Bayesian Models for Multiple Outcomes Nested in Domains

We consider the problem of estimating the effect of exposure on multiple continuous outcomes, when the outcomes are measured on different scales and are nested within multiple outcome classes, or "domains." Our Bayesian model extends the linear mixed models approach to allow the exposure effect to differ across domains and across outcomes within domains. Our model can be parameterized to allow shrinkage of the effects within the different levels of nesting, or to allow fixed domain-specific effects with no shrinkage. Our model also allows covariate effects to differ across outcomes and domains. Our methodology is applied to data on prenatal methylmercury exposure and multiple outcomes in four domains measured at 9 years of age on children enrolled in the Seychelles Child Development Study. We use three different priors and found that our main conclusions were not sensitive to the choice of prior. Simulation studies examine the model performance under alternative scenarios. Our results demonstrate that a sizeable increase in power is possible.

[1]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[2]  Roberta F. White,et al.  Cognitive deficit in 7-year-old children with prenatal exposure to methylmercury. , 1997, Neurotoxicology and teratology.

[3]  L Ryan,et al.  Multivariate linear mixed models for multiple outcomes. , 1999, Statistics in medicine.

[4]  Christopher Cox,et al.  Prenatal methylmercury exposure from ocean fish consumption in the Seychelles child development study , 2003, The Lancet.

[5]  L Ryan,et al.  A Scaled Linear Mixed Model for Multiple Outcomes , 2000, Biometrics.

[6]  P. Robson,et al.  Associations of maternal long-chain polyunsaturated fatty acids, methyl mercury, and infant development in the Seychelles Child Development Nutrition Study. , 2008, Neurotoxicology.

[7]  K. Eto,et al.  Review Article: Pathology of Minamata Disease , 1997 .

[8]  Esben Budtz-Jørgensen,et al.  Structural Equation Models , 2005 .

[9]  B. Muthén.  BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[10]  G. Warnes.  The Normal Kernel Coupler: An Adaptive Markov Chain Monte Carlo Method for Efficiently Sampling From Multi-Modal Distributions , 2001 .

[11]  Esben Budtz-Jørgensen,et al.  Statistical methods for the evaluation of health effects of prenatal mercury exposure , 2003 .

[12]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[13]  Esben Budtz-Jørgensen,et al.  Separation of Risks and Benefits of Seafood Intake , 2006, Environmental health perspectives.

[14]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[15]  T. Clarkson.  The three modern faces of mercury. , 2002, Environmental health perspectives.

[16]  Jason Roy,et al.  Scaled marginal models for multiple continuous outcomes. , 2003, Biostatistics.

[17]  L. Lapham,et al.  ABNORMAL NEURONAL MIGRATION, DERANGED CEREBRAL CORTICAL ORGANIZATION, AND DIFFUSE WHITE MATTER ASTROCYTOSIS OF HUMAN FETAL BRAIN: A MAJOR EFFECT OF METHYLMERCURY POISONING IN UTERO , 1978, Journal of neuropathology and experimental neurology.

[18]  Esben Budtz-Jørgensen,et al.  Estimation of health effects of prenatal methylmercury exposure using structural equation models , 2002, Environmental health : a global access science source.

[19]  Louise Ryan,et al.  Combining data from multiple sources, with applications to environmental risk assessment , 2008, Statistics in medicine.

[20]  D. Dunson,et al.  Bayesian latent variable models for clustered mixed outcomes , 2000 .

[21]  M. Longnecker,et al.  Fish Intake During Pregnancy and Early Cognitive Development of Offspring , 2004, Epidemiology.

[22]  James P. Hobert,et al.  Crossed Random Effect Models for Multiple Outcomes in a Study of Teratogenesis , 2001 .

[23]  P. Robson,et al.  Neurodevelopmental effects of maternal nutritional status and exposure to methylmercury from eating fish during pregnancy. , 2008, Neurotoxicology.

[24]  Louise Ryan,et al.  EFFECTS OF COVARIANCE MISSPECIFICATION IN A LATENT VARIABLE MODEL FOR MULTIPLE OUTCOMES , 2002 .

[25]  Jean Golding,et al.  Fish intake during pregnancy and early cognitive development of offspring , 2005 .

[26]  Tracey J. Woodruff,et al.  Dose–Response Relationship of Prenatal Mercury Exposure and IQ: An Integrative Analysis of Epidemiologic Data , 2007, Environmental health perspectives.

[27]  Roberta F. White,et al.  Milestone development in infants exposed to methylmercury from human milk. , 1995, Neurotoxicology.