A compound sampling model, where a unit‐specific parameter is sampled from a prior distribution and then observeds are generated by a sampling distribution depending on the parameter, underlies a wide variety of biopharmaceutical data. For example, in a multi‐centre clinical trial the true treatment effect varies from centre to centre. Observed treatment effects deviate from these true effects through sampling variation. Knowledge of the prior distribution allows use of Bayesian analysis to compute the posterior distribution of clinic‐specific treatment effects (frequently summarized by the posterior mean and variance). More commonly, with the prior not completely specified, observed data can be used to estimate the prior and use it to produce the posterior distribution: an empirical Bayes (or variance component) analysis. In the empirical Bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects. In both the Bayes and empirical Bayes approaches, estimated clinic effects are shrunken towards a common value from estimates based on single clinics. This shrinkage produces more efficient estimates. In addition, the compound model helps structure approaches to ranking and selection, provides adjustments for multiplicity, allows estimation of the histogram of clinic‐specific effects, and structures incorporation of external information. This paper outlines the empirical Bayes approach. Coverage will include development and comparison of approaches based on parametric priors (for example, a Gaussian prior with unknown mean and variance) and non‐parametric priors, discussion of the importance of accounting for uncertainty in the estimated prior, comparison of the output and interpretation of fixed and random effects approaches to estimating population values, estimating histograms, and identification of key considerations in the use and interpretation of empirical Bayes methods.
ASJC Scopus subject areas
- Statistics and Probability