Correction of logistic regression relative risk estimates and confidence intervals for systematic within‐person measurement error

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Abstract
Errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value. Two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random (unbiased) within-person variation or to systematic errors for individual subjects. These methods require a separate validation study to estimate the regression coefficient λ relating the surrogate measure to true exposure. In the linear approximation method, the true logistic regression coefficient β* is estimated by bT/λ, where β is the observed logistic regression coefficient based on the surrogate measure. In the likelihood approximation method, a second-order Taylor series expansion is used to approximate the logistic function, enabling closed-form likelihood estimation of β*. Confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of λ. Based on simulation studies, both methods perform well for true odds ratios up to 3·0; for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability. An example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to asses dietary fat intake.