arXiv subjects

Christopher J. Paciorek

Publications and source records attributed to Christopher J. Paciorek.

25 records · Page 2Linked to original sources

arXiv2014

Bayesian Estimation of Population-Level Trends in Measures of Health Status

Improving health worldwide will require rigorous quantification of population-level trends in health status. However, global-level surveys are not available, forcing researchers to rely on fragmentary country-specific data of varying quality. We present a Bayesian model that systematically combines disparate data to make country-, region- and global-level estimates of time trends in important health indicators. The model allows for time and age nonlinearity, and it borrows strength in time, age, covariates, and within and across regional country clusters to make estimates where data are sparse. The Bayesian approach allows us to account for uncertainty from the various aspects of missingness as well as sampling and parameter uncertainty. MCMC sampling allows for inference in a high-dimensional, constrained parameter space, while providing posterior draws that allow straightforward inference on the wide variety of functionals of interest. Here we use blood pressure as an example health metric. High blood pressure is the leading risk factor for cardiovascular disease, the leading cause of death worldwide. The results highlight a risk transition, with decreasing blood pressure in high-income regions and increasing levels in many lower-income regions.

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arXiv2013

Measurement error in two-stage analyses, with application to air pollution epidemiology

Public health researchers often estimate health effects of exposures (e.g., pollution, diet, lifestyle) that cannot be directly measured for study subjects. A common strategy in environmental epidemiology is to use a first-stage (exposure) model to estimate the exposure based on covariates and/or spatio-temporal proximity and to use predictions from the exposure model as the covariate of interest in the second-stage (health) model. This induces a complex form of measurement error. We propose an analytical framework and methodology that is robust to misspecification of the first-stage model and provides valid inference for the second-stage model parameter of interest. We decompose the measurement error into components analogous to classical and Berkson error and characterize properties of the estimator in the second-stage model if the first-stage model predictions are plugged in without correction. Specifically, we derive conditions for compatibility between the first- and second-stage models that guarantee consistency (and have direct and important real-world design implications), and we derive an asymptotic estimate of finite-sample bias when the compatibility conditions are satisfied. We propose a methodology that (1) corrects for finite-sample bias and (2) correctly estimates standard errors. We demonstrate the utility of our methodology in simulations and an example from air pollution epidemiology.

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arXiv2013

Parallelizing Gaussian Process Calculations in R

We consider parallel computation for Gaussian process calculations to overcome computational and memory constraints on the size of datasets that can be analyzed. Using a hybrid parallelization approach that uses both threading (shared memory) and message-passing (distributed memory), we implement the core linear algebra operations used in spatial statistics and Gaussian process regression in an R package called bigGP that relies on C and MPI. The approach divides the matrix into blocks such that the computational load is balanced across processes while communication between processes is limited. The package provides an API enabling R programmers to implement Gaussian process-based methods by using the distributed linear algebra operations without any C or MPI coding. We illustrate the approach and software by analyzing an astrophysics dataset with n=67,275 observations.

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arXiv2013

Spatial models for point and areal data using Markov random fields on a fine grid

I consider the use of Markov random fields (MRFs) on a fine grid to represent latent spatial processes when modeling point-level and areal data, including situations with spatial misalignment. Point observations are related to the grid cell in which they reside, while areal observations are related to the (approximate) integral over the latent process within the area of interest. I review several approaches to specifying the neighborhood structure for constructing the MRF precision matrix, presenting results comparing these MRF representations analytically, in simulations, and in two examples. The results provide practical guidance for choosing a spatial process representation and highlight the importance of this choice. In particular, the results demonstrate that, and explain why, standard CAR models can behave strangely for point-level data. They show that various neighborhood weighting approaches based on higher-order neighbors that have been suggested for MRF models do not produce smooth fields, which raises doubts about their utility. Finally, they indicate that an MRF that approximates a thin plate spline compares favorably to standard CAR models and to kriging under many circumstances.

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arXiv2011

Combining spatial information sources while accounting for systematic errors in proxies

Environmental research increasingly uses high-dimensional remote sensing and numerical model output to help fill space-time gaps between traditional observations. Such output is often a noisy proxy for the process of interest. Thus one needs to separate and assess the signal and noise (often called discrepancy) in the proxy given complicated spatio-temporal dependencies. Here I extend a popular two-likelihood hierarchical model using a more flexible representation for the discrepancy. I employ the little-used Markov random field approximation to a thin plate spline, which can capture small-scale discrepancy in a computationally efficient manner while better modeling smooth processes than standard conditional auto-regressive models. The increased flexibility reduces identifiability, but the lack of identifiability is inherent in the scientific context. I model particulate matter air pollution using satellite aerosol and atmospheric model output proxies. The estimated discrepancies occur at a variety of spatial scales, with small-scale discrepancy particularly important. The examples indicate little predictive improvement over modeling the observations alone. Similarly, in simulations with an informative proxy, the presence of discrepancy and resulting identifiability issues prevent improvement in prediction. The results highlight but do not resolve the critical question of how best to use proxy information while minimizing the potential for proxy-induced error.

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arXiv2010

The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators

Residuals in regression models are often spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When unmeasured confounding introduces spatial structure into the residuals, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual: one can reduce bias by fitting a spatial model only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals are independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

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arXiv2009

Practical large-scale spatio-temporal modeling of particulate matter concentrations

The last two decades have seen intense scientific and regulatory interest in the health effects of particulate matter (PM). Influential epidemiological studies that characterize chronic exposure of individuals rely on monitoring data that are sparse in space and time, so they often assign the same exposure to participants in large geographic areas and across time. We estimate monthly PM during 1988--2002 in a large spatial domain for use in studying health effects in the Nurses' Health Study. We develop a conceptually simple spatio-temporal model that uses a rich set of covariates. The model is used to estimate concentrations of $PM_{10}$ for the full time period and $PM_{2.5}$ for a subset of the period. For the earlier part of the period, 1988--1998, few $PM_{2.5}$ monitors were operating, so we develop a simple extension to the model that represents $PM_{2.5}$ conditionally on $PM_{10}$ model predictions. In the epidemiological analysis, model predictions of $PM_{10}$ are more strongly associated with health effects than when using simpler approaches to estimate exposure. Our modeling approach supports the application in estimating both fine-scale and large-scale spatial heterogeneity and capturing space--time interaction through the use of monthly-varying spatial surfaces. At the same time, the model is computationally feasible, implementable with standard software, and readily understandable to the scientific audience. Despite simplifying assumptions, the model has good predictive performance and uncertainty characterization.

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