Estimating and testing interactions in linear regression models when explanatory variables are subject to classical...

Area of Science:

• Biostatistics
• Statistical Modeling

Background:

• Classical measurement error in explanatory variables complicates linear regression, especially for interaction terms.
• Existing methods often require strict assumptions or struggle with correlated errors and low reliability.

Purpose of the Study:

• To develop simple, consistent methods for estimating and testing interactions in linear regression with measurement error.
• To compare the performance of method of moments (MM) and regression calibration (RC) under various conditions.

Main Methods:

• Development of moment-based (MM) and regression calibration (RC) estimators for regression coefficients and standard errors.
• Simulation studies to evaluate bias, variance, and type I error rates under normality and non-normality assumptions.
• Application to a real-world example involving homocysteine, serum folate, and B12 levels.

Main Results:

• Regression calibration (RC) provides nearly unbiased estimators with superior performance over MM in bias and variance under normality.
• RC correctly controls the type I error rate for interaction term testing.
• Method of moments (MM) is recommended when true covariates deviate from normality.

Conclusions:

• RC is a robust and accurate method for handling measurement error in interaction terms within linear regression models, particularly under normality.
• MM serves as a viable alternative when normality assumptions are violated.
• The developed methods offer practical solutions for complex statistical modeling in observational studies.