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1.  Reduced hierarchical models with application to estimating health effects of simultaneous exposure to multiple pollutants 
Summary
Hierarchical models (HM) have been used extensively in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for other pollutants and other time-varying factors. Recently, Environmental Protection Agency (EPA) has called for research quantifying health effects of simultaneous exposure to many air pollutants. However, straightforward application of HM in this context is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters. Here we introduce reduced HM as a general statistical approach for analyzing correlated data with many nuisance parameters. For reduced HM we first calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants), and we then specify a flexible random-effect distribution directly on this parameter. Simulation studies show that the reduced HM performs comparably to the full HM in many scenarios, and even performs better in some cases, particularly when the multivariate random-effect distribution of the full HM is misspecified. Methods are applied to estimate relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during 1999–2005.
doi:10.1111/rssc.12006
PMCID: PMC3864808  PMID: 24357883
Air pollution; Multilevel models; Multisite time series data; Nuisance parameters; Random effects
2.  Cross-sectional and longitudinal association of body mass index and brain volume 
Human brain mapping  2012;35(1):10.1002/hbm.22159.
While a link between body mass index (BMI) and brain volume has been established in several cross-sectional studies, evidence of the association between change in BMI over time and changes in brain structure is limited. Using data from a cohort of 347 former lead workers and community controls with two MRI scans over an approximately 5-year period, we estimated cross-sectional and longitudinal associations of BMI and brain volume using both region-of-interest (ROI) and voxel-based morpho-metric (VBM) methods. We found that associations of BMI and brain volume were not significantly different in former lead workers as compared to community controls. In the cross-sectional analysis, higher BMIs were associated with smaller brain volumes in gray matter (GM) using both ROI and VBM approaches. No associations with white matter (WM) were observed. In the longitudinal analysis, higher baseline BMI was associated with greater decline in temporal and occipital GM ROI volumes. Change in BMI over the five-year period was only associated with change in hippocampal volume and was not associated with change in any of the GM ROIs. Overall, higher BMI was associated with lower GM volume in several ROIs and with declines in volume in temporal and occipital GM over time. These results suggest that sustained high body mass may contribute to progressive temporal and occipital atrophy.
doi:10.1002/hbm.22159
PMCID: PMC3615109  PMID: 23008165
Obesity; Brain Structure; Aging; BMI; MRI
3.  Perinatal Air Pollutant Exposures and Autism Spectrum Disorder in the Children of Nurses’ Health Study II Participants 
Environmental Health Perspectives  2013;121(8):978-984.
Objective: Air pollution contains many toxicants known to affect neurological function and to have effects on the fetus in utero. Recent studies have reported associations between perinatal exposure to air pollutants and autism spectrum disorder (ASD) in children. We tested the hypothesis that perinatal exposure to air pollutants is associated with ASD, focusing on pollutants associated with ASD in prior studies.
Methods: We estimated associations between U.S. Environmental Protection Agency–modeled levels of hazardous air pollutants at the time and place of birth and ASD in the children of participants in the Nurses’ Health Study II (325 cases, 22,101 controls). Our analyses focused on pollutants associated with ASD in prior research. We accounted for possible confounding and ascertainment bias by adjusting for family-level socioeconomic status (maternal grandparents’ education) and census tract–level socioeconomic measures (e.g., tract median income and percent college educated), as well as maternal age at birth and year of birth. We also examined possible differences in the relationship between ASD and pollutant exposures by child’s sex.
Results: Perinatal exposures to the highest versus lowest quintile of diesel, lead, manganese, mercury, methylene chloride, and an overall measure of metals were significantly associated with ASD, with odds ratios ranging from 1.5 (for overall metals measure) to 2.0 (for diesel and mercury). In addition, linear trends were positive and statistically significant for these exposures (p < .05 for each). For most pollutants, associations were stronger for boys (279 cases) than for girls (46 cases) and significantly different according to sex.
Conclusions: Perinatal exposure to air pollutants may increase risk for ASD. Additionally, future studies should consider sex-specific biological pathways connecting perinatal exposure to pollutants with ASD.
doi:10.1289/ehp.1206187
PMCID: PMC3734496  PMID: 23816781
air pollution; autism; diesel; heavy metals; prenatal exposure
4.  A Bayesian Model Averaging Approach for Estimating the Relative Risk of Mortality Associated with Heat Waves in 105 U.S. Cities 
Biometrics  2011;67(4):1605-1616.
Summary
Estimating the risks heat waves pose to human health is a critical part of assessing the future impact of climate change. In this paper we propose a flexible class of time series models to estimate the relative risk of mortality associated with heat waves and conduct Bayesian model averaging (BMA) to account for the multiplicity of potential models. Applying these methods to data from 105 U.S. cities for the period 1987–2005, we identify those cities having a high posterior probability of increased mortality risk during heat waves, examine the heterogeneity of the posterior distributions of mortality risk across cities, assess sensitivity of the results to the selection of prior distributions, and compare our BMA results to a model selection approach. Our results show that no single model best predicts risk across the majority of cities, and that for some cities heat wave risk estimation is sensitive to model choice. While model averaging leads to posterior distributions with increased variance as compared to statistical inference conditional on a model obtained through model selection, we find that the posterior mean of heat wave mortality risk is robust to accounting for model uncertainty over a broad class of models.
doi:10.1111/j.1541-0420.2011.01583.x
PMCID: PMC3128186  PMID: 21447046
Climate change; Generalized Additive Models; Model Uncertainty; Time series data
5.  Association of Social Engagement with Brain Volumes Assessed by Structural MRI 
Journal of Aging Research  2012;2012:512714.
We tested the hypothesis that social engagement is associated with larger brain volumes in a cohort study of 348 older male former lead manufacturing workers (n = 305) and population-based controls (n = 43), age 48 to 82. Social engagement was measured using a summary scale derived from confirmatory factor analysis. The volumes of 20 regions of interest (ROIs), including total brain, total gray matter (GM), total white matter (WM), each of the four lobar GM and WM, and 9 smaller structures were derived from T1-weighted structural magnetic resonance images. Linear regression models adjusted for age, education, race/ethnicity, intracranial volume, hypertension, diabetes, and control (versus lead worker) status. Higher social engagement was associated with larger total brain and GM volumes, specifically temporal and occipital GM, but was not associated with WM volumes except for corpus callosum. A voxel-wise analysis supported an association in temporal lobe GM. Using longitudinal data to discern temporal relations, change in ROI volumes over five years showed null associations with current social engagement. Findings are consistent with the hypothesis that social engagement preserves brain tissue, and not consistent with the alternate hypothesis that persons with smaller or shrinking volumes become less socially engaged, though this scenario cannot be ruled out.
doi:10.1155/2012/512714
PMCID: PMC3446736  PMID: 22997582
6.  Multiple Imputation of Missing Phenotype Data for QTL Mapping 
Missing phenotype data can be a major hurdle to mapping quantitative trait loci (QTL). Though in many cases experiments may be designed to minimize the occurrence of missing data, it is often unavoidable in practice; thus, statistical methods to account for missing data are needed. In this paper we describe an approach for conjoining multiple imputation and QTL mapping. Methods are applied to map genes associated with increased breathing effort in mice after lung inflammation due to allergen challenge in developing lines of the Collaborative Cross, a new mouse genetics resource. Missing data poses a particular challenge in this study because the desired phenotype summary to be mapped is a function of incompletely observed dose-response curves. Comparison of the multiple imputation approach to two naive approaches for handling missing data suggest that these simpler methods may yield poor results: ignoring missing data through a complete case analysis may lead to incorrect conclusions, while using a last observation carried forward procedure, which does not account for uncertainty in the imputed values, may lead to anti-conservative inference. The proposed approach is widely applicable to other studies with missing phenotype data.
doi:10.2202/1544-6115.1676
PMCID: PMC3404522
multiple imputation; missing data; quantitative trait loci
7.  Toward a Quantitative Estimate of Future Heat Wave Mortality under Global Climate Change 
Environmental Health Perspectives  2010;119(5):701-706.
Background
Climate change is anticipated to affect human health by changing the distribution of known risk factors. Heat waves have had debilitating effects on human mortality, and global climate models predict an increase in the frequency and severity of heat waves. The extent to which climate change will harm human health through changes in the distribution of heat waves and the sources of uncertainty in estimating these effects have not been studied extensively.
Objectives
We estimated the future excess mortality attributable to heat waves under global climate change for a major U.S. city.
Methods
We used a database comprising daily data from 1987 through 2005 on mortality from all nonaccidental causes, ambient levels of particulate matter and ozone, temperature, and dew point temperature for the city of Chicago, Illinois. We estimated the associations between heat waves and mortality in Chicago using Poisson regression models.
Results
Under three different climate change scenarios for 2081–2100 and in the absence of adaptation, the city of Chicago could experience between 166 and 2,217 excess deaths per year attributable to heat waves, based on estimates from seven global climate models. We noted considerable variability in the projections of annual heat wave mortality; the largest source of variation was the choice of climate model.
Conclusions
The impact of future heat waves on human health will likely be profound, and significant gains can be expected by lowering future carbon dioxide emissions.
doi:10.1289/ehp.1002430
PMCID: PMC3094424  PMID: 21193384
climate models; extreme weather events; global warming; population health; time-series models

Results 1-7 (7)