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Bayesian Inference for Two-Phase Studies with Categorical Covariates

This talk concerns the development of Bayesian methods for two-phase studies. Two-phase designs are appealing from an efficiency perspective since they allow sampling to be concentrated in informative cells. A number of likelihood-based methods have been developed for the analysis of two-phase data, but we describe a Bayesian approach that has previously been unavailable. We extend the methodology to include random effects terms in the model to perform different kinds of smoothing. In particular, we are interested in the use of two-phase studies in a spatial epidemiological context where one may wish to acknowledge confounding by location via the introduction of spatial random effects, however random effects can also be included to smooth the cell probabilities in large contingency tables, particularly in the case of sparse data. The Bayesian two-phase approach is illustrated using data collected on Wilms tumour, as well as infant mortality in North Carolina.