Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization

Conventional estimation methods require complete knowledge about all the instruments’ validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments’ validity is equivalent to complete knowledge about the involved genes’ functions.

In this article, we propose a method for estimation of causal effects when this complete knowledge is absent. It is shown that causal effects are identified and can be estimated as long as less than 50% of instruments are invalid, without knowing which of the instruments are invalid. We also introduce conditions for identification when the 50% threshold is violated.