Measurement error is well recognized to be a potential source of bias on the estimated association of the adverse effects of the air pollution on health. Because air pollution is often measured using one or few ambient monitors, these measurements are surrogate indexes of personal exposure and can be weak predictors of it.

This paper presents hierarchical modeling strategies for evaluating the effects of measurement error on estimates of mortality in time series studies of air pollution, using five epidemiological studies on personal and ambient concentrations of PM₁₀. The studies present irregularly spaced observations, different personal and outdoor sampling of particles, and different subject characteristics. Our goal is to combine information across these heterogeneous studies to investigate the association between average personal exposure and ambient concentrations, and to estimate the size of bias in estimated PM₁₀-mortality regression coefficients due to using ambient monitors rather than personal exposure data about PM₁₀.

At the first stage of our hierarchical model, we introduce study-specific longitudinal regressions of personal exposures versus ambient concentrations of particles. Because exploratory analyses have shown that the association between average personal exposure and ambient concentration is higher in longest-term variations than shortest-term variations, we replace the ambient concentration time series with its decomposition in three time scales variations. At the second and third stage of the model, we introduce distributions on the longitudinal regressions parameters to borrow strength between subjects and between studies respectively.

Finally, to enable the decomposition of ambient concentrations into three different time scales, provisions must be made to account for irregularly spaced observations. Under the assumption that ambient concentrations follow an autoregressive time series model, we fill the gaps of the missing observations by a Gibbs Sampler. Taking into account of the heterogeneity across locations, the different sampling schemes, and the missing data observations, we found that the measurement error tends to bias the result toward the null hypothesis of no effect, and that the precision of such estimates is generally overstated.