Regression calibration for models with two predictor variables measured with error and their interaction, using...

Area of Science:

• Environmental Epidemiology
• Biostatistics
• Longitudinal Data Analysis

Background:

• Measurement error in predictors complicates regression modeling.
• Existing methods often do not handle interactions or correlated longitudinal data simultaneously.
• Accurate estimation of environmental exposure effects requires addressing these challenges.

Purpose of the Study:

• To develop and validate regression calibration estimators for longitudinal models with interaction terms involving error-prone predictors.
• To provide methods for estimating asymptotic variances in such models.
• To apply these methods to assess the interactive toxicity of pollutants on leukotriene E4 levels in asthmatic children.

Main Methods:

• Derivation of novel regression calibration estimators and their asymptotic variances.
• Application of linear mixed models accounting for random intercepts, serial correlation, and unequal spacing.
• Utilizing instrumental and unbiased surrogate variables when direct predictor measurements are absent.
• Employing simulations to confirm the accuracy of asymptotic inferential methods.

Main Results:

• Explicit forms of regression calibration estimators and their variances were derived for complex longitudinal models.
• The methods successfully estimated the interactive effects of outdoor fine particulate matter and cigarette smoke on leukotriene E4 levels.
• Simulations supported the accuracy of the developed inferential techniques.

Conclusions:

• The novel regression calibration approach provides unbiased estimation for longitudinal models with interacting, measured-error predictors.
• This methodology is crucial for accurately assessing environmental exposures and their combined health impacts.
• The findings offer a robust tool for epidemiological studies with complex exposure data.