# Potential Areas of Application

In the recent past, Bayesian methods have been applied in the design and analyses of clinical trials in every stage of clinical development. The impact has especially been visible in areas where it is critical to enhance efficiency or when there are unmet medical needs.

In early development phases, Bayesian approaches are often used to implement adaptive dose-finding study designs, as opposed to the customary Phase I dose-escalation studies. One common approach in this regard, discussed elsewhere in this monograph, is the Continual Reassessment Method (CRM), which enables the estimation of the Maximum Tolerated Dose (MTD) using historical data, and data accumulated from previously studied doses (O’Quigley et al. 1990). Although the approach requires defining and implementing a suitable model to characterize the doseresponse relationship, it is often preferred to rule-based methods, which may lack the rigor and reliability of CRMs.

Another potential application of Bayesian approaches is in the design of proof-of-concept studies, used in making important decisions about subsequent stages of a drug development program. Traditional Phase IIA trials often involve either a single arm, comparing a new drug against historical references, or a randomization scheme comparing the new drug with the standard treatment or placebo. Such fixed designs may not only unnecessarily expose patients to ineffective or toxic doses, but may also prolong the time to make go/no-go decisions. Bayesian adaptive designs may become viable options by allowing the use of accumulating data to inform decision to stop or continue a study in a stepwise fashion (Chung and Schultz 2007).

When there is interest to accelerate the drug development process, it is often proposed to integrate Phase II and Phase III programs seamlessly. This may be achieved using adaptive procedures to modify various aspects of the trial design, including doses, sample size, as well as development objectives (see, e.g., Schmidli et al. 2007). One feature of a seamless Phase II/III study design is that the final analyses will be based on data from both stages, typically in a Bayesian framework (Kimani et al. 2012). However, in the current regulatory framework it would be essential to ensure that the overall Type I error rate is controlled, and that there is strong evidence in support of the decision made at the end of the confirmatory stage.

As discussed in Section 2.5, adaptive designs are useful to enhance the efficiency of clinical trials, by incorporating flexibility in the design and conduct of the trial. One appealing feature of the Bayesian approach is the ability to incorporate accumulating or historical data to inform actions about various aspects of an ongoing trial while adhering to prespecified plans (FDA 2010). However, caution should be exercised in the implementation of these designs to mitigate the potential for operational bias. In particular, special effort should be made to ensure protection of type I error rates through extensive simulations (see, e.g., Spiegelhalter et al. 2000).

Evaluation of the safety of a drug based on postapproval data is often challenging due to the observational nature of the data, its high dimensionality, and the need to synthesize information from disparate sources. Bayesian approaches have been proposed as viable options for postapproval drugsafety signal detection, as they permit information borrowing from preapproval as well as across data sources and drug-adverse-effect combinations (Madigan et al. 2010). In addition, Type I error is not a concern in postapproval safety monitoring. However, Bayesian approaches are not solutions to other issues with such data, including confounding and other sources of bias.

In comparative effectiveness research, traditional and network metaanalysis methods are routinely used, since it is essential to combine studies from two or more trials to improve the precision of estimates of treatment effects or to perform indirect comparisons in cases where data from head-to-head RCTs is not available. Bayesian approaches have found appeal in such cases, since they permit the combining of information in a natural way (Greco et al. 2015).

# Regulatory Considerations

Although the frequentist approach is predominantly used in trials intended for regulatory submissions, the role of Bayesian statistics in drug development is widely recognized by regulatory bodies (FDA 2010; ICH E9 Expert Working Group 1999). However, for a successful implementation of Bayesian methods in clinical trials, there should be upfront discussions and agreements between sponsors and the regulatory bodies about pertinent aspects of the approach, including the choice of priors, exchangeability of trials, and control of Type I error rates.

While the idea of controlling Type I error rates is central to the frequentist paradigm and is not an explicit feature of Bayesian decision-making, it is still of regulatory relevance, especially when informative priors are constructed using external information. Simulation experiments are generally required to assess Type I error rates, taking into consideration the pertinent features of the study design, including prior information, sample size, and any interim analyses planned or performed. It is generally recommended that the simulation involve alternative scenarios to provide adequate assurance about the estimated Type I error rate. In the event of inflated Type I error rate, it may be appropriate to take corrective measures, such as increasing the predictive probability of success, increasing the sample size to mitigate the influence of the prior, reducing the number of interim analyses, or discounting the prior information (see, e.g., FDA 2010).

The choice of priors is another cause for concern by regulatory agencies and advisory committees. Generally, subjective priors are difficult to justify. When historical data is used to inform priors, it is important to ensure that there is no selection bias in the choice of the data source. In some cases, the historical data may have been selected omitting unfavorable data for the study drug. This may be due to logistical constraints, especially when there are legal constraints to obtain prior information or possibly a publication bias, if data are taken from the literature. When the information from historical data appears to be dominant, it may be worthwhile to discount the prior through suitable criteria. Some approaches for discounting priors include increasing the sample size of the new trial, reducing the number of patients “borrowed” from the historical control, weighting the historical data, and employing hierarchical models with conservative hyper parameters (FDA 2010). An alternative strategy, is the use of the power prior, which incorporates a parameter к (0 < к < 1) that is intended to adjust the influence of the external information, especially in situations where there is imbalance in sample sizes or heterogeneity among studies (Zellner 1988). Technically, the power prior distribution is a product of the prior before the historical data was collected and the likelihood function of the historical data, the latter raised to the power *of *к. Since the choice of к requires a thorough understanding of the influence of the external information, it is good practice to perform extensive sensitivity analyses in order to understand the impact of different values of к, ranging from 0 (non-informative) to 1 (full borrowing). Detailed discussions of various aspects of power priors may be found, among others, in Ibrahim et al. (2015).

The assumption of exchangeability or consistency between the current study and historical studies is not directly testable, and it may not be straightforward to validate. This is especially concerning when using hierarchical models in which prior information is obtained from only one historical study, since it is not possible to get an estimate of inter-study variability. As reported earlier, if the various sources of data are not exchangeable, the consequence might be reduced power, inflation of Type I error rate, or biased estimates (Viele et al. 2014). Typically, exchangeability should be assessed at the planning stage based on various statistical, clinical, and manufacturing considerations. For example, one statistical approach involves computing the posterior predictive probability of observing a discrepancy in the value of a given outcome between the current study and historical studies at least as large as that observed, under exchangeability (Pennello and Thompson 2008).

# Challenges with Bayesian Statistics

One of the major impediments for wider use of Bayesian methods in drug development is the lack of a clear regulatory framework for its acceptance in the drug-approval process. While there are positive steps in that direction, such as the FDA guideline for use of Bayesian statistics in devices (FDA 2010), most of the widely referenced guidelines, including ICH E9 (ICH E9 Expert Working Group 1999), give greater emphasis to frequentist approaches.

Bayesian trials also have certain inherent difficulties that may make them less appealing to clinical trialists. For example, it may require substantial effort to prespecify some important decisions at the design stage, including the choice of the prior information, and how it would be incorporated with the trial data. Further, despite the considerable progress made in the implementation of Bayesian models, the approach is still computationally intensive compared to corresponding frequentist techniques, especially the requirement to perform extensive simulations to assess the operating characteristics of the procedure. Nevertheless, Bayesian reasoning parallels human thinking, i.e., what we know about the parameter of interest going into an experiment and how the experimental results change our knowledge.

# Concluding Remarks

Despite the growing interest in Bayesian statistics, the broader application of the approach has not been fully realized. In this section, we highlighted some of the opportunities and challenges from regulatory and drugdevelopment perspectives. With the increasing focus on enhancing the efficiency of clinical trials, Bayesian methods will arguably continue to garner acceptability, especially given their role in facilitating decision-making through use of historical and accumulating data.