Regression analysis with covariates that have heteroscedastic measurement error.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Accurate regression analysis requires precise covariate measurement.
• Measurement error in covariates (X) is common, often observed through a related variable (W).
• Existing methods often assume constant measurement error variance, which is frequently violated in practice.

Purpose of the Study:

• To extend Regression Calibration (RC) and Multiple Imputation (MI) methods to address heteroscedastic measurement error.
• To compare the performance of these extended methods via simulation.
• To apply the methods to real-world data from the BioCycle study.

Main Methods:

• Developed extensions of RC and MI to accommodate non-constant measurement error variance.
• Utilized calibration samples for estimating measurement error models (internal and external calibration).
• Performed simulation studies to evaluate method performance under heteroscedasticity.

Main Results:

• The extended Multiple Imputation (MI) method provided more accurate inferences compared to Regression Calibration (RC) under heteroscedastic measurement error.
• Simulation results confirmed the superiority of MI in this setting.
• The methods were successfully applied to the BioCycle study dataset.

Conclusions:

• Multiple Imputation (MI) is a robust approach for regression analysis with heteroscedastic measurement error.
• The proposed extensions enhance the applicability of statistical methods in the presence of complex measurement error structures.
• These methods are valuable for observational studies, particularly in fields like epidemiology and biostatistics.