Corrections for measurement error due to delayed onset of illness for case‐crossover designs

Epidemiologic studies of the short‐term effects of ambient particulate matter (PM) on the risk of acute cardiovascular or cerebrovascular events often use data from administrative databases in which only the date of hospitalization is known. A common study design for analyzing such data is the case‐crossover design, in which exposure at a time when a patient experiences an event is compared to exposure at times when the patient did not experience an event within a case‐control paradigm. However, the time of true event onset may precede hospitalization by hours or days, which can yield attenuated effect estimates. In this article, we consider a marginal likelihood estimator, a regression calibration estimator, and a conditional score estimator, as well as parametric bootstrap versions of each, to correct for this bias. All considered approaches require validation data on the distribution of the delay times. We compare the performance of the approaches in realistic scenarios via simulation, and apply the methods to analyze data from a Boston‐area study of the association between ambient air pollution and acute stroke onset. Based on both simulation and the case study, we conclude that a two‐stage regression calibration estimator with a parametric bootstrap bias correction is an effective method for correcting bias in health effect estimates arising from delayed onset in a case‐crossover study.