  The availability of multi-omics data has revolutionized the life sciences by
creating avenues for integrated system-level approaches. Data integration links
the information across datasets to better understand the underlying biological
processes. However, high-dimensionality, correlations and heterogeneity pose
statistical and computational challenges. We propose a general framework,
probabilistic two-way partial least squares (PO2PLS), which addresses these
challenges. PO2PLS models the relationship between two datasets using joint and
data-specific latent variables. For maximum likelihood estimation of the
parameters, we implement a fast EM algorithm and show that the estimator is
asymptotically normally distributed. A global test for testing the relationship
between two datasets is proposed, and its asymptotic distribution is derived.
Notably, several existing omics integration methods are special cases of
PO2PLS. Via extensive simulations, we show that PO2PLS performs better than
alternatives in feature selection and prediction performance. In addition, the
asymptotic distribution appears to hold when the sample size is sufficiently
large. We illustrate PO2PLS with two examples from commonly used study designs:
a large population cohort and a small case-control study. Besides recovering
known relationships, PO2PLS also identified novel findings. The methods are
implemented in our R-package PO2PLS. Supplementary materials for this article
are available online.
