The Bayesian approach provides a mathematically rigorous and principled methodology for making decisions under arbitrarily complex scenarios. It provides a powerful framework for determining optimal behavior in the face of uncertainty. The Bayesian approach is ideal for many adaptive designs because it provides a naturally sequential learning framework, and allows the efficient and transparent integration of complex clinical trial and external data and natural prediction of future events (e.g., clinical trial results).
In contrast to traditional methods, the Bayesian approach itself is very flexible. It is naturally sequential, and can create updated distributions based on the information from a trial – and can be done continuously, without constraints that traditional methods pose. Essentially doing complex adaptive trials from a traditional approach is impossible – whereas from a Bayesian perspective is quite natural and straightforward.
The flexibility of modeling is also a huge advantage in flexible designs. Bayesian methods provide a flexible, coherent, and transparent method for the creation and evaluation of disparate information. The approach has computational advantages, the ability to model early predictors and biomarkers, the ability to incorporate prediction in to trial design, combining multiple endpoints together, and synthesizing possibly related populations in to combined analyses.
Modeling and Meta-Analysis:
In addition to the advantages of using the Bayesian approach in trial design, a key strength of the Bayesian approach is hierarchical modeling. The approach is critical for evaluating the sufficiency and reliability of evidence for supporting a treatment guideline or a payers reimbursement decision—is that the degree of evidence integration or borrowing across multiple information sources is not defined a priori but, instead, depends on the consistency of evidence across the information sources. This provides a quantitative and rigorous methodology that allows firm conclusions to be drawn when the evidence is concordant and, just as important, avoids such conclusions, capturing the increased uncertainty when the heterogeneity in the information is large.
Bayesian methods allow for a formal synthesis of information from clinical trials that ask the same or related questions and are uniquely suited to comparative effectiveness research. There are three important aspects to the modeling. The first is the ability to model study-to-study heterogeneity, the second is the ability to handle indirect treatment comparisons, also called mixed treatment comparisons, and the third is the ability to model nested treatments and combinations of treatments.
Differences between trials include varying study designs, eligibility criteria, patient populations, treatment regimens, and outcome measures. Bayesian hierarchical models view the trials included in the meta-analysis as sampled from a larger population of trials. A Bayesian hierarchical model is a random effects model that explicitly accounts for trial heterogeneity and allows for “borrowing of strength” across the trials. If results of trials are similar, there will be greater borrowing of information and this will increase the precision of the estimates. If trial results differ substantially, then there will be less borrowing and appropriately increased uncertainty regarding the conclusions of the meta-analysis. The amount of borrowing across trials is not specified in advance, but is determined by the heterogeneity of the available data.