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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 PM2.5$\text{PM}_{2.5}$, 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 μg/m3$\mu \text{g/m}^3$ increase in PM2.5$\text{PM}_{2.5}$ exposure. After correction, the estimated impact of PM2.5$\text{PM}_{2.5}$ on cognitive decline increased to 0.027 (95% CI, −0.059 to 0.005) units lower per 10 μg/m3$\mu \text{g/m}^3$ 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. [ABSTRACT FROM AUTHOR]

When a ranking of institutions such as medical centers or universities is based on a numerical measure of performance provided with a standard error, confidence intervals (CIs) should be calculated to assess the uncertainty of these ranks. We present a novel method based on Tukey's honest significant difference test to construct simultaneous CIs for the true ranks. When all the true performances are equal, the probability of coverage of our method attains the nominal level. In case the true performance measures have no exact ties, our method is conservative. For this situation, we propose a rescaling method to the nominal level that results in shorter CIs while keeping control of the simultaneous coverage. We also show that a similar rescaling can be applied to correct a recently proposed Monte‐Carlo based method, which is anticonservative. After rescaling, the two methods perform very similarly. However, the rescaling of the Monte‐Carlo based method is computationally much more demanding and becomes infeasible when the number of institutions is larger than 30–50. We discuss another recently proposed method similar to ours based on simultaneous CIs for the true performance. We show that our method provides uniformly shorter CIs for the same confidence level. We illustrate the superiority of our new methods with a data analysis for travel time to work in the United States and on rankings of 64 hospitals in the Netherlands. [ABSTRACT FROM AUTHOR]