Efficient Measurement Error Correction with Spatially Misaligned Data
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Abstract:
Association studies in environmental statistics often involve exposure and outcome data that are misaligned in space. A common strategy is to employ a spatial model such as universal kriging to predict exposures at locations with outcome data and then to estimate the regression parameter of interest based on the predicted exposures. This procedure results in measurement error because the predicted exposures do not correspond exactly to the true values. We characterize the measurement error by decomposing it into Berkson-like and classical-like components. An important effect is to increase the variability of parameter estimates, so naive standard errors are too small. The classical-like component can also introduce bias in the parameter estimates. We focus on deriving corrected standard errors, and one approach to doing this is the parametric bootstrap. While effective, the parametric bootstrap is computationally intensive since it requires solving a nonlinear optimization problem to estimate the exposure model parameters in each bootstrap sample. We propose a less computationally intensive alternative termed the ``parameter bootstrap'' that exploits our decomposition of the measurement error into Berkson-like and classical-like components. The primary advantage of the parameter bootstrap is that it only requires solving one nonlinear optimization problem. We illustrate our methodology in a simulation study.
Subject Area:
Statistical Theory and Methods
Suggested Citation:
Adam A. Szpiro, Lianne Sheppard, and Thomas Lumley, "Efficient Measurement Error Correction with Spatially Misaligned Data" (September 10, 2009). UW Biostatistics Working Paper Series. Working Paper 350.
http://www.bepress.com/uwbiostat/paper350