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Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error.

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 (CI) 1.14-1.55); after correcting for measurement error, the relative risk increased to 1.62 (95% CI 1.23-2.12). Similarly, for a 10 g increment in saturated fat intake, the age-adjusted relative risk was 0.94 (95% CI 0.83-1.06); after correcting for measurement error, the relative risk was 0.84 (95% CI 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.