We are thankful that Igl and Constant1 are joining the creation of the virtuous cycle for the use of Bayesian approaches in clinical trials. Their comments help to expand the considerations from the original paper2 and bring additional perspectives to bear on Bayesian approaches. We are in general agreement with their Correspondence. We will make a few additional comments on topics in the order they appear in their Correspondence.

First, rather than the term ‘non-informative’ prior, we prefer the term ‘vague’ prior (as noted in the original paper). All priors contain some information; even a prior that is a normal distribution centred at zero with variance 10,000 conveys that the mean is zero, albeit with little certainty. Furthermore, at the planning stages of a clinical trial, there must be some belief or knowledge that leads researchers to investigate an intervention in a formal clinical trial. One could argue that it would be unethical to plan a clinical trial of that intervention without such knowledge or belief (that is, prior data to support the investigation). Thus, we believe that it is important to do the hard work upfront and quantify that belief or knowledge in a formal way, which should lead to a prior distribution of the intervention effect that is informative in some way. As Igl and Constant note, frequentist and Bayesian analyses may come to the same conclusion. However, when results are borderline or mixed, at least the Bayesian approach has considered the external data a priori (that is, unbiased by the results of the current trial) rather than a post hoc interpretation that compares the current trial results with the historical record.

Second, Igl and Constant give some examples of suitable domains for the application of Bayesian methods. Their list includes the usual suspects — “studies on medical devices, early-phase trials, trials involving patients with rare diseases and extrapolation of data from adult to paediatric populations”. While these are presented as examples, we are keen that readers are not limited by this list. We believe that Bayesian methods are broadly applicable and, in particular, can and should be part of mainstream phase II and phase III clinical development programmes that can lead to regulatory approval. Bayesian methods could also be very useful in phase IV trials for which there can be highly relevant clinical data from phases II–III that are incorporated into a Bayesian analysis relating to different uses of an approved treatment. Furthermore, they can be important tools in government-sponsored trials in which regulatory approval may not be the desired outcome, but posterior probabilities may be quite informative for medical decisions or developing treatment guidelines. The same may be true for healthcare reimbursement considerations. Overall, we do not see any limits to the possible applications of Bayesian methods in clinical trials as long as there is relevant external data of sufficient quality available and appropriate study design considerations warrant the use of these methods.

Third, whether to relax the significance level of a hypothesis test or not is not just a regulatory issue. Most clinical trials do not fall under the auspices of regulatory authorities. The medical literature contains many investigations of interventions — pharmaceutical or otherwise — that base conclusions on the conventional p-value cut-off of 0.05. Such trials and results are reported as a success or failure largely based on whether that p-value threshold is met or not. This is exactly the point of the THAPCA-OH trial that compared therapeutic hypothermia with therapeutic normothermia (that is, palliative care) for the treatment of children with cardiac arrest. Too many conclusions are based on that conventional p-value, and even if there was a relaxing of the significance level by regulatory agencies or journal editors, there would always be debate about how much to relax it (Igl and Constant use 0.15 as an example). Rather than have that debate, we believe that the posterior distribution of effect size for the intervention contains the necessary information for making any decision — be it by a regulator, a reimbursement organization, a treating physician or a journal editor.

Finally, Igl and Constant suggest Bayesian approaches other than hierarchical models for investigating the vexing problem of heterogeneity of response across different subgroups. We acknowledge this and note that there are many Bayesian approaches that can be applied in the clinical trial setting. Our goal was not to compare and contrast various Bayesian methods, but rather to provide a meaningful review and to spark discussion of Bayesian thinking and applications across the clinical research community. The correspondence from Igl and Constant could be considered an indicator of some success in this respect.