Doctoral candidate in Biostatistics, Clara Drew, will present:
“Instrument Selection to Maximize Power and Minimize Bias for Nonlinear Mendelian Randomization in Finite Samples”
PhD Adviser: Cavan Reilly
Abstract: Mendelian randomization (MR) can be a useful tool to understand causal pathways outside of a randomized controlled trial. Many of the preferred methods for MR make assumptions of linearity, large sample size and/or a single strong instrument. However, in practice many outcomes of interest are binary and one SNP may only weakly identify our model parameters leading to imprecise estimates. There are existing methods that can handle nonlinear data with multiple instruments to increase identification, such as the generalized method of moments (GMM), but these methods may have undesirable properties for finite samples and tend to become more biased when too many instruments are included. Thus, it is important to carefully select the best subset of instruments to decrease overall bias and mean squared error (MSE) in finite samples. In the first portion of this presentation, we examine how different estimation procedures perform with varying numbers of instruments selected using a restricted LASSO method. We find that the restricted LASSO with carefully specified parameters can be useful to select a subset of correlated SNPs to use as instruments to maximize power and minimize MSE while maintaining appropriate coverage probability. In the second portion of this presentation, we shift to a Bayesian context where we are able to simultaneously select instruments and estimate causal parameters using Markov Chain Monte Carlo (MCMC) methods. We explore how differing prior specifications can affect the usefulness of this method and how its performance compares to Bayesian GMM without instrument selection and our previous frequentist results.