Correction for regression dilution bias using replicates from subjects with extreme first measurements.

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Linear regression slope estimators are biased towards zero due to predictor measurement error (e.g., intra-individual variation, technical error).
• Correction factors for this bias are typically estimated from reliability studies with replicate measurements.
• Existing methods assume reliability studies use random subsamples from the main study cohort.

Purpose of the Study:

• To propose and evaluate an efficient design for reliability studies using extreme value selection.
• To compare the precision of regression coefficient estimation using extreme selection versus random subsampling.
• To derive variance formulas for the correction factor and corrected regression coefficient under extreme selection.

Main Methods:

• Developed a theoretical framework for estimating correction factors using replicates from subjects with extreme values.
• Derived variance formulas for the correction factor estimator and the corrected regression coefficient.
• Utilized Monte Carlo simulations and real-world data (ULSAM study) for validation and comparison.

Main Results:

• Extreme value selection significantly reduces the variance of corrected regression coefficients compared to random subsampling.
• The variance gain achieved with extreme selection can be estimated directly from main study data.
• Simulations and the ULSAM study application demonstrated the practical benefits of the extreme selection design.

Conclusions:

• Extreme value selection is a more efficient design for reliability studies, enhancing precision in regression analysis.
• Investigators can improve statistical power or reduce sample size requirements by employing extreme selection.
• This design offers a valuable strategy for planning future reliability studies to mitigate bias from measurement error.