Addressing a central challenge encountered in Mendelian randomization (MR) studies, where MR primarily focuses on discerning the effects of individual exposures on specific outcomes and establishes causal links between them. Using a network-based methodology, the intricacy involving interdependent outcomes due to numerous factors has been tackled through this routine. Based on Ni et al. (2018) <doi:10.1214/17-BA1087>, 'MR.RGM' extends to a broader exploration of the causal landscape by leveraging on network structures and involves the construction of causal graphs that capture interactions between response variables and consequently between responses and instrument variables. The resulting Graph visually represents these causal connections, showing directed edges with effect sizes labeled. 'MR.RGM' facilitates the navigation of various data availability scenarios effectively by accommodating three input formats, i.e., individual-level data and two types of summary-level data. In the process, causal effects, adjacency matrices, and other essential parameters of the complex biological networks, are estimated. Besides, 'MR.RGM' provides uncertainty quantification for specific network structures among response variables.

Implementations of an estimator for the multivariate regression association measure (MRAM) proposed in Shih and Chen (2025) <in revision> and its associated variable selection algorithm. The MRAM quantifies the predictability of a random vector Y from a random vector X given a random vector Z. It takes the maximum value 1 if and only if Y is almost surely a measurable function of X and Z, and the minimum value of 0 if Y is conditionally independent of X given Z. The MRAM generalizes the Kendall's tau copula correlation ratio proposed in Shih and Emura (2021) <doi:10.1016/j.jmva.2020.104708> by employing the spatial sign function. The estimator is based on the nearest neighbor method, and the associated variable selection algorithm is adapted from the feature ordering by conditional independence (FOCI) algorithm of Azadkia and Chatterjee (2021) <doi:10.1214/21-AOS2073>. For further details, see the paper Shih and Chen (2025) <in revision>.