A critical element to clinical trial design is determining the sample size needed to ensure sufficient power to detect a clinically meaningful effect[1]. Traditionally, sample size calculations rely heavily on estimates of effect size, variability, and other parameters obtained from previous studies or preliminary data[2]. However, the advent of Bayesian methods has introduced more sophisticated approaches, one of which is the use of meta-analytic predictive (MAP) prior distributionsThis approach leverages historical data more comprehensively and systematically, offering potential advantages in terms of reducing sample size and increasing statistical power.
The Bayesian Framework in Clinical Trials
The Bayesian approach to clinical trial design incorporates prior knowledge with current data to update the probability of a hypothesis. This is particularly useful in the medical field, where previous studies often provide a wealth of information that can inform future research[4]. In contrast to frequentist methods, which rely solely on the data from the current trial, Bayesian methods allow for the inclusion of prior information, potentially reducing the required sample size while maintaining or increasing the power of the study[5].
Prior distributions can be used in two phases of Bayesian trial design: First, in the generative model, stating the initial probabilities to build the simulations (Design Priors). Second, in the analysis of the data, obtaining the operating characteristics from the posterior distribution (Analysis Priors)[6].
Meta-Analytic Predictive Prior
The MAP prior is a Bayesian technique that synthesizes data from multiple historical studies to form a prior distribution for the parameters of interest in a new study. This prior is then combined with the data collected in the current trial to update the parameter estimates. The MAP prior is particularly advantageous because it formally incorporates the variability and uncertainty from past studies, leading to more robust and reliable prior distributions1.
Effective Sample Size (ESS) of the Prior
A key concept in the application of MAP priors as Analysis Priors is the effective sample size (ESS), which quantifies the amount of information contributed by the prior distribution as if it were derived from an equivalent number of observations from the current study. The ESS provides a measure of how much the prior influences the posterior distribution. A higher ESS indicates a stronger influence of the prior, which can be particularly beneficial in early-phase trials or studies with limited sample sizes[7].
The advantages of MAP priors
In our opinion, there are several situations in which the use of MAP priors in clinical trial design is advantageous. These include:
- Reduction in Sample Size: One of the primary benefits of using a MAP prior is the potential reduction in the required sample size for a clinical trial. By leveraging existing data, researchers can achieve the same level of statistical power with fewer participants. This is particularly valuable in settings where recruiting participants is challenging, such as in rare diseases or pediatric populations. The reduction in sample size can lead to significant cost savings and shorter trial durations, expediting the overall research process.
- Increased Statistical Power: Incorporating historical data through MAP priors can enhance the statistical power of a trial. The additional information from previous studies helps to reduce the uncertainty around the parameter estimates, making it easier to detect a true effect if it exists. This is especially important in early-phase trials, where preliminary data are often sparse, and traditional methods might result in underpowered studies.
- Robustness and Credibility: The use of MAP priors can improve the robustness and credibility of clinical trial results. By formally incorporating data from multiple sources, the resulting posterior estimates are more stable and less prone to the variability inherent in small sample sizes. This increased stability can lead to more reliable decision-making in the clinical development process.
- Ethical Considerations: Reducing the required sample size through the use of MAP priors has ethical implications as well. Fewer participants need to be exposed to potentially ineffective or harmful treatments, which aligns with the ethical principle of minimizing harm. Additionally, it allows for more efficient use of resources, enabling researchers to investigate more treatments or interventions with the same level of funding and effort.
Practical Implementation
Implementing MAP priors in clinical trial design involves several key steps:
- Data Collection and Synthesis: The first step is to gather relevant historical data from previous studies. This data must be synthesized to form a prior distribution. Meta-analysis techniques are typically employed to combine results from different studies, taking into account variations in study design, population, and outcomes.
- Construction of the Prior: The next step is to construct the MAP prior distribution based on the synthesized data. This involves selecting an appropriate statistical model that captures the variability and uncertainty in the historical data. Hierarchical models are often used, as they can accommodate data from multiple sources with varying degrees of similarity to the current trial.
- Incorporation into the Trial Design: Once the MAP prior is constructed, it is incorporated into the trial design. This requires specifying the prior distribution in the statistical analysis plan and ensuring that the trial’s data collection and analysis procedures are compatible with Bayesian methods.
- Statistical Analysis: During the trial, the collected data are combined with the MAP prior to update the parameter estimates. Bayesian computational techniques, such as Markov Chain Monte Carlo (MCMC) methods, are typically used to derive the posterior distributions. The resulting posterior estimates are then used to make inferences about the treatment effect.
Case Studies and Applications
Numerous case studies have demonstrated the practical benefits of MAP priors in clinical trials[8],[9]. For instance, in oncology, where previous trials often provide substantial data on treatment effects and patient outcomes, the use of MAP priors has led to significant reductions in sample sizes and faster decision-making[10]. Similarly, in vaccine development, where historical data on immunogenicity and safety are available, MAP priors have enabled more efficient trial designs, accelerating the development of new vaccines[11].
One illustrative example is a pediatric trial for a rare genetic disorder, where recruiting a large number of participants was not feasible. By using a MAP prior based on data from adult studies and earlier pediatric trials, the researchers were able to design a study with a substantially smaller sample size while maintaining adequate power. The trial not only met its objectives more quickly but also provided robust evidence to support regulatory approval.
Challenges and Considerations
Despite the advantages, there are challenges and considerations when using MAP priors in clinical trial design:
- Quality and Relevance of Historical Data: The effectiveness of a MAP prior depends on the quality and relevance of the historical data. Inaccurate or biased data can lead to misleading prior distributions and, consequently, flawed inferences. It is crucial to carefully select and critically evaluate the historical studies used to construct the MAP prior.
- Model Complexity: The construction of a MAP prior often involves complex statistical models, which require expertise in Bayesian methods and computational techniques. Ensuring the appropriate model specification and convergence of MCMC algorithms can be technically challenging.
- Regulatory Acceptance: Regulatory agencies may have reservations about the use of MAP priors, because they might inflate the Type I error when they are used as Analysis priors. It is important to engage with regulators early in the trial design process and provide clear justifications and validations for the use of MAP priors.
- Integration with Traditional Methods: Integrating MAP priors with traditional frequentist methods can be challenging, particularly in trials that involve multiple endpoints or interim analyses. Hybrid approaches that combine Bayesian and frequentist methods may be necessary, requiring careful planning and coordination.
Conclusion
In our experience, the use of meta-analytic predictive priors in clinical trial design offers significant advantages in terms of sample size reduction, increased statistical power, and enhanced robustness of the results. By systematically incorporating historical data, MAP priors can provide a more efficient and ethical approach to clinical research, particularly in settings with limited sample sizes or preliminary data.
Despite challenges in terms of data quality, model complexity, and regulatory acceptance, the growing adoption of Bayesian methods in clinical trials underscores the potential of MAP priors to transform the landscape of medical research. As the field continues to evolve, the integration of MAP priors with traditional methods and the development of best practices will help design and analyze clinical trials more efficiently.
About the author:
Enrique Vidal is a Senior Manager in Data Science at Pharmalex. He has more than 15 years of experience applying statistical methods to healthcare.
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[11] Bayesian borrowing from historical control data in a vaccine efficacy trial, Pharmaceutical Statistics, May 2023. https://onlinelibrary.wiley.com/doi/10.1002/pst.2313
