Exposure Measurement Error Correction in Longitudinal Studies With Discrete Outcomes

Environmental epidemiologists are often interested in estimating the effect of time-varying functions of the exposure history on health outcomes. However, the individual exposure measurements that constitute the history upon which an exposure history function is constructed are usually subject to measurement errors. To obtain unbiased estimates of the effects of such mismeasured functions in longitudinal studies with discrete outcomes, a method applicable to the main study/validation study design is developed. Various estimation procedures are explored. Simulation studies were conducted to assess its performance compared to standard analysis, and we found that the proposed method had good performance in terms of finite sample bias reduction and nominal coverage probability improvement. As an illustrative example, we applied the new method to a study of long-term exposure to ${\text{PM}}_{2.5}$ , in relation to the occurrence of anxiety disorders in the Nurses' Health Study II. Failing to correct the error-prone exposure can lead to an underestimation of the chronic exposure effect of ${\text{PM}}_{2.5}$ .