Interaction analysis under misspecification of main effects: Some common mistakes and simple solutions

Area of Science:

• Statistical modeling
• Epidemiology
• Bioinformatics

Background:

• Interaction modeling with linear main effects and product terms is common in statistical and epidemiological research.
• Misspecification of main effects can lead to inflated Type I errors in interaction tests, causing spurious findings.

Purpose of the Study:

• To analyze the impact of linear main effect misspecification on statistical interaction tests.
• To propose and evaluate methods for correcting Type I error inflation in interaction testing.
• To investigate the performance of generalized additive models and sandwich estimators.

Main Methods:

• Characterizing the impact of linear main effect misspecification on interaction tests.
• Evaluating the sandwich variance estimator in linear regression for quantitative outcomes with independent factors.
• Applying generalized additive models for flexible main effect modeling.
• Conducting simulation studies and analyzing data from the Michigan Genomics Initiative.

Main Results:

• The sandwich variance estimator maintains correct Type I error rates for Wald and score tests in linear regression with independent factors and quantitative outcomes.
• The sandwich estimator does not resolve Type I error inflation when independence fails or the outcome is binary.
• Generalized additive models effectively reduce bias and maintain correct Type I error rates for both quantitative and binary outcomes, irrespective of independence assumptions.
• Flexible main effect modeling does not lead to asymptotic power loss for interaction tests.

Conclusions:

• Main effect misspecification is a critical issue in interaction testing, potentially leading to false positives.
• Generalized additive models offer a robust solution for accurate interaction testing by flexibly modeling main effects.
• The sandwich variance estimator is conditionally effective, but generalized additive models provide broader applicability and reliability.