Does more accurate exposure prediction necessarily improve health effect estimates?

Abstract

A unique challenge in air pollution cohort studies and similar applications in environmental epidemiology is that exposure is not measured directly at subjects' locations. Instead, pollution data from monitoring stations at some distance from the study subjects are used to predict exposures, and these predicted exposures are used to estimate the health effect parameter of interest. It is usually assumed that minimizing the error in predicting the true exposure will improve health effect estimation. We show in a simulation study that this is not always the case. We interpret our results in light of recently developed statistical theory for measurement error, and we discuss implications for the design and analysis of epidemiologic research.

Figure 1

Results from 80,000 Monte Carlo simulations with N = 10,000, N^* = 100, and σ² = 1.0. For the correctly specified exposure model the average out-of-sample prediction accuracy is ${\overline{R}}_W^2=0.74$ and the health effect estimation standard deviation is 0.12 with a bias of −0.007 (95% CI = −0.008 to −0.006). Corresponding statistics for the misspecified exposure model are ${\overline{R}}_W^{2\prime }$ and health effect estimation standard deviation 0.21 with a bias of (95% CI = −0.002 to 0.0006). The standard error of α̂₃ for the correctly specified model is 0.41, and α̂₃ is statistically significant in all simulations.

Figure 2

Results from 80,000 Monte Carlo simulations with N = 10,000, N^* = 100, and σ² = 0.1. For the correctly specified exposure model the average out-of-sample prediction accuracy is ${\overline{R}}_W^2=0.73$ and the health effect estimation standard deviation is 0.23 with a bias of −0.035 (95% CI = −0.037 to −0.034). Corresponding statistics for the misspecified exposure model are ${\overline{R}}_W^{2\prime }$ and health effect estimation standard deviation 0.16 with a bias of 0.001 (95% CI = −0.0003 to 0.002). The density plot for $R_W^2$ shows some small outliers for the full model, but the prediction accuracy is better than for the misspecified model in all but 144 of the 80,000 simulations. The standard deviation of α̂₃ for the correctly specified model is 1.37, and α̂₃ is statistically significant in 83% of simulations.

Figure 3

Results from 5,000 Monte Carlo simulations with N^* = 100, σ² = 0.1,1.0,4.0, and N ranging from 100 to 10,000. The vertical axis shows the difference between standard deviation (SD) of β̂_X from the misspecified and correct exposure models. A positive difference indicates that the correctly specified model is more efficient. For all values of σ², the average exposure model prediction accuracies are ${\overline{R}}_W^2$ between 0.73 and 0.75 and ${\overline{R}}_W^{2\prime }$ between 0.49 and 0.50 $0.50.N=N^{*}={\overline{R}}_W^2\mathrm{V}\overline{\mathrm{a}}\mathrm{r}(W)R_W^2{\widehat{\alpha }}_3{\widehat{\beta }}_X{\widehat{\beta }}_X{\widehat{\beta }}_{X}0.001N=N^{*}={\sigma }^2=1.0{\overline{R}}_W^2=0.740.12-0.007{\overline{R}}_W^{2\prime }=0.490.21-0.001{\widehat{\alpha }}_{3}0.41{\widehat{\alpha }}_{3}N=N^{*}={\sigma }^2=0.1{\overline{R}}_W^2=0.730.23-0.035{\overline{R}}_W^{2\prime }=0.500.160.001R_W^{2}144{\widehat{\alpha }}_{3}1.37{\widehat{\alpha }}_3{N}^{*}={\sigma }^2=0.1,1.0,4.0N{\widehat{\beta }}_X{\sigma }^2{\overline{R}}_W^{2}0.730.75{\overline{R}}_W^{2\prime }0.490.50$.