Survival analysis with functions of mismeasured covariate histories: the case of chronic air pollution exposure in relation to mortality in the nurses’ health study

Environmental epidemiologists are often interested in estimating the effect of functions of time varying exposure histories, such as the 12‐month moving average, in relation to chronic disease incidence or mortality. The individual exposure measurements that comprise such an exposure history are usually mismeasured, at least moderately, and, often, more substantially. To obtain unbiased estimates of Cox model hazard ratios for these complex mismeasured exposure functions, an extended risk set regression calibration method for Cox models is developed and applied to a study of long‐term exposure to the fine particulate matter, PM2.5, component of air pollution in relation to all‐cause mortality in the nurses’ health study. Simulation studies under several realistic assumptions about the measurement error model and about the correlation structure of the repeated exposure measurements were conducted to assess the finite sample properties of this new method and found that the method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage.