Approximate hierarchical modelling of discrete data in epidemiology.

Hierarchical models are used in epidemiology to estimate and analyse multiple, related relative risks. Examples include meta-analyses of series of 2 x 2 tables and mapping of spatially correlated disease rates. Empirical transform and penalized quasilikelihood procedures, both of which may be implemented using standard programs for mixed model analysis, provide satisfactory approximate inferences for these problems when cell frequencies are large. Simulation studies show that, in certain situations involving small cell frequencies, penalized quasilikelihood provides satisfactory estimates of variance components and regression coefficients whereas the empirical transform approach does not.