Infants born preterm or small for gestational age have elevated rates of morbidity and mortality. Using birth certificate records in Texas from 2002 to 2004 and Environmental Protection Agency air pollution estimates, we relate the quantile functions of birth weight and gestational age to ozone exposure and multiple predictors, including parental age, race, and education level. We introduce a semi-parametric Bayesian quantile approach that models the full quantile function rather than just a few quantile levels. Our multilevel quantile function model establishes relationships between birth weight and the predictors separately for each week of gestational age and between gestational age and the predictors separately across Texas Public Health Regions. We permit these relationships to vary nonlinearly across gestational age, spatial domain and quantile level and we unite them in a hierarchical model via a basis expansion on the regression coefficients that preserves interpretability. Very low birth weight is a primary concern, so we leverage extreme value theory to supplement our model in the tail of the distribution. Gestational ages are recorded in completed weeks of gestation (integer-valued), so we present methodology for modeling quantile functions of discrete response data. In a simulation study we show that pooling information across gestational age and quantile level substantially reduces MSE of predictor effects. We find that ozone is negatively associated with the lower tail of gestational age in south Texas and across the distribution of birth weight for high gestational ages. Our methods are available in the R package BSquare.
Distributed lag models (DLMs) have been widely used in environmental epidemiology to quantify the lagged effects of air pollution on a health outcome of interest such as mortality and morbidity. Most previous DLM approaches consider only one pollutant at a time. We propose a distributed lag interaction model to characterize the joint lagged effect of two pollutants. One natural way to model the interaction surface is by assuming that the underlying basis functions are tensor products of the basis functions that generate the main effect distributed lag functions. We extend Tukey's 1 degree-of-freedom interaction structure to the two-dimensional DLM context. We also consider shrinkage versions of the two to allow departure from the specified Tukey interaction structure and achieve bias—variance trade-off. We derive the marginal lag effects of one pollutant when the other pollutant is fixed at certain quantiles. In a simulation study, we show that the shrinkage methods have better average performance in terms of mean-squared error across various scenarios. We illustrate the methods proposed by using the ‘National morbidity, mortality, and air pollution study’ data to model the joint effects of particulate matter and ozone on mortality count in Chicago, Illinois, from 1987 to 2000.
more » « less- NSF-PAR ID:
- 10398884
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series C: Applied Statistics
- Volume:
- 68
- Issue:
- 1
- ISSN:
- 0035-9254
- Page Range / eLocation ID:
- p. 79-97
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Availability and implementation Source code and preprocessed datasets are at: http://snap.stanford.edu/decagon.
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