Linear mixed models for replication data to efficiently allow for covariate measurement error.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Measurement error in regression covariates biases parameter estimates.
• Internal validation or replication data are needed for bias correction.
• Regression calibration (RC) is a common but sometimes limited method.

Purpose of the Study:

• To present a more accessible maximum likelihood (ML) approach for handling covariate measurement error.
• To compare the performance of ML with RC in linear and logistic regression models.
• To enhance the viability of ML as an alternative to RC in medical statistics.

Main Methods:

• Utilizing a standard random-intercepts model for ML estimation.
• Applying ML to linear and logistic regression with internal replicate measurements.
• Conducting simulation studies to compare ML and RC under various conditions.

Main Results:

• ML provides more efficient estimates than RC in linear regression, with small gains.
• Both RC and ML estimates remain consistent when normality assumptions are violated.
• ML demonstrates less bias than RC in logistic regression, particularly when RC shows non-negligible biases.

Conclusions:

• The proposed ML method makes this powerful technique more accessible to researchers.
• ML offers a robust and less biased alternative to RC for covariate measurement error.
• This work encourages wider adoption of ML in biostatistics and epidemiology.