Quantile Regression for Discrete Data with Application to Birth Outcomes

• Activity Number: 603
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Luke Smith*+ and Montserrat Fuentes and Brian J. Reich and Amy Herring
• Companies: North Carolina State University and North Carolina State University and North Carolina State University and UNC CH
• Keywords: Air Pollution ; Bayesian ; Discrete ; Extremal inference ; Nonlinear ; Quantile regression

Abstract

Infants with low birth weight and/or preterm birth are associated with increased rates of infant morbidity and mortality, and the effect of maternal exposure to ambient air pollution remains uncertain. Using birth certificate records in Texas from 2002-2004 and EPA air pollution estimates, we relate the quantile function of birth weight to ozone exposure and multiple predictors, including parental age, race, and education level. We introduce a semi-parametric Bayesian quantile approach that models the relationship between birth weight and the predictors separately for each week of gestational age. We permit these relationships to vary nonlinearly across gestational age and quantile level and we unite them in a hierarchical model via a basis expansion on the regression coefficients that preserves interpretability. Since extremely low birth weight is a primary concern, we leverage extreme value theory to supplement our semiparametric quantile regression model in the tail of the distribution. By pooling information across gestational age and quantile level our model substantially reduces MSE relative to canonical Frequentist quantile regression.