Bayes and empirical Bayes methods enable the combining of information from similar and independent experiments, yielding improved estimation of both individual and shared model characteristics. Many complex public health problems offer ideal settings for this type of synthesis. For example, data on disease incidence in several adjacent counties may be partially pooled to yield a better estimate for each county, as a result of this borrowing of strength across studies. This proposal focuses on developing necessary sampling based methodological tools for improved analysis of public health and biomedical science data. These methods enable a much broader modeling framework since they allow exact propagation of variation throughout the various stages of the analysis, eliminating the need for approximations to distributional variability and shape. After a brief review of several past areas of application, two areas specific to the health sciences are proposed for in-depth exploration. First, the interim monitoring and final analysis of clinical trials data is shown to be a potentially fruitful area of application. Here, sampling based methods will allow real time evaluation of monitoring plans, and assessment of whether approximate results based on the assumption of normality are adequate. Further, the class of priors leading to a given decision, conditional on the data observed up to the decision point, may be characterized. Such results should help to alleviate concerns that a chosen prior might lead to premature stopping of the trial. A second area for investigation is the use of Bayes and empirical Bayes methods in the context of environmental and occupational health. For example, combining information on the mutagenic potency of several chemicals should produce a more accurate assessment of each. Again, the computer will permit complex, realistic hierarchical modeling of bioassay data without resort to simplifying assumptions or approximations. These two specific proposed problem areas are not intended to be exhaustive, but rather indicative of the broad issues which underlie all biomedical data analyses, and the inevitable future stream of opportunities for combining biostatistical theory with public health application.
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