title: Multilevel quantile function modeling with application to birth outcomes.
abstract: 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.
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A.
authors.forename: Luke B
authors.initials: LB
authors.lastname: Smith
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A.
authors.forename: Brian J
authors.initials: BJ
authors.lastname: Reich
authors.affiliation: Department of Biostatistics and Carolina Population Center, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
authors.forename: Amy H
authors.initials: AH
authors.lastname: Herring
authors.affiliation: Texas Department of State Health Services, Austin, Texas 78714-9347, U.S.A.
authors.forename: Peter H
authors.initials: PH
authors.lastname: Langlois
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A.
authors.forename: Montserrat
authors.initials: M
authors.lastname: Fuentes
mesh_terms: D000393:Air Pollutants / Q000009:adverse effects; D001499:Bayes Theorem; D001699:Biometry; D001724:Birth Weight; D003198:Computer Simulation; D005260:Female; D005865:Gestational Age; D006801:Humans; D007223:Infant; D007226:Infant Mortality; D007231:Infant, Newborn; D007234:Infant, Premature; D007236:Infant, Small for Gestational Age; D008297:Male; D015233:Models, Statistical; D010126:Ozone / Q000009:adverse effects; D011247:Pregnancy; D012044:Regression Analysis; D013781:Texas / Q000453:epidemiology
chemical_list: D000393:Air Pollutants; D010126:Ozone
keywords: Birth weight; Discrete; Extremes; Gestational Age; Graphics processing units; Ozone; Quantile