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The increasing availability of high-dimensional, longitudinal measures ofgenetic expression can facilitate analysis of the biological mechanisms ofdisease and prediction of future trajectories, as required for precisionmedicine. Biological knowledge suggests that it may be best to describe complexdiseases at the level of underlying pathways, which may interact with oneanother. We propose a Bayesian approach that allows for characterising suchcorrelation among different pathways through Dependent Gaussian Processes (DGP)and mapping the observed high-dimensional gene expression trajectories intounobserved low-dimensional pathway expression trajectories via Bayesian SparseFactor Analysis. Compared to previous approaches that model each pathwayexpression trajectory independently, our model demonstrates better performancein recovering the shape of pathway expression trajectories, revealing therelationships between genes and pathways, and predicting gene expressions(closer point estimates and narrower predictive intervals), as demonstrated inthe simulation study and real data analysis. To fit the model, we propose aMonte Carlo Expectation Maximization (MCEM) scheme that can be implementedconveniently by combining a standard Markov Chain Monte Carlo sampler and an Rpackage GPFDA (Konzen and others, 2021), which returns the maximum likelihoodestimates of DGP parameters. The modular structure of MCEM makes itgeneralizable to other complex models involving the DGP model component. An Rpackage has been developed that implements the proposed approach.

Dynamic Factor Analysis with Dependent Gaussian Processes for High-Dimensional Gene Expression Trajectories