Primary Submission Category: Instrumental Variables
Nonparametric Mendelian Randomisation for Characterising Nonlinear Exposure-Outcome Relationship with Discrete Instrumental Variables
Authors: Cunhao Liu, Stephen Burgess,
Presenting Author: Cunhao Liu*
Nonlinear Mendelian randomisation is an extension to standard MR to characterise the nonlinear exposure-outcome relationship using genetic variants as instrumental variables. The approach divides the population into strata with different average levels of the exposure, and estimates average causal effect in each stratum, known as the localised average causal effect (LACE). However, this method typically requires a strong constant genetic effect assumption, and is unable to capture complex nonlinearities, for example a threshold relationship. We propose a nonparametric extension to nonlinear MR with discrete instruments, which we call nonparametric MR, that does not rely on the constant genetic effect assumption and is able to flexibly characterise more complex nonlinear relationships. We argue that our nonparametric MR estimates converge to a different version of localised average causal effect, which we call quantile average causal effect (QACE), that approximates the derivative of the true exposure-outcome function. Our method works well when the instrument is weak and takes only two or three values, a situation which most of the existing nonparametric IV methods struggle to deal with. Our simulation study shows that nonparametric MR consistently outperforms nonlinear MR under various scenarios and is robust to very weak instruments. We also illustrate our method using a real data example from UK Biobank, showing a nonlinear causal relationship between BMI and pulse rate.