  We propose a distributed quadratic inference function framework to jointly
estimate regression parameters from multiple potentially heterogeneous data
sources with correlated vector outcomes. The primary goal of this joint
integrative analysis is to estimate covariate effects on all outcomes through a
marginal regression model in a statistically and computationally efficient way.
We develop a data integration procedure for statistical estimation and
inference of regression parameters that is implemented in a fully distributed
and parallelized computational scheme. To overcome computational and modeling
challenges arising from the high-dimensional likelihood of the correlated
vector outcomes, we propose to analyze each data source using Qu, Lindsay and
Li (2000)'s quadratic inference functions, and then to jointly reestimate
parameters from each data source by accounting for correlation between data
sources using a combined meta-estimator in a similar spirit to Hansen (1982)'s
generalised method of moments. We show both theoretically and numerically that
the proposed method yields efficiency improvements and is computationally fast.
We illustrate the proposed methodology with the joint integrative analysis of
the association between smoking and metabolites in a large multi-cohort study
and provide an R package for ease of implementation.
