Therefore, proposing a statistical tool evaluating the similarity between two populations dose–response curves is of most interest. The aim of our work is to propose several indicators to evaluate the distance and the similarity of dose–toxicity curves and MTD distributions at the end of some of the Phase I trials, conducted on two populations or regions. For this purpose, we extended and adapted the commensurability criterion, initially proposed by Ollier et al. (2019), in the setting of completed phase I clinical trials. We evaluated their performance using three synthetic sets, built as examples, and six case studies found in the literature. Visualization plots and guidelines on the way to interpret the results are proposed. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models
Int. J. Environ. Res. Public Health 2021, 18(2), 809; https://doi.org/10.3390/ijerph18020809 - 19 Jan 2021
Cited by 1 | Viewed by 924
Abstract
In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster [...] Read more.
In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster models through model selection. The meta-parameter is then estimated using Bayesian model averaging techniques. Although an objective Bayesian meta-analysis is proposed for each type of heterogeneity, we concentrate the attention of this paper on priors over the models. We consider four alternative priors which are motivated by reasonable but different assumptions. A frequentist validation with simulated data has been carried out to analyze the properties of each prior distribution for a set of different number of studies and sample sizes. The results show the importance of choosing an adequate model prior as the posterior probabilities for the models are very sensitive to it. The hierarchical Poisson prior and the hierarchical uniform prior show a good performance when the real model is the homogeneity, or when the sample sizes are high enough. However, the uniform prior can detect the true model when it is an intermediate model (neither homogeneity nor heterogeneity) even for small sample sizes and few studies. An illustrative example with real data is also given, showing the sensitivity of the estimation of the meta-parameter to the model prior. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials
Int. J. Environ. Res. Public Health 2021, 18(2), 595; https://doi.org/10.3390/ijerph18020595 - 12 Jan 2021
Cited by 2 | Viewed by 1311
Abstract
In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In [...] Read more.
In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Article
Using an Interaction Parameter in Model-Based Phase I Trials for Combination Treatments? A Simulation Study
Int. J. Environ. Res. Public Health 2021, 18(1), 345; https://doi.org/10.3390/ijerph18010345 - 05 Jan 2021
Cited by 2 | Viewed by 1494
Abstract
There is growing interest in Phase I dose-finding studies studying several doses of more than one agent simultaneously. A number of combination dose-finding designs were recently proposed to guide escalation/de-escalation decisions during the trials. The majority of these proposals are model-based: a parametric [...] Read more.
There is growing interest in Phase I dose-finding studies studying several doses of more than one agent simultaneously. A number of combination dose-finding designs were recently proposed to guide escalation/de-escalation decisions during the trials. The majority of these proposals are model-based: a parametric combination-toxicity relationship is fitted as data accumulates. Various parameter shapes were considered but the unifying theme for many of these is that typically between 4 and 6 parameters are to be estimated. While more parameters allow for more flexible modelling of the combination-toxicity relationship, this is a challenging estimation problem given the typically small sample size in Phase I trials of between 20 and 60 patients. These concerns gave raise to an ongoing debate whether including more parameters into combination-toxicity model leads to more accurate combination selection. In this work, we extensively study two variants of a 4-parameter logistic model with reduced number of parameters to investigate the effect of modelling assumptions. A framework to calibrate the prior distributions for a given parametric model is proposed to allow for fair comparisons. Via a comprehensive simulation study, we have found that the inclusion of the interaction parameter between two compounds does not provide any benefit in terms of the accuracy of selection, on average, but is found to result in fewer patients allocated to the target combination during the trial. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Review

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Review
Prior Elicitation for Use in Clinical Trial Design and Analysis: A Literature Review
Int. J. Environ. Res. Public Health 2021, 18(4), 1833; https://doi.org/10.3390/ijerph18041833 - 13 Feb 2021
Cited by 3 | Viewed by 1661
Abstract
Bayesian inference is increasingly popular in clinical trial design and analysis. The subjective knowledge derived from an expert elicitation procedure may be useful to define a prior probability distribution when no or limited data is available. This work aims to investigate the state-of-the-art [...] Read more.
Bayesian inference is increasingly popular in clinical trial design and analysis. The subjective knowledge derived from an expert elicitation procedure may be useful to define a prior probability distribution when no or limited data is available. This work aims to investigate the state-of-the-art Bayesian prior elicitation methods with a focus on clinical trial research. A literature search on the Current Index to Statistics (CIS), PubMed, and Web of Science (WOS) databases, considering “prior elicitation” as a search string, was run on 1 November 2020. Summary statistics and trend of publications over time were reported. Finally, a Latent Dirichlet Allocation (LDA) model was developed to recognise latent topics in the pertinent papers retrieved. A total of 460 documents pertinent to the Bayesian prior elicitation were identified. Of these, 213 (45.4%) were published in the “Probability and Statistics” area. A total of 42 articles pertain to clinical trial and the majority of them (81%) reports parametric techniques as elicitation method. The last decade has seen an increased interest in prior elicitation and the gap between theory and application getting narrower and narrower. Given the promising flexibility of non-parametric approaches to the experts’ elicitation, more efforts are needed to ensure their diffusion also in applied settings. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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Review
Bayesian Approaches for Confirmatory Trials in Rare Diseases: Opportunities and Challenges
Int. J. Environ. Res. Public Health 2021, 18(3), 1022; https://doi.org/10.3390/ijerph18031022 - 24 Jan 2021
Cited by 2 | Viewed by 1318
Abstract
The aim of this narrative review is to introduce the reader to Bayesian methods that, in our opinion, appear to be the most important in the context of rare diseases. A disease is defined as rare depending on the prevalence of the affected [...] Read more.
The aim of this narrative review is to introduce the reader to Bayesian methods that, in our opinion, appear to be the most important in the context of rare diseases. A disease is defined as rare depending on the prevalence of the affected patients in the considered population, for example, about 1 in 1500 people in U.S.; about 1 in 2500 people in Japan; and fewer than 1 in 2000 people in Europe. There are between 6000 and 8000 rare diseases and the main issue in drug development is linked to the challenge of achieving robust evidence from clinical trials in small populations. A better use of all available information can help the development process and Bayesian statistics can provide a solid framework at the design stage, during the conduct of the trial, and at the analysis stage. The focus of this manuscript is to provide a review of Bayesian methods for sample size computation or reassessment during phase II or phase III trial, for response adaptive randomization and of for meta-analysis in rare disease. Challenges regarding prior distribution choice, computational burden and dissemination are also discussed. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
Review
The Bayesian Design of Adaptive Clinical Trials
Int. J. Environ. Res. Public Health 2021, 18(2), 530; https://doi.org/10.3390/ijerph18020530 - 10 Jan 2021
Cited by 3 | Viewed by 1937
Abstract
This paper presents a brief overview of the recent literature on adaptive design of clinical trials from a Bayesian perspective for statistically not so sophisticated readers. Adaptive designs are attracting a keen interest in several disciplines, from a theoretical viewpoint and also—potentially—from a [...] Read more.
This paper presents a brief overview of the recent literature on adaptive design of clinical trials from a Bayesian perspective for statistically not so sophisticated readers. Adaptive designs are attracting a keen interest in several disciplines, from a theoretical viewpoint and also—potentially—from a practical one, and Bayesian adaptive designs, in particular, have raised high expectations in clinical trials. The main conceptual tools are highlighted here, with a mention of several trial designs proposed in the literature that use these methods, including some of the registered Bayesian adaptive trials to this date. This review aims at complementing the existing ones on this topic, pointing at further interesting reading material. Full article
(This article belongs to the Special Issue Bayesian Design in Clinical Trials)
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