Measurement error correction for logistic regression models with an "alloyed gold standard"

Area of Science:

• Epidemiology
• Biostatistics
• Measurement Error in Exposure Assessment

Background:

• Methods correcting relative risk for measurement error assume a perfect "gold standard" for validation.
• Recent work questions the validity of these methods when the gold standard itself is imperfect ("alloyed").
• Bias in regression calibration for relative risks with alloyed gold standards is a function of error correlations and variances.

Purpose of the Study:

• To derive the bias in regression calibration when an alloyed gold standard is used.
• To prove that regression calibration is unbiased if errors between exposure assessment methods are uncorrelated.
• To develop and illustrate a modified regression calibration method accounting for error in two exposure assessment methods.

Main Methods:

• Derivation of bias in regression calibration using an alloyed gold standard.
• Proof of unbiasedness for regression calibration when exposure assessment errors are uncorrelated.
• Development of methods to estimate error correlations and a modified regression calibration approach using a third exposure assessment method.

Main Results:

• Regression calibration is unbiased even with an alloyed gold standard if errors in exposure assessment methods (Z and X) are uncorrelated.
• Methods for estimating error correlations (between X and Z) were derived using a third, uncorrelated exposure assessment method.
• A modified regression calibration method was developed to correct for measurement error in both X and Z.
• Illustrative data analyses showed small correlations between errors in X and Z, with corrected relative risks similar to those assuming a perfect gold standard.

Conclusions:

• Regression calibration remains a valid method for correcting relative risk estimates even when the gold standard is imperfect, provided exposure assessment errors are uncorrelated.
• The developed modified regression calibration method offers improved accuracy by accounting for measurement error in multiple exposure assessment tools.
• Findings suggest that assumptions about gold standard perfection may not significantly impact relative risk estimates in practice, especially when error correlations are low.