Hazard ratio estimation for biomarker-calibrated dietary exposures

Uncertainty concerning the measurement error properties of self-reported diet has important implications for the reliability of nutritional epidemiology reports. Biomarkers based on the urinary recovery of expended nutrients can provide an objective measure of short-term nutrient consumption for certain nutrients and, when applied to a subset of a study cohort, can be used to calibrate corresponding self-report nutrient consumption assessments. A nonstandard measurement error model that makes provision for systematic error and subject-specific error, along with the usual independent random error, is needed for the self-report data. Three estimation procedures for hazard ratio (Cox model) parameters are extended for application to this more complex measurement error structure. These procedures are risk set regression calibration, conditional score, and nonparametric corrected score. An estimator for the cumulative baseline hazard function is also provided. The performance of each method is assessed in a simulation study. The methods are then applied to an example from the Women's Health Initiative Dietary Modification Trial.