Bayesian perspectives for epidemiological research: I. Foundations and basic methods

One misconception (of many) about Bayesian analyses is that prior distributions introduce assumptions that are more questionable than assumptions made by frequentist methods; yet the assumptions in priors can be more reasonable than the assumptions implicit in standard frequentist models. Another misconception is that Bayesian methods are computationally difficult and require special software. But perfectly adequate Bayesian analyses can be carried out with common software for frequentist analysis. Under a wide range of priors, the accuracy of these approximations is just as good as the frequentist accuracy of the software--and more than adequate for the inaccurate observational studies found in health and social sciences. An easy way to do Bayesian analyses is via inverse-variance (information) weighted averaging of the prior with the frequentist estimate. A more general method expresses the prior distributions in the form of prior data or 'data equivalents', which are then entered in the analysis as a new data stratum. That form reveals the strength of the prior judgements being introduced and may lead to tempering of those judgements. It is argued that a criterion for scientific acceptability of a prior distribution is that it be expressible as prior data, so that the strength of prior assumptions can be gauged by how much data they represent.