Logistic regression with correlated measurement error and misclassification in covariates

Area of Science:

• Nutritional epidemiology
• Biostatistics
• Chronic disease research

Background:

• Measurement errors in continuous covariates and misclassification of categorical variables are common in nutritional epidemiology.
• Ignoring these errors leads to biased results, but few methods address both simultaneously.
• Existing research often tackles measurement error and misclassification independently.

Purpose of the Study:

• To propose a new correction method for logistic regression handling correlated measurement errors in continuous covariates and misclassification in a categorical variable.
• To provide a computationally efficient method with a derived closed-form approximate likelihood function.
• To establish the asymptotic normality of the proposed estimator.

Main Methods:

• Developed a logistic regression correction method for simultaneous handling of measurement error and misclassification.
• Derived a closed-form approximate likelihood function conditional on observed covariates for computational efficiency.
• Evaluated finite-sample performance using simulation studies and established asymptotic normality.

Main Results:

• Applied the method to the European Prospective Investigation into Cancer and Nutrition-InterAct Study data.
• Identified a negative association between fruit intake and type 2 diabetes risk in women with active physical activity.
• Found a positive association between protein intake and type 2 diabetes risk in less active individuals.
• Demonstrated that actual physical activity has a greater impact on reducing type 2 diabetes risk than observed physical activity.

Conclusions:

• The proposed method effectively addresses correlated measurement errors and misclassification in logistic regression models.
• Accurate measurement of physical activity and nutrient intake is crucial for understanding type 2 diabetes risk.
• The findings highlight the importance of considering both diet and physical activity in type 2 diabetes prevention strategies.