LAUSR

Epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories in relation to continuous outcomes, for example, cognitive function. However, the individual exposure measurements that constitute the history upon which an exposure history function is constructed are usually mismeasured. To obtain unbiased estimates of the effects for mismeasured functions in longitudinal studies, a method incorporating main and validation studies was developed. Simulation studies under several realistic assumptions were conducted to assess its performance compared to standard analysis, and we found that the proposed method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage. We applied it to a study of long-term exposure to PM 2.5 $\text{PM}_{2.5}$ , in relation to cognitive decline in the Nurses' Health Study Previously, it was found that the 2-year decline in the standard measure of cognition was 0.018 (95% CI, -0.034 to -0.001) units worse per 10 μ g/m 3 $\mu \text{g/m}^3$ increase in PM 2.5 $\text{PM}_{2.5}$ exposure. After correction, the estimated impact of PM 2.5 $\text{PM}_{2.5}$ on cognitive decline increased to 0.027 (95% CI, -0.059 to 0.005) units lower per 10 μ g/m 3 $\mu \text{g/m}^3$ increase. To put this into perspective, effects of this magnitude are about 2/3 of those found in our data associated with each additional year of aging: 0.044 (95% CI, -0.047 to -0.040) units per 1 year older after applying our correction method.