Using a centered general linear model for detection of interactions among biomarkers

Area of Science:

• Statistics
• Biostatistics
• Genomics

Background:

• General linear models (gLM) commonly model categorical factors but often exhibit correlations between main factors and their interactions, even with independent factors.
• Classical two-way factorial analysis of variance (ANOVA) avoids these correlations but has limitations in regular regression models with covariates due to parameter constraints.

Purpose of the Study:

• To propose a centered general linear model (cgLM) for modeling interactions between categorical factors using centered dummy variables.
• To demonstrate that cgLM can avoid factor-interaction correlations, similar to ANOVA, when factors are independent.
• To show cgLM's applicability in regular regression analysis and its ease of fitting using standard least squares.

Main Methods:

• Development of the centered general linear model (cgLM) utilizing centered dummy variables for categorical factors.
• Theoretical analysis to demonstrate the avoidance of correlation between main factors and interactions.
• Comparison with the standard general linear model (gLM) and analysis of variance (ANOVA) models.
• Simulation studies to evaluate the performance of cgLM in interaction detection.

Main Results:

• The proposed cgLM effectively avoids the correlation between main factors and their interactions when factors are independently distributed.
• cgLM integrates seamlessly into regular linear regression frameworks and can be fitted using standard least squares by selecting appropriate baselines, overcoming parameter constraints.
• Simulation studies indicate potential advantages of cgLM over gLM for detecting interactions in model-building procedures.

Conclusions:

• The centered general linear model (cgLM) provides a statistically sound and computationally convenient alternative to gLM for analyzing interactions involving categorical factors.
• cgLM's ability to avoid factor-interaction correlations and its compatibility with standard regression techniques make it a valuable tool for various statistical modeling applications.
• The application of cgLM to postmortem brain gene expression data highlights its practical utility in biological research.