Measurement error caused by spatial misalignment in environmental epidemiology

Abstract

In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.

Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions

“…Alternatively, it would be possible to refer to the measurement error modeling framework (see e.g. Gryparis et al, 2009;MacNab, 2009;Szpiro et al, 2011;Lopiano et al, 2013;Szpiro and Paciorek, 2013) and define an ecological regression model accounting for errors in covariates. In a fully Bayesian framework the natural approach would consist in a joint model of exposure and health, which would allow to propagate properly all the uncertainty sources (due to spatial misalignment, measurement error, etc.).…”

Controlling for confounding in the presence of measurement error in hierarchical models: a Bayesian approach

“…One could extend the applicability of this approach to larger data sets by programming the Markov chain Monte Carlo fitting procedure in a programming language that is faster than WinBUGS, such as the R software package. We have found this to be helpful in other Bayesian settings (Gryparis et al, 2006).…”

“…Part of this is due to the fact that the mixing of the Markov chains used to fit the model can be slow. We have found in previous work (Gryparis et al, 2006) that if one is not interested in estimating the true latent exposure itself (just the health effect associated with that exposure), mixing can be improved by integrating these latent variables out of the model. This practice increases the complexity of the model, since some parameters appear both in the mean and the variance structure of some posterior distributions.…”

Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models

“…This problem, usually named misalignment, has gained a lot of attention in the literature [see Gotway and Young (2002), Gelfand (2010) and Chapter 7 of Banerjee et al (2014) and references cited therein for very good and detailed descriptions of the problem], the most important reason behind being that not taking it into account could clearly influence results. Gryparis et al (2009) and Wannemuehler et al (2009) are good examples of epidemiological studies presenting misalignment in which the usual models cannot be applied.The naïve solution to this problem would be to predict the value of the covariates at those locations on which we want to predict the occurrence of the disease by using geostatistical methods (for instance, using kriging), and then, plug-in these values in the prediction process, using them instead of the true (but unknown) values. This two-stage analysis is used in preference to forming a joint geostatistical model for the covariates and the response variable.…”