Inference in generalized linear models with robustness to misspecified variances.

Area of Science:

• Statistics
• Bioinformatics
• Computational Biology

Background:

• Generalized linear models (GLMs) commonly assume a single dispersion parameter, which is often inaccurate in real-world data.
• This inaccuracy can lead to a significant loss of Type I error control in standard parametric methods.
• Overdispersion in count data, such as RNA sequencing data, presents a particular modeling challenge.

Purpose of the Study:

• To develop a robust statistical method for generalized linear models that is insensitive to variance misspecification.
• To provide a reliable alternative to standard parametric tests that are vulnerable to incorrect dispersion assumptions.
• To address the challenges of modeling overdispersion in high-throughput sequencing count data.

Main Methods:

• A semi-parametric group-invariance method based on the sign-flipping of score contributions was developed.
• The proposed method requires only the correct specification of the mean model, offering robustness against variance misspecification.
• Tests for both single and multiple regression coefficients were formulated.

Main Results:

• The developed test demonstrates asymptotic validity.
• The method exhibits excellent performance even in small sample sizes.
• Illustrative analysis using RNA sequencing count data highlights the method's utility in handling difficult-to-model overdispersion.

Conclusions:

• The proposed semi-parametric method provides a robust approach to hypothesis testing in generalized linear models, irrespective of variance model specification.
• This method offers improved Type I error control compared to standard methods when variance assumptions are violated.
• The R library `flipscores` implements this novel technique, making it accessible for applications in fields like bioinformatics.