Generalized linear models with linear constraints for microbiome compositional data.

Area of Science:

• Microbiome research
• Statistical modeling
• Bioinformatics

Background:

• Microbiome compositional data presents unique analytical challenges.
• Standard regression methods may not adequately handle the constraints of compositional data.
• Understanding the relationship between gut microbiome and diseases like inflammatory bowel disease (IBD) is crucial.

Purpose of the Study:

• To develop a generalized linear regression framework for compositional covariates.
• To impose linear constraints on regression coefficients for subcompositional coherence.
• To enable accurate identification of bacterial species associated with IBD and prediction of IBD status.

Main Methods:

• Developed a penalized likelihood estimation procedure using a generalized accelerated proximal gradient method.
• Introduced a de-biased procedure for asymptotically unbiased and normally distributed estimates.
• Applied the methods to analyze fecal microbiome data for IBD prediction.

Main Results:

• Simulation results demonstrated correct coverage probabilities for confidence intervals.
• The proposed method yielded smaller variance estimates when appropriate linear constraints were applied.
• The methods were successfully illustrated on a real-world microbiome dataset.

Conclusions:

• The developed regression method effectively handles compositional microbiome data.
• The approach provides valid confidence intervals for regression coefficients, crucial for identifying disease-associated microbes.
• This methodology can advance our understanding of the gut microbiome's role in inflammatory bowel disease.