If several risk factors for disease are considered in the same multiple logistic regression model, and some of these risk factors are measured with error, the point and interval estimates of relative risk corresponding to any of these factors may be biased either toward or away from the null value. A method is provided for correcting point and interval estimates of relative risk obtained from logistic regression for measurement error in one or more continuous variables. The method requires a separate validation study to estimate the coefficients from the multivariate linear regression model relating the surrogate variables to the vector of true risk factors. Similar methods have been suggested by other authors, but none provides a means of correcting the confidence intervals which include a component of variability due to estimation of the measurement error parameters from a validation study. An example is provided from a prospective study of dietary fat, calories, and alcohol in relation to breast cancer, and from a validation study of the questionnaire used to assess these nutrients. Before correcting for measurement error, the age-adjusted relative risk for a 25 g increment in alcohol intake was 1.33 (95% confidence interval (Cl) 1.14-1.55); after correcting for measurement error, the relative risk increased to 1.62 (95% Cl 1.23-2.12). Similarly, for a 10 g increment in saturated fat intake, the age-adjusted relative risk was 0.94 (95% Cl 0.83-1.06); after correcting for measurement error, the relative risk was 0.84 (95% Cl 0.59-1.20). These results indicate that the failure to find a substantial positive association between breast cancer risk and saturated fat intake cannot be explained by measurement error in fat, calories, or alcohol.
Regression calibration is a statistical method for adjusting point and interval estimates of effect obtained from regression models commonly used in epidemiology for bias due to measurement error in assessing nutrients or other variables. Previous work developed regression calibration for use in estimating odds ratios from logistic regression. We extend this here to estimating incidence rate ratios from Cox proportional hazards models and regression slopes from linear-regression models. Regression calibration is appropriate when a gold standard is available in a validation study and a linear measurement error with constant variance applies or when replicate measurements are available in a reliability study and linear random within-person error can be assumed. In this paper, the method is illustrated by correction of rate ratios describing the relations between the incidence of breast cancer and dietary intakes of vitamin A, alcohol, and total energy in the Nurses' Health Study. An example using linear regression is based on estimation of the relation between ultradistal radius bone density and dietary intakes of caffeine, calcium, and total energy in the Massachusetts Women's Health Study.
Several statistical approaches have been proposed to assess and correct for exposure measurement error. We aimed to provide a critical overview of the most common approaches used in nutritional epidemiology.