Modeling adverse birth outcomes via confirmatory factor quantile regression

Bayesian Analysis of a Quantile Multilevel Item Response Theory Model

Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.

Commensurate Priors on a Finite Mixture Model for Incorporating Repository Data in Clinical Trials

Docosahexaenoic acid (DHA) is a good source of fat that can be taken up through food, such as fish, or taken as a supplement. Evidence is building that DHA provides a high yield, low risk strategy to reduce preterm birth and/or low birth weight. These births are great costs to society. A recently completed phase III trial revealed that higher birth weight and gestational age were associated with DHA dosed at 600 mg/day. In this paper we take a posterior predictive approach to assess impacts of these findings on public health. Simple statistical models are not adequate for accurate posterior predictive distribution estimation. Of particular interest is a paper by Schwartz et al. (2010) who discovered that the joint distribution of birth weight and gestational age is well modeled by a finite mixture of three normal distributions. Data from our own clinical trial exhibit similar features. Using the mean and variance-covariance matrices from Schwartz et al. (2010) and flexible commensurate priors (Hobbs et al., 2012) for the mixing parameters, we estimate the effect of DHA supplementation on the over 20,000 infants born in hospitals demographically similar to the hospital where the clinical trial was conducted.

Multilevel quantile function modeling with application to birth outcomes

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.

Quantile Mediation Models: A Comparison of Methods for Assessing Mediation Across the Outcome Distribution

Recent introduction of quantile regression methods to analysis of epidemiologic data suggests that traditional mean regression approaches may not suffice for some health outcomes such as Body Mass Index (BMI). In the same vein, the traditional mean-based approach to mediation modeling may not be sufficient to capture the potentially different mediating effects of behavioral interventions across the outcome distribution. By combining methods for estimating conditional quantiles with traditional mediation modeling techniques, mediation effects can be estimated for any quantile of the outcome distribution (so-called quantile mediation effects). Estimation and inference techniques for quantile mediation effects are compared through simulation studies, and recommendations are given. The quantile mediation methods are further compared with the traditional mean-based regression approaches to mediation analysis through analysis of data from Healthy Places, a trial that is examining the effects of the community-built environment on resident obesity risk. We found the magnitudes of indirect (mediating) effects of walkability on BMI and waist circumference were substantially larger for the upper quantiles compared with the median or mean. Results suggest that restricting the examination of mediation to the mean of the outcome distribution provides an incomplete picture of proposed mediating mechanisms and in some cases may miss important mediational relationships to outcomes.

Estimation of regression quantiles in complex surveys with data missing at random: An application to birthweight determinants

The estimation of population parameters using complex survey data requires careful statistical modelling to account for the design features. This is further complicated by unit and item nonresponse for which a number of methods have been developed in order to reduce estimation bias. In this paper, we address some issues that arise when the target of the inference (i.e. the analysis model or model of interest) is the conditional quantile of a continuous outcome. Survey design variables are duly included in the analysis and a bootstrap variance estimation approach is proposed. Missing data are multiply imputed by means of chained equations. In particular, imputation of continuous variables is based on their empirical distribution, conditional on all other variables in the analysis. This method preserves the distributional relationships in the data, including conditional skewness and kurtosis, and successfully handles bounded outcomes. Our motivating study concerns the analysis of birthweight determinants in a large UK-based cohort of children. A novel finding on the parental conflict theory is reported. R code implementing these procedures is provided.