Bayesian Prediction of Mean Indoor Radon Concentrations for Minnesota Counties

Abstract

Past efforts to identify areas with higher than average indoor radon concentrations by examining the statistical relationship between local mean concentrations and physical parameters such as the soil radium concentration have been hampered by the variation in local means caused by the small number of homes monitored in most areas. In this paper, indoor radon data from a survey in Minnesota are analyzed to minimize the effect of finite sample size within counties, to determine the true county-to-county variation of indoor radon concentrations in the state, and to find the extent to which this variation is explained by the variation in surficial radium concentration among counties. The analysis uses hierarchical modeling, in which some parameters of interest (such as county geometric mean (GM) radon concentrations) are assumed to be drawn from a single population, for which the distributional parameters are estimated from the data. Extensions of this technique, known as a random effects regression and mixed effects regression, are used to determine the relationship between predictive variables and indoor radon concentrations; the results are used to refine the predictions of each county's radon levels, resulting in a great decrease in uncertainty.The true county-to-county variation of GM radon levels is found to be substantially less than the county-to-county variation of the observed GMs, much of which is due to the small sample size in each county. The variation in the logarithm of surficial radium content is shown to explain approximately 80% of the variation of the logarithm of GM radon concentration among counties. The influences of housing and measurement factors, such as whether the monitored home has a basement and whether the measurement was made in a basement, are also discussed. The statistical method can be used to predict mean radon concentrations, or applied to other geographically distributed environmental parameters.

Multilevel (Hierarchical) Modeling: What It Can and Cannot Do

“…For the purposes of this paper, however, model (1) is general enough. We further simplify by focusing on a subset of our data-the 919 houses from the state radon survey of the 85 counties of Minnesota (Price, Gelman, and Nero, 1996). We fit the model using hierarchical Bayes methods (e.g., Gelman et al, 2003).…”

“…For each cross-validation step, we compare complete-pooling, no-pooling, and multilevel estimates. Other cross-validation tests for this example were performed in Price, Nero, and Gelman (1996). When removing entire counties one at a time, we summarize by the errors of the predicted county mean responses (given the county-level uranium and the basement information for the houses in the excluded county).…”

“…This analysis arose in a real research problem (Price, Nero, and Gelman, 1996) and is not a "trick" example. The houses in the study were sampled at random from the counties of Minnesota, and there were no problems of selection bias.…”

Centralized Analysis of Local Data, with Dollars and Lives on the Line: Lessons from the Home Radon Experience

“…Also, radon measurements are made in individual homes, but the available data on soil uranium content (a useful predictive variable) were available only as spatial averages. Finding ways to jointly analyze all of the available data was a significant challenge (Price and Nero, 1996).…”

“…Also, radon measurements are made in individual homes, but the available data on soil uranium content (a useful predictive variable) were available only as spatial averages. Finding ways to jointly analyze all of the available data was a significant challenge (Price and Nero, 1996).We made several time-consuming false starts in our analyses when trying to figure out ways to exploit various types of data. For example, due to confidentiality constraints some of our data provided house locations only as zip codes, which are large enough in rural areas that we were unable to determine the local geology except in very crude terms.…”