Probabilistic Sensitivity Analysis: Be a Bayesian

Objective:  To give guidance in defining probability distributions for model inputs in probabilistic sensitivity analysis (PSA) from a full Bayesian perspective.
Methods:  A common approach to defining probability distributions for model inputs in PSA on the basis of input-related data is to use the likelihood of the data on an appropriate scale as the foundation for the distribution around the inputs. We will look at this approach from a Bayesian perspective, derive the implicit prior distributions in two examples (proportions and relative risks), and compare these to alternative prior distributions.
Results:  In cases where data are sparse (in which case sensitivity analysis is crucial), commonly used approaches can lead to unexpected results. Weshow that this is because of the prior distributions that are implicitly assumed, namely that these are not as "uninformative" or "vague" as believed. We propose priors that we believe are more sensible for two examples and which are just as easy to apply.
Conclusions:  Input probability distributions should not be based on the likelihood of the data, but on the Bayesian posterior distribution calculated from this likelihood and an explicitly stated prior distribution.