Method adapted from the Anderson-Rubin (AR) test in econometrics for a two-sample MR context that tests for invalid instrumental variables (IVs), predominantly due to weak IVs, when estimating the causal effect of an exposure on an outcome.
This test is a modified version of the original test so that it can be applied within a two-sample MR setting with summary-level data. This test is similar to the Cochran's Q test for detecting the presence of potentially invalid IVs. Similar methods have been proposed (e.g., the "mrK" and "mrCLR" tests, derived from the Kleibergen (K) and conditional likelihood ratio (CLR) tests in econometrics) but, unlike mrAR, these suffer bias when the magnitude of direct effects of the IV on the outcome and the number of invalid IVs increase. Amongst many other methods, this method can be used as an exercise for screening for violations of MR assumptions before estimating the causal effect.