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Register a new userA 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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Anqi Wang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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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.
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Mendelian randomization (MR) is a powerful approach to examine the causal relationships between health risk factors and outcomes from observational studies. Due to the proliferation of genome-wide association studies (GWASs) and abundant fully accessible GWASs summary statistics, a variety of two-sample MR methods for summary data have been developed to either detect or account for horizontal pleiotropy, primarily based on the assumption that the effects of variants on exposure ({gamma}) and horizontal pleiotropy ({alpha}) are independent. This assumption is too strict and can be easily violated because of the correlated horizontal pleiotropy (CHP). To account for this CHP, we propose a Bayesian approach, MR-Corr2, that uses the orthogonal projection to reparameterize the bivariate normal distribution for {gamma} and {alpha}, and a spike-slab prior to mitigate the impact of CHP. We develop an efficient algorithm with paralleled Gibbs sampling. To demonstrate the advantages of MR-Corr2 over existing methods, we conducted comprehensive simulation studies to compare for both type-I error control and point estimates in various scenarios. By applying MR-Corr2 to study the relationships between pairs in two sets of complex traits, we did not identify the contradictory causal relationship between HDL-c and CAD. Moreover, the results provide a new perspective of the causal network among complex traits. The developed R package and code to reproduce all the results are available at https://github.com/QingCheng0218/MR.Corr2.
Mendelian randomization (MR) is a popular instrumental variable (IV) approach, in which one or several genetic markers serve as IVs that can sometimes be leveraged to recover valid inferences about a given exposure-outcome causal association subject to unmeasured confounding. A key IV identification condition known as the exclusion restriction states that the IV cannot have a direct effect on the outcome which is not mediated by the exposure in view. In MR studies, such an assumption requires an unrealistic level of prior knowledge about the mechanism by which genetic markers causally affect the outcome. As a result, possible violation of the exclusion restriction can seldom be ruled out in practice. To address this concern, we introduce a new class of IV estimators which are robust to violation of the exclusion restriction under data generating mechanisms commonly assumed in MR literature. The proposed approach named MR G-Estimation under No Interaction with Unmeasured Selection (MR GENIUS) improves on Robins G-estimation by making it robust to both additive unmeasured confounding and violation of the exclusion restriction assumption. In certain key settings, MR GENIUS reduces to the estimator of Lewbel (2012) which is widely used in econometrics but appears largely unappreciated in MR literature. More generally, MR GENIUS generalizes Lewbels estimator to several key practical MR settings, including multiplicative causal models for binary outcome, multiplicative and odds ratio exposure models, case control study design and censored survival outcomes.
Mendelian randomization (MR) has become a popular approach to study causal effects by using genetic variants as instrumental variables. We propose a new MR method, GENIUS-MAWII, which simultaneously addresses the two salient phenomena that adversely affect MR analyses: many weak instruments and widespread horizontal pleiotropy. Similar to MR GENIUS citep{Tchetgen2019_GENIUS}, we achieve identification of the treatment effect by leveraging heteroscedasticity of the exposure. We then derive the class of influence functions of the treatment effect, based on which, we construct a continuous updating estimator and establish its consistency and asymptotic normality under a many weak invalid instruments asymptotic regime by developing novel semiparametric theory. We also provide a measure of weak identification and graphical diagnostic tool. We demonstrate in simulations that GENIUS-MAWII has clear advantages in the presence of directional or correlated horizontal pleiotropy compared to other methods. We apply our method to study the effect of body mass index on systolic blood pressure using UK Biobank.
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.
Standard Mendelian randomization analysis can produce biased results if the genetic variant defining the instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment. We provide novel identification conditions for the causal effect of a treatment in presence of unmeasured confounding, by leveraging an invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian Randomization Mixed-Scale Treatment Effect Robust Identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the invalid IV on the additive scale; and (ii) that the selection bias due to confounding does not vary with the invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroscedastic and thus varies with the invalid IV. We formally establish that their conjunction can identify a causal effect even with an invalid IV subject to pleiotropy. MiSTERI is shown to be particularly advantageous in presence of pervasive heterogeneity of pleiotropic effects on additive scale, a setting in which two recently proposed robust estimation methods MR GxE and MR GENIUS can be severely biased. In order to incorporate multiple, possibly correlated and weak IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved accuracy MaWII MiSTERI is shown to be robust to horizontal pleiotropy, violation of IV independence assumption and weak IV bias. Both simulation studies and real data analysis results demonstrate the robustness of the proposed MR MiSTERI methods.
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