Small area estimation methods are used commonly for modeling epidemiological outcomes. Direct estimates, usually based on area-level sample data, are very imprecise due to small sample sizes from each area. Numerous frequentist and Bayesian methods that rely on the principle of “borrowing information” have been developed to enhance the precision of these estimates. In this dissertation we employ a spatial-hierarchical model to estimate the prevalence of early childhood respiratory problems in the 2003 birth cohort in Los Angeles County. More specifically, we explore the relationship between respiratory outcomes in young children and air pollution exposure of the mother during pregnancy.

Our methodology works by dividing LA County into small geographic areas where women within each area are similar in terms of demographics and pollution exposure. Using a spatial-hierarchical model where spatial dependency is based on a neighborhood matrix, we are able to obtain a smooth distribution of the respiratory outcomes of interest using air pollution metrics and variables that come from birth certificates. By including a spatial variability component in the models, we are able to explain much of the variability in the distribution of the respiratory outcomes using only demographic data that come from birth certificates. We also show that including a spatial variability component in the models shrinks the coefficient estimates for the demographic variables while the coefficient estimates for the air pollution metrics remain unaffected.