The prediction of mean levels of exposure has wide applicability in epidemiologic studies. However, the properties of common prediction methods may be suspect when predicting extreme (high or low) true mean levels, which are a focal point in some applications. We take specific motivation from the context of occupational epidemiology to study prediction of workers' mean levels under a random effects model for log-transformed exposure measurements. In this context, we consider an analog to the best linear predictor and we highlight its negative conditional bias with respect to highly-exposed individuals. We adapt existing methodology to propose alternatives representing various levels of compromise with regard to shrinkage. Candidate predictors are compared in terms of unconditional mean squared error of prediction and conditional bias and mean squared error at given percentiles of the distribution of mean exposures. Estimated versions of the predictors are assessed via simulation, and are computed based on shift-long exposure datasets from the nickel-producing and boat manufacturing industries. Our study details prediction properties under conjugate lognormality, and it suggests approaches to prediction in studies of occupational exposure with a view toward conservatism in assessing prevailing conditions for sampled workers.

Key Words
Best prediction; Constrained Bayes estimation; Exposure assessment; Variance components.

Robert H. Lyles is Assistant Scientist, Department of Epidemiology, School of Hygiene and Public Health, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, MD 21205. Lawrence L. Kupper is Professor, Department of Biostatistics, and Stephen M. Rappaport is Professor, Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, CB #7400, Chapel Hill, NC 27599-7400.