ZINQ-L: a zero-inflated quantile approach for differential abundance analysis of longitudinal microbiome data.

Background: Identifying bacterial taxa associated with disease phenotypes or clinical treatments over time is critical for understanding the underlying biological mechanism. Association testing for microbiome data is already challenging due to its complex distribution that involves sparsity, over-dispersion, heavy tails, etc. The longitudinal nature of the data adds another layer of complexity - one needs to account for the within-subject correlations to avoid biased results. Existing longitudinal differential abundance approaches usually depend on strong parametric assumptions, such as zero-inflated normal or negative binomial. However, the complex microbiome data frequently violate these distributional assumptions, leading to inflated false discovery rates. In addition, the existing methods are mostly mean-based, unable to identify heterogeneous associations such as tail events or subgroup effects, which could be important biomedical signals. Methods: We propose a zero-inflated quantile approach for longitudinal (ZINQ-L) microbiome differential abundance test. A mixed-effects quantile rank-score-based test was proposed for hypothesis testing, which consists of a test in mixed-effects logistic model for the presence-absence status of the investigated taxon, and a series of mixed-effects quantile rank-score tests adjusted for zero inflation given its presence. As a regression method with minimal distributional assumptions, it is robust to the complex microbiome data, controlling false discovery rate, and is flexible to adjust for important covariates. Its comprehensive examination of the abundance distribution enables the identification of heterogeneous associations, improving the testing power. Results: Extensive simulation studies and an application to a real kidney transplant microbiome study demonstrate the improved power of ZINQ-L in detecting true signals while controlling false discovery rates. Conclusion: ZINQ-L is a zero-inflated quantile-based approach for detecting individual taxa associated with outcomes or exposures in longitudinal microbiome studies, providing a robust and powerful option to improve and complement the existing methods in the field.