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Bayesian Methods for Historical Borrowing: Conjugate Priors

The wider availability of electronic health data, medical registries, and even larger proprietary datasets means that sponsors can now create stronger regulatory submissions by utilizing advanced quantitative methods for historical borrowing. A natural question arises as to which clinical trial designs will best allow sponsors to utilize such datasets.

Since the use of historical data is often a strategic choice to overcome low patient samples or bolster scenarios with underpowered interim results, it is important to ensure that a clinical trial’s statistical design can make the most flexible use of new Bayesian methodologies for historical borrowing. Essential to this is the use of trial software like East Bayes®, which ensures that trials are enabled for new methods of historical borrowing.

In Bayesian statistics, when a posterior distribution has the same mathematical form as a prior distribution, then the prior distribution is called a conjugate prior. Such conjugate priors enable probability distributions to “play nice” with the likelihood function.1 In the case of historical borrowing, this means that the historical dataset can be integrated into the new analysis in a relatively straightforward way, without the need for approximations that can affect results and introduce bias.

As an example, in situations where the endpoint is categorical, such as in the form of a response rate, one way to try to ensure that sponsors are working with probabilities where the prior and posterior probability distributions will be conjugate is to simply test out different Beta-distribution functions and determine which are the best for the current trial and related datasets. In principle, only a small number of situations will meet this requirement; they are highly unlikely in real life situations.

Therefore, it is also necessary to use Markov Chain Monte Carlo Methods to generate approximate conjugate priors, where actual conjugate priors are not possible. This requires access to higher-than-normal levels of computing power, but new platforms like East Bayes® makes this possible.

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Endnotes

1 John K. Kruschke, Doing Bayesian Data Analysis, 2nd ed. (London: Elsevier, 2011).

 

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