A joint mixture Tobit method with latent microbial abundance improves detection of microbiome–disease associations in zero-inflated data

Zero inflation remains a major challenge in microbiome differential abundance analysis, often resulting in inflated type I error rates or reduced statistical power. Although numerous methods have been proposed to address excess zeros, many existing approaches do not explicitly distinguish between distinct zero-generating mechanisms, and censoring-based modeling perspectives remain relatively underexplored in microbiome data analysis. To advance methodological development in this area, we introduce a novel censoring-based modeling perspective for microbiome differential abundance analysis. Specifically, we develop a joint mixture Tobit (joint mTobit) method for zero-inflated microbiome data. Building on a mixture Tobit formulation, the model incorporates a point-mass component to represent structural zeros, while modeling latent microbial abundance via a Tobit regression component. The proposed framework jointly links disease status, latent true microbial abundance, and relevant covariates within a unified probabilistic model, allowing appropriate adjustment for confounding factors and facilitating more reliable statistical inference. By explicitly modeling the latent abundance underlying observed counts, the joint mTobit method improves estimation stability and enhances detection power under zero inflation. Extensive simulation studies demonstrate that the joint mTobit method achieves effective type I error control while maintaining high statistical power and stable coefficient estimation across a wide range of settings. Application to a real-world colorectal cancer and adenoma microbiome dataset further illustrates its ability to identify biologically meaningful differentially abundant taxa. Overall, this work develops a joint mTobit modeling framework for zero-inflated microbiome data, enabling inference on latent microbial abundance and providing a censoring-based statistical framework for investigating disease–microbiome associations in differential abundance analysis.Author summary: Microbiome studies seek to understand how microbial communities are associated with human diseases, yet this goal is often hindered by the large number of zero measurements in sequencing data. These zeros arise for fundamentally different reasons: some microbes are truly absent from a sample, whereas others are present at low abundance but remain undetected due to limited sampling depth, a phenomenon that can be naturally viewed as censoring. Despite this, censoring-based approaches remain relatively underexplored in microbiome data analysis, and many existing methods do not explicitly distinguish between these distinct sources of zeros. In this study, we develop a joint mixture Tobit modeling method that explicitly separates these two sources of zeros and leverages this distinction to improve disease association inference. Rather than linking disease status directly to observed measurements, our approach introduces latent true microbial abundance as an intermediate representation that more closely reflects the underlying biological state. This enables microbiome–disease relationships to be inferred at the level of true abundance, while remaining consistent with the sparsity observed in sequencing data. Through simulation studies and application to colorectal cancer and adenoma microbiome data, we demonstrate that this modeling strategy leads to more stable and reliable identification of disease-associated microbial features. Our results highlight the importance of accounting for distinct zero-generating mechanisms and modeling latent microbial abundance when studying microbiome–disease associations.