Hierarchical Bayesian Regression for Multiple Correlated Exposures: An Application to Prenatal Phthalate Metabolites and Length of Gestation

Abstract

O-30C7-5 Background/Aims: In previous results, several metabolites of Di(2-ethylhexyl) phthalate (DEHP) measured in prenatal urine were found individually and as a molar sum to be associated with shortened length of gestation in an inner-city pregnancy cohort. The high multicollinearity of exposure to some phthalate metabolites (Pearson correlation on log-transformed concentrations >0.9) poses a challenge in modeling multiple exposures simultaneously. Shrinkage methods such as ridge regression and hierarchical Bayesian models, which may reduce variance driven by multicollinearity, have not been widely applied to biomonitoring data. We predict that without known relative weighting, hierarchical Bayesian models can be used to estimate effects of phthalate mixtures. Methods: We used ridge regression with generalized cross-validation to select an optimal shrinkage parameter value and then drew Markov Chain Monte Carlo samples from the equivalent posterior distribution of Bayesian models using WinBUGS software. Three covariates from the prior analysis were retained (smoking during pregnancy, premature rupture of the membrane, pre-planned C-section). Results: Shrinkage estimates using single DEHP metabolites were consistent with our prior findings. The largest effect size was likewise MEHHP, a secondary oxidative metabolite of DEHP (−0.18 weeks gestation for a 1 SD increase in the log concentration of MEHHP, 95% credible interval −0.31 to −0.05, n = 267). After adjusting for other metabolites of DEHP, the 95% credible interval included 0. In contrast, the 95% CI of an indicator for the proportion of DEHP metabolites made up of the primary metabolite, MEHP, proposed by others as a crude phenotype for phthalate metabolism, was negative and did not include 0. The addition of metabolites of other phthalates besides DEHP did not substantially reduce the deviance indicating that they may not be associated with our outcome. Conclusion: These preliminary results indicate the potential importance of the metabolism of phthalates in modeling epidemiologic effects. Future analysis will work to model metabolism more explicitly.