A Zero-Inflated Logistic Normal Multinomial Model for Extracting Microbial Compositions

Abstract

High throughput sequencing data collected to study the microbiome provide information in the form of relative abundances and should be treated as compositions. Although many approaches including scaling and rarefaction have been proposed for converting raw count data into microbial compositions, most of these methods simply return zero values for zero counts. However, zeros can distort downstream analyses, and they can also pose problems for composition-aware methods. This problem is exacerbated with microbiome abundance data because they are sparse with excessive zeros. In addition to data sparsity, microbial composition estimation depends on other data characteristics such as high dimensionality, over-dispersion, and complex co-occurrence relationships. To address these challenges, we introduce a zero-inflated probabilistic PCA (ZIPPCA) model that accounts for the compositional nature of microbiome data, and propose an empirical Bayes approach to estimate microbial compositions. An efficient iterative algorithm, called classification variational approximation, is developed for carrying out maximum likelihood estimation. Moreover, we study the consistency and asymptotic normality of variational approximation estimator from the perspective of profile M-estimation. Extensive simulations and an application to a dataset from the Human Microbiome Project are presented to compare the performance of the proposed method with that of the existing methods. The method is implemented in R and available at https://github.com/YanyZeng/ZIPPCAlnm. Supplementary materials for this article are available online.

Keywords:

• Compositional data
• Logistic normal distribution
• Multivariate count data
• Poisson-multinomial
• Zero-inflation

Supplementary Materials

It includes details on classification VA algorithm for ZIPPCA-LNM, details on proofs of theoretical properties, and supplementary figures and tables. (ZIPPCA-LNM.appendix.pdf)

Acknowledgments

We are grateful to the Editor, the Associate Editor, and two anonymous referees for their helpful comments.

Additional information

Funding

This research was supported in part by the National Natural Science Foundation of China (11971017), Shanghai Municipal Science and Technology Major Project (2017SHZDZX01), Multidisciplinary Cross Research Foundation of Shanghai Jiao Tong University (19X190020184, 19X190020194, 21X010301669), and Neil Shen’s SJTU Medical Research Fund of Shanghai Jiao Tong University.