OutlineMain TalkIntroductionDBPs and SABRight From the StartFrequentist AnalysisModelResultsModel P1 (semi-Bayes)Model P2 (fully Bayes)Dirichlet Process Prior Model (SP1)DPP with selection component (SP2)ResultsSimulationsHierarchical Models and RFTSConclusionsFuture/Current ResearchOutlineBayesian Methods for Highly CorrelatedExposures:An Application to Disinfection By-products andSpontaneous AbortionRich MacLehose, David Dunson, Amy HerringNovember 8, 2007Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataOutlineOutline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataOutlineOutline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataOutlineOutline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataOutlineOutline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartOutline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartSpontaneous Abortion (SAB)Pregnancy loss prior to 20 weeks gestationVery common (> 30% of all pregnancies)Relatively little known about its causesmaternal age, smoking, prior pregnancy loss, occupationalexposures, caffeinedisinfection by-products (DBPs)?Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartSpontaneous Abortion (SAB)Pregnancy loss prior to 20 weeks gestationVery common (> 30% of all pregnancies)Relatively little known about its causesmaternal age, smoking, prior pregnancy loss, occupationalexposures, caffeinedisinfection by-products (DBPs)?Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartDisinfection By-ProductsA vast array of DBPs are formed in the disinfection processWe focus on 2 main types:Trihalomethanes (THMs)CHCl3, CHBr3, CHCl2Br, CHClBr2Haloacetic Acids (HAAs)ClAA, Cl2AA, Cl3AA, BrAA, Br2AA, Br3AA, BrClAA, Br2ClAA,BrCl2AARich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartDisinfection By-ProductsA vast array of DBPs are formed in the disinfection processWe focus on 2 main types:Trihalomethanes (THMs)CHCl3, CHBr3, CHCl2Br, CHClBr2Haloacetic Acids (HAAs)ClAA, Cl2AA, Cl3AA, BrAA, Br2AA, Br3AA, BrClAA, Br2ClAA,BrCl2AARich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartDBPs and SABsEarly StudiesNoted an increased risk of SAB with increased tap-waterconsumptionMore Recent StudiesIncreased risk of SAB with exposure to THMsNotably, CHBrCl2in Waller et al (1998)OR=2.0 (1.2, 3.5)Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartDBPs and SABsEarly StudiesNoted an increased risk of SAB with increased tap-waterconsumptionMore Recent StudiesIncreased risk of SAB with exposure to THMsNotably, CHBrCl2in Waller et al (1998)OR=2.0 (1.2, 3.5)Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartSpecific AimTo estimate the effect of each of the 13 constituent DBPs (4THMs and 9 HAAs) on SABThe ProblemDBPs are very highly correlatede.g., ρ=0.91 between Cl2AA and Cl3AARich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartSpecific AimTo estimate the effect of each of the 13 constituent DBPs (4THMs and 9 HAAs) on SABThe ProblemDBPs are very highly correlatede.g., ρ=0.91 between Cl2AA and Cl3AARich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartRFTS - briefly2507 enrolled in three metropolitan areas in U.S.Years: 2001-2004RecruitmentPrenatal care practices (52%)Health departments (32%)Promotional mailings (3%)Drug stores, referrals, etc. (13%)Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartEligibility criteria≥ 18 yearslived in area served by 1 of the water utilitiesnot using assisted reproductive technologypositive pregnancy testintended to carry to termintended to remain in areaRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsDBPs and SABRight From the StartData CollectionBaseline Interviewdemographic information, medical history, other confoundersPregnancy lossself report or chart abstractionDBP concentrationDisinfecting utilitiesWeekly samples at two sites with high DBPsEvery other week at thirdy site with low DBPsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsModelResultsModel P1 (semi-Bayes)Model P2 (fully Bayes)Dirichlet Process Prior Model (SP1)DPP with selection component (SP2)Outline1Introduction2Frequentist Analysis3Results4ConclusionsRich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly Correlated DataIntroductionFrequentist AnalysisResultsConclusionsModelResultsModel P1 (semi-Bayes)Model P2 (fully Bayes)Dirichlet Process Prior Model (SP1)DPP with selection component (SP2)Preliminary AnalysisDiscrete time hazard model including all 13 DBPsTime to event: gestational weeks until lossDBP concentrations were measured weekly, included astime-varying covariatesAllow for non-linear relationships (crudely) by categorizingDBPs (now have 32 coefficients)Rich MacLehose, David Dunson, Amy Herring Bayesian Methods for Highly