CoDa-PhD thesis: Bayesian analysis of human microbiome compositional data. Modelling and prediction of the changes in its composition

CoDa-PhD Thesis in Statistics and Optimization

(UNIVERSITAT DE VALÈNCIA)

Bayesian analysis of human microbiome compositional data. Modelling and prediction of the changes in its composition

by
Irene Creus Martí

Supervised by
Andrés Moya Simarro,
and Francisco José Santonja Gómez
in the Faculty of Mathematics, Department of Statistics and Operations Research

Abstract

Gut microbiome is related with the health status of subjects and recent studies highlight the importance of studying longitudinal microbiome data to analyse microbiome dynamics. However, it is known that microbiome data are highdimensional and compositional which leads to strong statistical and computational challenges. In this thesis, we develop two models whose objective is to analyse microbiome time series in order to extract information about bacterial behaviour. These models are not focus on pair-wise interaction and take into account interactions between groups of bacterial taxa using balances (Egozcue and Pawlowsky-Glahn, 2005). Balances are a compositional tool useful to extract information about the relationship between the group of bacteria present at the numerator and the group of bacterial present at the denominator of the balance. Both models consider that the relative abundance of the bacterial taxa at time point t follow a Dirichlet distribution.

In the Frequency Balances Model (FBM) (Creus Martí et al., 2021), presented in Chapter 2, we model relative abundances of microbial taxa with a Dirichlet distribution with time-varying parameters. We assume that these relative abundances, after a log-ratio transformation, can be explained by an autoregressive structure which takes into account the effect of the bacterial community as a whole. This proposal can be useful to understand the relationships between microbes and the identification of keystone members of the microbial ecosystem that may play an important role.

The Bayesian Principal Balances Model (BPBM) (Creus Martí et al., 2022) is presented in Chapter 3. In this chapter, our proposal is based on modeling a normalized transformation of the observed counts. We assume that normalized transformation of the observed counts can be explained by an autoregressive structure considering Dirichlet distribution with time-varying parameters which takes into account principal balances.

Finally, we use these models to extract relevant biological information about the bacterial dynamics when there is antibiotic intake. We found that there is evidence of the evidence of the cooperative response of Blattella germanica gut microbiota to antibiotic treatment (Creus Martí et al., 2023).