On using summary statistics from an external calibration sample to correct for covariate measurement error

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Covariate measurement error is prevalent in epidemiologic studies.
• Existing methods for correcting measurement error using external calibration samples often yield insufficient adjusted inferences.
• Accurate covariate measurement is crucial for valid epidemiologic research.

Purpose of the Study:

• To develop a novel method for estimating regression models with covariate measurement error.
• To provide valid adjusted inferences when the primary covariate (X) is unobserved but measured with error (W).
• To improve upon existing statistical techniques for handling measurement error in regression analysis.

Main Methods:

• The proposed method utilizes summary statistics from a calibration sample to perform multiple imputation of the unobserved covariate (X).
• It employs standard multiple imputation combining rules for estimating regression coefficients and standard errors.
• The method assumes a multivariate normal distribution for valid statistical inferences.

Main Results:

• Simulations demonstrate that the proposed method provides superior inferences compared to naive, classical calibration, and regression calibration methods.
• The new approach shows particular strength in bias correction and achieving nominal confidence levels.
• An example application examines the relationship between hormone levels and bone mineral density in midlife women.

Conclusions:

• Established methods inadequately adjust for bias stemming from measurement error in regression analyses, especially with substantial error.
• The newly proposed multiple imputation method effectively corrects for this deficiency, enhancing the validity of statistical inferences.
• This advancement offers a more reliable approach for epidemiologic studies affected by covariate measurement error.