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

TL;DR

This paper introduces a new method called sisVIVE for estimating causal effects using instrumental variables when some instruments are invalid, particularly useful in Mendelian randomization where instrument validity is uncertain.

Contribution

The paper proposes a novel penalized L1 estimation method, sisVIVE, that identifies causal effects with less than 50% invalid instruments without knowing which are invalid.

Findings

Method performs well on simulated data.

Applied successfully to Mendelian randomization study.

Provides theoretical guarantees for estimation accuracy.

Abstract

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. 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 paper, 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. A fast penalized $\ell_1$ estimation method, called sisVIVE, is introduced for estimating the causal effect without knowing which instruments are valid, with theoretical guarantees on its performance. The proposed method is demonstrated on simulated data and a real Mendelian randomization study concerning the effect of body mass index on health-related quality of life index. An R package \emph{sisVIVE} is available online.