Joint modeling of zero‐inflated longitudinal proportions and time‐to‐event data with application to a gut microbiome study

Recent studies have suggested that the temporal dynamics of the human microbiome may have associations with human health and disease. An increasing number of longitudinal microbiome studies, which record time to disease onset, aim to identify candidate microbes as biomarkers for prognosis. Owing to the ultra‐skewness and sparsity of microbiome proportion (relative abundance) data, directly applying traditional statistical methods may result in substantial power loss or spurious inferences. We propose a novel joint modeling framework [JointMM], which is comprised of two sub‐models: a longitudinal sub‐model called zero‐inflated scaled‐beta generalized linear mixed‐effects regression to depict the temporal structure of microbial proportions among subjects; and a survival sub‐model to characterize the occurrence of an event and its relationship with the longitudinal microbiome proportions. JointMM is specifically designed to handle the zero‐inflated and highly skewed longitudinal microbial proportion data and examine whether the temporal pattern of microbial presence and/or the nonzero microbial proportions are associated with differences in the time to an event. The longitudinal sub‐model of JointMM also provides the capacity to investigate how the (time‐varying) covariates are related to the temporal microbial presence/absence patterns and/or the changing trend in nonzero proportions. Comprehensive simulations and real data analyses are used to assess the statistical efficiency and interpretability of JointMM.