A Two-Sample Robust Bayesian Mendelian Randomization Method Accounting for Linkage Disequilibrium and Idiosyncratic Pleiotropy with Applications to the COVID-19 Outcome
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Mendelian randomization (MR) is a statistical method exploiting genetic variants as instrumental variables to estimate the causal effect of modifiable risk factors on an outcome of interest. Despite wide uses of various popular two-sample MR methods based on genome-wide association study summary level data, however, those methods could suffer from potential power loss or/and biased inference when the chosen genetic variants are in linkage disequilibrium (LD), and also have relatively large direct effects on the outcome whose distribution might be heavy-tailed which is commonly referred to as the idiosyncratic pleiotropy phenomenon. To resolve those two issues, we propose a novel Robust Bayesian Mendelian Randomization (RBMR) model that uses the more robust multivariate generalized t-distribution to model such direct effects in a probabilistic model framework which can also incorporate the LD structure explicitly. The generalized t-distribution can be represented as a Gaussian scaled mixture so that our model parameters can be estimated by the EM-type algorithms. We compute the standard errors by calibrating the evidence lower bound using the likelihood ratio test. Through extensive simulation studies, we show that our RBMR has robust performance compared to other competing methods. We also apply our RBMR method to two benchmark data sets and find that RBMR has smaller bias and standard errors. Using our proposed RBMR method, we find that coronary artery disease is associated with increased risk of critically ill coronavirus disease 2019 (COVID-19). We also develop a user-friendly R package RBMR for public use.
基于贝叶斯加性回归树的灵活工具变量模型
Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and public health. However, such methods usually make constricting linearity and additivity assumptions that are inapplicable to the complex modeling challenges of today. The growing body of observational data being collected will necessitate…
多工具变量线性 IV 回归的贝叶斯因子模型收缩
A Bayesian approach for the many instruments problem in linear instrumental variable models is presented. The new approach has two components. First, a slice sampler is developed, which leverages a decomposition of the likelihood function that is a Bayesian analogue to two-stage least squares. The new sampler permits nonconjugate shrinkage priors to be implemented easily and efficiently. The new computational approach permits a Bayesian analysis of problems that were…
BGM-IV:面向高维协变量工具变量回归的贝叶斯生成建模
Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing methods typically operate in observed or generic learned feature spaces, and they often yield point estimates without uncertainty quantification. We introduce BGM-IV, a Bayesian generative modeling approach that performs nonlinear IV regression through posterior inference in a causally…
连接局部与总体因果效应:近端工具变量方法
Instrumental variable (IV) methods address treatment endogeneity, but with non-compliance and heterogeneous treatment effects a binary instrument generally identifies the local average treatment effect (LATE) among compliers rather than the population average treatment effect (ATE). When treatment effects and compliance probabilities are heterogeneous and dependent through latent factors, the ATE need not be identified by IV variation alone. We develop a proximal…
修正局部错设的 GMM:经验贝叶斯方法
Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification errors, establishing their consistency in an asymptotic framework where the number of overidentifying restrictions grows with the sample size. These…
利用鞅后验推断反事实分布
Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and…