  Existing statistical methods for the analysis of micro-randomized trials
(MRTs) are designed to estimate causal excursion effects using data from a
single MRT. In practice, however, researchers can often find previous MRTs that
employ similar interventions. In this paper, we develop data integration
methods that capitalize on this additional information, leading to statistical
efficiency gains. To further increase efficiency, we demonstrate how to combine
these approaches according to a generalization of multivariate precision
weighting that allows for correlation between estimates, and we show that the
resulting meta-estimator possesses an asymptotic optimality property. We
illustrate our methods in simulation and in a case study involving two MRTs in
the area of smoking cessation.
