Determination of the optimal sample size for a clinical trial accounting for the population size

Innovations in Clinical Development in Rare Diseases of Children and Adults: Small Populations and/or Small Patients

Many of the afflictions of children are rare diseases. This creates numerous drug development challenges related to small populations, including limited information about the disease state, enrollment challenges, and diminished incentives for pediatric development of novel therapies by pharmaceutical and biotechnology sponsors. We review selected innovations in clinical development that may partially mitigate some of these difficulties, starting with the concept of development efficiency for individual clinical trials, clinical programs (involving multiple trials for a single drug), and clinical portfolios of multiple drugs, and decision analysis as a tool to optimize efficiency. Development efficiency is defined as the ability to reach equally rigorous or more rigorous conclusions in less time, with fewer trial participants, or with fewer resources. We go on to discuss efficient methods for matching targeted therapies to biomarker-defined subgroups, methods for eliminating or reducing the need for natural history data to guide rare disease development, the use of basket trials to enhance efficiency by grouping multiple similar disease applications in a single clinical trial, and the use of alternative data sources including historical controls to augment or replace concurrent controls in clinical studies. Greater understanding and broader application of these methods could lead to improved therapies and/or more widespread and rapid access to novel therapies for rare diseases in both children and adults.

N-of-1 Trials in Pediatric Oncology: From a Population-Based Approach to Personalized Medicine-A Review

Pediatric oncology is a critical area where the more efficient development of new treatments is urgently needed. The speed of approval of new drugs is still limited by regulatory requirements and a lack of innovative designs appropriate for trials in children. Childhood cancers meet the criteria of rare diseases. Personalized medicine brings it even closer to the horizon of individual cases. Thus, not all the traditional research tools, such as large-scale RCTs, are always suitable or even applicable, mainly due to limited sample sizes. Small samples and traditional versus subject-specific evidence are both distinctive issues in personalized pediatric oncology. Modern analytical approaches and adaptations of the paradigms of evidence are warranted. We have reviewed innovative trial designs and analytical methods developed for small populations, together with individualized approaches, given their applicability to pediatric oncology. We discuss traditional population-based and individualized perspectives of inferences and evidence, and explain the possibilities of using various methods in pediatric personalized oncology. We find that specific derivatives of the original N-of-1 trial design adapted for pediatric personalized oncology may represent an optimal analytical tool for this area of medicine. We conclude that no particular N-of-1 strategy can provide a solution. Rather, a whole range of approaches is needed to satisfy the new inferential and analytical paradigms of modern medicine. We reveal a new view of cancer as continuum model and discuss the "evidence puzzle".

Selection bias, investment decisions and treatment effect distributions

When making decisions regarding the investment and design for a Phase 3 programme in the development of a new drug, the results from preceding Phase 2 trials are an important source of information. However, only projects in which the Phase 2 results show promising treatment effects will typically be considered for a Phase 3 investment decision. This implies that, for those projects where Phase 3 is pursued, the underlying Phase 2 estimates are subject to selection bias. We will in this article investigate the nature of this selection bias based on a selection of distributions for the treatment effect. We illustrate some properties of Bayesian estimates, providing shrinkage of the Phase 2 estimate to counteract the selection bias. We further give some empirical guidance regarding the choice of prior distribution and comment on the consequences for decision-making in investment and planning for Phase 3 programmes.

The Use of Translational Modelling and Simulation to Develop Immunomodulatory Therapy as an Adjunct to Antibiotic Treatment in the Context of Pneumonia

The treatment of respiratory tract infections is threatened by the emergence of bacterial resistance. Immunomodulatory drugs, which enhance airway innate immune defenses, may improve therapeutic outcome. In this concept paper, we aim to highlight the utility of pharmacometrics and Bayesian inference in the development of immunomodulatory therapeutic agents as an adjunct to antibiotics in the context of pneumonia. For this, two case studies of translational modelling and simulation frameworks are introduced for these types of drugs up to clinical use. First, we evaluate the pharmacokinetic/pharmacodynamic relationship of an experimental combination of amoxicillin and a TLR4 agonist, monophosphoryl lipid A, by developing a pharmacometric model accounting for interaction and potential translation to humans. Capitalizing on this knowledge and associating clinical trial extrapolation and statistical modelling approaches, we then investigate the TLR5 agonist flagellin. The resulting workflow combines expert and prior knowledge on the compound with the in vitro and in vivo data generated during exploratory studies in order to construct high-dimensional models considering the pharmacokinetics and pharmacodynamics of the compound. This workflow can be used to refine preclinical experiments, estimate the best doses for human studies, and create an adaptive knowledge-based design for the next phases of clinical development.

Collaborative Platform Trials to Fight COVID-19: Methodological and Regulatory Considerations for a Better Societal Outcome

For the development of coronavirus disease 2019 (COVID‐19) drugs during the ongoing pandemic, speed is of essence whereas quality of evidence is of paramount importance. Although thousands of COVID‐19 trials were rapidly started, many are unlikely to provide robust statistical evidence and meet regulatory standards (e.g., because of lack of randomization or insufficient power). This has led to an inefficient use of time and resources. With more coordination, the sheer number of patients in these trials might have generated convincing data for several investigational treatments. Collaborative platform trials, comparing several drugs to a shared control arm, are an attractive solution. Those trials can utilize a variety of adaptive design features in order to accelerate the finding of life‐saving treatments. In this paper, we discuss several possible designs, illustrate them via simulations, and also discuss challenges, such as the heterogeneity of the target population, time‐varying standard of care, and the potentially high number of false hypothesis rejections in phase II and phase III trials. We provide corresponding regulatory perspectives on approval and reimbursement, and note that the optimal design of a platform trial will differ with our societal objective and by stakeholder. Hasty approvals may delay the development of better alternatives, whereas searching relentlessly for the single most efficacious treatment may indirectly diminish the number of lives saved as time is lost. We point out the need for incentivizing developers to participate in collaborative evidence‐generation initiatives when a positive return on investment is not met.

Bayesian Approaches for Confirmatory Trials in Rare Diseases: Opportunities and Challenges

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.

Combination of Vinpocetine and Dexamethasone Alleviates Cognitive Impairment in Nasopharyngeal Carcinoma Patients following Radiation Injury

BACKGROUND

Nasopharyngeal carcinoma (NPC) originates in the nasopharyngeal epithelium. The most common treatments for NPC rT1-4 are radiotherapy and surgery. The pathogenesis of radiation-induced cognitive impairment is complex and includes oxidative stress, mitochondrial dysfunction, neuro-inflammation, and even apoptosis and cell death. Principally, toll-like receptors (TLRs) could regulate the inflammatory/anti-inflammatory balance in patients with radiation-induced brain injury. Vinpocetine has an anti-inflammatory effect as shown in both animal and in vitro studies. Also, dexamethasone is a widely used anti-inflammatory drug. Thus, it is important to test whether addition of vinpocetine could improve the anti-inflammatory properties of dexamethasone for the treatment of NPC patients with radiation-induced brain injuries.

METHODS

A total of 60 NPC patients with radiation-related brain injury were recruited for this study. All subjects were randomly and blindly assigned to the following groups: the dexamethasone group (D group, n = 30) and the vinpocetine and dexamethasone group (VD group, n = 30). Both medicine treatments were uninterrupted for 14 days of administration.

RESULTS

Combined administration of vinpocetine and dexamethasone lowered the expression levels of serum inflammatory cytokines, including TLR2, TLR4, interleukin (IL)-20, IL-8, tumor necrosis factor-α, interferon-γ, monocyte chemoattractant protein 2, and interferon-induced protein 20, when compared to dexamethasone monotherapy. Notably, combination therapy increased antioxidants (superoxide dismutase, glutathione, glutathione peroxidase, and glutathione reductase) and decreased oxidants (thiobarbituric acid reactive substances). Furthermore, combination therapy significantly increased the Mini Mental State Examination score, when compared to dexamethasone monotherapy.

CONCLUSION

Administration of a combination of vinpocetine and dexamethasone may enhance the anti-inflammatory and anti-oxidative effects when compared to dexamethasone monotherapy, which leads to alleviated cognitive impairment in NPC patients with radiation injury.

Bayesian Methods in Regulatory Science

Regulatory science comprises the tools, standards, and approaches that regulators use to assess safety, efficacy, quality, and performance of drugs and medical devices. A major focus of regulatory science is the design and analysis of clinical trials. Clinical trials are an essential part of clinical research programs that aim to improve therapies and reduce the burden of disease. These clinical experiments help us learn about what works clinically and what does not work. The results of clinical trials support therapeutic and policy decisions. When designing clinical trials, investigators make many decisions regarding various aspects of how they will carry out the study, such as the primary objective of the study, primary and secondary endpoints, methods of analysis, sample size, etc. This paper provides a brief review of the clinical development of new treatments and argues for the use of Bayesian methods and decision theory in clinical research.

Practical help for specifying the target difference in sample size calculations for RCTs: the DELTA2 five-stage study, including a workshop

BACKGROUND

The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the 'target difference' and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups.

OBJECTIVE

The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives.

METHODS

The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document.

RESULTS

Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered.

CONCLUSIONS

Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items.

FUNDING

Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC-National Institute for Health Research Methodology Research programme.

To add or not to add a new treatment arm to a multiarm study: A decision-theoretic framework

Multiarm clinical trials, which compare several experimental treatments against control, are frequently recommended due to their efficiency gain. In practise, all potential treatments may not be ready to be tested in a phase II/III trial at the same time. It has become appealing to allow new treatment arms to be added into on‐going clinical trials using a “platform” trial approach. To the best of our knowledge, many aspects of when to add arms to an existing trial have not been explored in the literature. Most works on adding arm(s) assume that a new arm is opened whenever a new treatment becomes available. This strategy may prolong the overall duration of a study or cause reduction in marginal power for each hypothesis if the adaptation is not well accommodated. Within a two‐stage trial setting, we propose a decision‐theoretic framework to investigate when to add or not to add a new treatment arm based on the observed stage one treatment responses. To account for different prospect of multiarm studies, we define utility in two different ways; one for a trial that aims to maximise the number of rejected hypotheses; the other for a trial that would declare a success when at least one hypothesis is rejected from the study. Our framework shows that it is not always optimal to add a new treatment arm to an existing trial. We illustrate a case study by considering a completed trial on knee osteoarthritis.

A Bayesian decision analysis approach to assess voice disorder risks by using acoustic features

Vocal fold nodules are recognized as an occupational disease for all collective of workers performing activities for which maintained and continued use of voice is required. Computer-aided systems based on features extracted from voice recordings have been considered as potential noninvasive and low cost tools to diagnose some voice-related diseases. A Bayesian decision analysis approach has been proposed to classify university lectures in three levels of risk: low, medium, and high, based on the information provided by acoustic features extracted from healthy controls and people suffering from vocal fold nodules. The proposed risk groups are associated with different treatments. The approach is based on the calculation of posterior probabilities of developing vocal fold nodules and considers utility functions that include the financial cost and the probability of recovery for the corresponding treatment. Maximization of the expected utilities is considered. By using this approach, the risk of having vocal fold nodules is identified for each university lecturer, so he/she can be properly assigned to the right treatment. The approach has been applied to university lecturers according to the Disease Prevention Program of the University of Extremadura. However, it can also be applied to other voice professionals (singers, speakers, coaches, actors…).

DELTA2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial

Background

A key step in the design of a RCT is the estimation of the number of participants needed in the study. The most common approach is to specify a target difference between the treatments for the primary outcome and then calculate the required sample size. The sample size is chosen to ensure that the trial will have a high probability (adequate statistical power) of detecting a target difference between the treatments should one exist.

The sample size has many implications for the conduct and interpretation of the study. Despite the critical role that the target difference has in the design of a RCT, the way in which it is determined has received little attention. In this article, we summarise the key considerations and messages from new guidance for researchers and funders on specifying the target difference, and undertaking and reporting a RCT sample size calculation. This article on choosing the target difference for a randomised controlled trial (RCT) and undertaking and reporting the sample size calculation has been dual published in the BMJ and BMC Trials journals

Methods

The DELTA² (Difference ELicitation in TriAls) project comprised five major components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a two-day consensus meeting bringing together researchers, funders and patient representatives (stage 4); and the preparation and dissemination of a guidance document (stage 5).

Results and Discussion

The key messages from the DELTA² guidance on determining the target difference and sample size calculation for a randomised caontrolled trial are presented. Recommendations for the subsequent reporting of the sample size calculation are also provided.

DELTA2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial

BACKGROUND

A key step in the design of a RCT is the estimation of the number of participants needed in the study. The most common approach is to specify a target difference between the treatments for the primary outcome and then calculate the required sample size. The sample size is chosen to ensure that the trial will have a high probability (adequate statistical power) of detecting a target difference between the treatments should one exist. The sample size has many implications for the conduct and interpretation of the study. Despite the critical role that the target difference has in the design of a RCT, the way in which it is determined has received little attention. In this article, we summarise the key considerations and messages from new guidance for researchers and funders on specifying the target difference, and undertaking and reporting a RCT sample size calculation. This article on choosing the target difference for a randomised controlled trial (RCT) and undertaking and reporting the sample size calculation has been dual published in the BMJ and BMC Trials journals METHODS: The DELTA² (Difference ELicitation in TriAls) project comprised five major components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a two-day consensus meeting bringing together researchers, funders and patient representatives (stage 4); and the preparation and dissemination of a guidance document (stage 5).

RESULTS AND DISCUSSION

The key messages from the DELTA² guidance on determining the target difference and sample size calculation for a randomised caontrolled trial are presented. Recommendations for the subsequent reporting of the sample size calculation are also provided.

Recent advances in methodology for clinical trials in small populations: the InSPiRe project

Where there are a limited number of patients, such as in a rare disease, clinical trials in these small populations present several challenges, including statistical issues. This led to an EU FP7 call for proposals in 2013. One of the three projects funded was the Innovative Methodology for Small Populations Research (InSPiRe) project. This paper summarizes the main results of the project, which was completed in 2017.The InSPiRe project has led to development of novel statistical methodology for clinical trials in small populations in four areas. We have explored new decision-making methods for small population clinical trials using a Bayesian decision-theoretic framework to compare costs with potential benefits, developed approaches for targeted treatment trials, enabling simultaneous identification of subgroups and confirmation of treatment effect for these patients, worked on early phase clinical trial design and on extrapolation from adult to pediatric studies, developing methods to enable use of pharmacokinetics and pharmacodynamics data, and also developed improved robust meta-analysis methods for a small number of trials to support the planning, analysis and interpretation of a trial as well as enabling extrapolation between patient groups. In addition to scientific publications, we have contributed to regulatory guidance and produced free software in order to facilitate implementation of the novel methods.

Vinpocetine regulates levels of circulating TLRs in Parkinson's disease patients

BACKGROUND

The pathogenesis of Parkinson's disease (PD) is complex; it includes mitochondrial dysfunction, oxidative stress, and neuroinflammation. Notably, Toll-like receptors (TLRs) may activate inflammatory or anti-inflammatory responses in Parkinson's disease. Vinpocetine has been tested as an anti-inflammatory in both animal and in vitro research. Thus, it is important to test whether the anti-inflammatory properties of vinpocetine may have a protective effect in PD patients.

METHODS

Eighty-nine Parkinson's disease patients and 42 healthy controls were recruited for this study. All patients were randomly assigned to either the traditional therapy group (T PD group, n = 46) or the vinpocetine group (V PD group, n = 43), in a blinded manner. Both treatments were administered for 14 days.

RESULTS

Administration of vinpocetine reduced mRNA levels of TLR2/4, as well as protein levels of the downstream signalling molecules, MyD88 and NF-κB; moreover, it lowered the expression levels of serum inflammatory cytokines, TNF-α and MCP-1. Notably, vinpocetine increased TLR3 mRNA levels, as well as protein levels of the downstream signalling molecules TRIF-β and IRF-3, and serum levels of the anti-inflammatory cytokines IL-10 and IL-8. Furthermore, vinpocetine produced a robust increase in the Mini Mental State Examination score, compared to that achieved by using levodopa therapy.

CONCLUSION

Vinpocetine treatment may exhibit anti-inflammatory activity and alleviate cognitive impairment.

Value of information methods to design a clinical trial in a small population to optimise a health economic utility function

Background

Most confirmatory randomised controlled clinical trials (RCTs) are designed with specified power, usually 80% or 90%, for a hypothesis test conducted at a given significance level, usually 2.5% for a one-sided test. Approval of the experimental treatment by regulatory agencies is then based on the result of such a significance test with other information to balance the risk of adverse events against the benefit of the treatment to future patients. In the setting of a rare disease, recruiting sufficient patients to achieve conventional error rates for clinically reasonable effect sizes may be infeasible, suggesting that the decision-making process should reflect the size of the target population.

Methods

We considered the use of a decision-theoretic value of information (VOI) method to obtain the optimal sample size and significance level for confirmatory RCTs in a range of settings. We assume the decision maker represents society. For simplicity we assume the primary endpoint to be normally distributed with unknown mean following some normal prior distribution representing information on the anticipated effectiveness of the therapy available before the trial. The method is illustrated by an application in an RCT in haemophilia A. We explicitly specify the utility in terms of improvement in primary outcome and compare this with the costs of treating patients, both financial and in terms of potential harm, during the trial and in the future.

Results

The optimal sample size for the clinical trial decreases as the size of the population decreases. For non-zero cost of treating future patients, either monetary or in terms of potential harmful effects, stronger evidence is required for approval as the population size increases, though this is not the case if the costs of treating future patients are ignored.

Conclusions

Decision-theoretic VOI methods offer a flexible approach with both type I error rate and power (or equivalently trial sample size) depending on the size of the future population for whom the treatment under investigation is intended. This might be particularly suitable for small populations when there is considerable information about the patient population.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0475-0) contains supplementary material, which is available to authorized users.

Approaches to sample size calculation for clinical trials in rare diseases

We discuss 3 alternative approaches to sample size calculation: traditional sample size calculation based on power to show a statistically significant effect, sample size calculation based on assurance, and sample size based on a decision-theoretic approach. These approaches are compared head-to-head for clinical trial situations in rare diseases. Specifically, we consider 3 case studies of rare diseases (Lyell disease, adult-onset Still disease, and cystic fibrosis) with the aim to plan the sample size for an upcoming clinical trial. We outline in detail the reasonable choice of parameters for these approaches for each of the 3 case studies and calculate sample sizes. We stress that the influence of the input parameters needs to be investigated in all approaches and recommend investigating different sample size approaches before deciding finally on the trial size. Highly influencing for the sample size are choice of treatment effect parameter in all approaches and the parameter for the additional cost of the new treatment in the decision-theoretic approach. These should therefore be discussed extensively.

A decision theoretical modeling for Phase III investments and drug licensing

For a new candidate drug to become an approved medicine, several decision points have to be passed. In this article, we focus on two of them: First, based on Phase II data, the commercial sponsor decides to invest (or not) in Phase III. Second, based on the outcome of Phase III, the regulator determines whether the drug should be granted market access. Assuming a population of candidate drugs with a distribution of true efficacy, we optimize the two stakeholders' decisions and study the interdependence between them. The regulator is assumed to seek to optimize the total public health benefit resulting from the efficacy of the drug and a safety penalty. In optimizing the regulatory rules, in terms of minimal required sample size and the Type I error in Phase III, we have to consider how these rules will modify the commercial optimization made by the sponsor. The results indicate that different Type I errors should be used depending on the rarity of the disease.

Choosing the target difference ('effect size') for a randomised controlled trial - DELTA2 guidance protocol

BACKGROUND

A key step in the design of a randomised controlled trial (RCT) is the estimation of the number of participants needed. By far the most common approach is to specify a target difference and then estimate the corresponding sample size; this sample size is chosen to provide reassurance that the trial will have high statistical power to detect such a difference between the randomised groups (at the planned statistical significance level). The sample size has many implications for the conduct of the study, as well as carrying scientific and ethical aspects to its choice. Despite the critical role of the target difference for the primary outcome in the design of an RCT, the manner in which it is determined has received little attention. This article reports the protocol of the Difference ELicitation in TriAls (DELTA2) project, which will produce guidance on the specification and reporting of the target difference for the primary outcome in a sample size calculation for RCTs.

METHODS/DESIGN

The DELTA2 project has five components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a 2-day consensus meeting bringing together researchers, funders and patient representatives, as well as one-off engagement sessions at relevant stakeholder meetings (stage 4); and the preparation and dissemination of a guidance document (stage 5).

DISCUSSION

Specification of the target difference for the primary outcome is a key component of the design of an RCT. There is a need for better guidance for researchers and funders regarding specification and reporting of this aspect of trial design. The aim of this project is to produce consensus based guidance for researchers and funders.