Smith Luke B, Reich Brian J, Herring Amy H, Langlois Peter H, Fuentes Montserrat
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A.
Department of Biostatistics and Carolina Population Center, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
Biometrics. 2015 Jun;71(2):508-19. doi: 10.1111/biom.12294. Epub 2015 Mar 11.
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.
早产或小于胎龄出生的婴儿发病率和死亡率较高。利用2002年至2004年得克萨斯州的出生证明记录以及美国环境保护局的空气污染估计数据，我们将出生体重和胎龄的分位数函数与臭氧暴露及多个预测因素相关联，这些预测因素包括父母年龄、种族和教育水平。我们引入了一种半参数贝叶斯分位数方法，该方法对整个分位数函数进行建模，而不仅仅是几个分位数水平。我们的多层分位数函数模型分别针对胎龄的每一周建立出生体重与预测因素之间的关系，以及在得克萨斯州公共卫生区域内分别建立胎龄与预测因素之间的关系。我们允许这些关系在胎龄、空间域和分位数水平上呈非线性变化，并通过对回归系数进行基展开将它们统一在一个层次模型中，同时保持可解释性。极低出生体重是一个主要关注点，因此我们利用极值理论在分布的尾部对我们的模型进行补充。胎龄以完整的孕周记录（整数值），所以我们提出了对离散响应数据的分位数函数进行建模的方法。在一项模拟研究中，我们表明跨胎龄和分位数水平汇总信息可大幅降低预测因素效应的均方误差。我们发现，臭氧与得克萨斯州南部胎龄的较低尾部以及高胎龄出生体重分布呈负相关。我们的方法可在R包BSquare中获取。
