  The increasing availability of high-dimensional, longitudinal measures of
gene expression can facilitate understanding of biological mechanisms, as
required for precision medicine. Biological knowledge suggests that it may be
best to describe complex diseases at the level of underlying pathways, which
may interact with one another. We propose a Bayesian approach that allows for
characterising such correlation among different pathways through Dependent
Gaussian Processes (DGP) and mapping the observed high-dimensional gene
expression trajectories into unobserved low-dimensional pathway expression
trajectories via Bayesian Sparse Factor Analysis. Our proposal is the first
attempt to relax the classical assumption of independent factors for
longitudinal data and has demonstrated a superior performance in recovering the
shape of pathway expression trajectories, revealing the relationships between
genes and pathways, and predicting gene expressions (closer point estimates and
narrower predictive intervals), as demonstrated through simulations and real
data analysis. To fit the model, we propose a Monte Carlo Expectation
Maximization (MCEM) scheme that can be implemented conveniently by combining a
standard Markov Chain Monte Carlo sampler and an R package GPFDA (Konzen and
others, 2021), which returns the maximum likelihood estimates of DGP
hyperparameters. The modular structure of MCEM makes it generalizable to other
complex models involving the DGP model component. Our R package DGP4LCF that
implements the proposed approach is available on CRAN.
