Bayesian survival analysis for high-Dimensional compositional data

Survival analysis integrating microbiome and clinical data offers powerful insights into human health. Combining microbial profiles with clinical factors like tumor stage, treatment, and demographics enhances understanding of how host-microbe interactions affect survival. To analyze these complex datasets, advanced statistical methods, including Bayesian models, Cox proportional hazards models, and machine learning techniques are employed. These approaches can uncover novel biomarkers and therapeutic targets, leading to personalized treatment strategies that optimize patient outcome. However, challenges remain due to the compositionality, high-dimensionality, and phylogenetic relation between taxa in microbiome data. In this paper, we proposed a Bayesian compositional Cox proportional hazards model with a regularized horseshoe prior analyzing compositional microbiome and clinical data. We applied a soft sum-to-zero constraint to microbiome coefficients to deal with compositionality. Also, we introduced a structured shrinkage prior incorporating the similarity of microbiome taxa to address the phylogenetic structure. To evaluate the predictive performance of our model, we conducted an analysis on extensive simulations and a real dataset. The implementation was carried out using the R package brms, with results summarized based on two Markov Chain Monte Carlo (MCMC) algorithms executed in Stan.