This paper proposes a modified Cochran's $Q$ statistic to detect horizontal pleiotropy in Mendelian randomization. This extension is quite important when there are many weak genetic instruments.
We provide a comprehensive theoretical basis for two-sample summary-data Mendelian randomization. We find that horizontal pleiotropy is pervasive in MR studies. We propose a new method---robust adjusted profile score---that can consistently estimate …
Many modern IV studies (especially Mendelian Randomization) are carried out with the two-sample design, where the samples may come from different populations. We derive a new class of linear IV estimates that are robust to sample heterogeneity. We …