scholarly journals Reciprocal causation mixture model for robust mendelian randomization analysis using genome-scale summary data

2021 ◽  
Author(s):  
Zipeng Liu ◽  
Yiming Qin ◽  
Tian Wu ◽  
Justin Tubbs ◽  
Larry Baum ◽  
...  
Keyword(s):  
Mixture Model ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Error Rates ◽  
Type I ◽  
Summary Statistics ◽  
Reciprocal Causation ◽  
Novel Strategy ◽  
Genome Scale ◽  
Summary Data

Abstract Mendelian randomization (MR) using GWAS summary statistics has become a popular method to infer causal relationships across complex diseases. However, the widespread pleiotropy observed in GWAS has made the selection of valid instrumental variables (IVs) problematic, leading to possible violations of MR assumptions and thus potentially invalid inferences concerning causation. Furthermore, current MR methods can examine causation in only one direction, so that two separate analyses are required for bi-directional analysis. In this study, we propose a novel strategy, MRCI (Mixture model Reciprocal Causation Inference), to estimate reciprocal causation between two phenotypes simultaneously using the genome-scale summary statistics of the two phenotypes and reference linkage disequilibrium (LD) information. Simulation studies, including strong correlated pleiotropy, showed that MRCI obtained nearly unbiased estimates of causation in both directions, and correct Type I error rates under the null hypothesis. In applications to real GWAS data, MRCI detected significant bi-directional and uni-directional causal influences between common diseases and putative risk factors.

scholarly journals Combining the strengths of inverse-variance weighting and Egger regression in Mendelian randomization using a mixture of regressions model

PLoS Genetics ◽  
2021 ◽  
Vol 17 (11) ◽  
pp. e1009922
Author(s):  
Zhaotong Lin ◽  
Yangqing Deng ◽  
Wei Pan
Keyword(s):  
Large Scale ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Meta Analysis ◽  
Type I ◽  
Perturbation Scheme ◽  
Analysis Model ◽  
Component Mixture ◽  
Inverse Variance ◽  
Summary Data

With the increasing availability of large-scale GWAS summary data on various traits, Mendelian randomization (MR) has become commonly used to infer causality between a pair of traits, an exposure and an outcome. It depends on using genetic variants, typically SNPs, as instrumental variables (IVs). The inverse-variance weighted (IVW) method (with a fixed-effect meta-analysis model) is most powerful when all IVs are valid; however, when horizontal pleiotropy is present, it may lead to biased inference. On the other hand, Egger regression is one of the most widely used methods robust to (uncorrelated) pleiotropy, but it suffers from loss of power. We propose a two-component mixture of regressions to combine and thus take advantage of both IVW and Egger regression; it is often both more efficient (i.e. higher powered) and more robust to pleiotropy (i.e. controlling type I error) than either IVW or Egger regression alone by accounting for both valid and invalid IVs respectively. We propose a model averaging approach and a novel data perturbation scheme to account for uncertainties in model/IV selection, leading to more robust statistical inference for finite samples. Through extensive simulations and applications to the GWAS summary data of 48 risk factor-disease pairs and 63 genetically uncorrelated trait pairs, we showcase that our proposed methods could often control type I error better while achieving much higher power than IVW and Egger regression (and sometimes than several other new/popular MR methods). We expect that our proposed methods will be a useful addition to the toolbox of Mendelian randomization for causal inference.

scholarly journals Mendelian Randomization Analysis Using Multiple Biomarkers of an Underlying Common Exposure

2021 ◽  
Author(s):  
Jin Jin ◽  
Guanghao Qi ◽  
Zhi Yu ◽  
Nilanjan Chatterjee
Keyword(s):  
Structural Equation ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Causal Effect ◽  
Association Studies ◽  
Error Rates ◽  
Type I ◽  
Genome Wide Association Studies ◽  
Increased Risk ◽  
Multiple Biomarkers

AbstractMendelian Randomization (MR) analysis is increasingly popular for testing the causal effect of exposures on disease outcomes using data from genome-wide association studies. In some settings, the underlying exposure, such as systematic inflammation, may not be directly observable, but measurements can be available on multiple biomarkers, or other types of traits, that are co-regulated by the exposure. We propose method MRLE, which tests the significance for, and the direction of, the effect of a latent exposure by leveraging information from multiple related traits. The method is developed by constructing a set of estimating functions based on the second-order moments of summary association statistics, under a structural equation model where genetic variants are assumed to have indirect effects through the latent exposure and potentially direct effects on the traits. Simulation studies showed that MRLE has well-controlled type I error rates and increased power compared to single-trait MR tests under various types of pleiotropy. Applications of MRLE using genetic association statistics across five inflammatory biomarkers (CRP, IL-6, IL-8, TNF-α and MCP-1) provided evidence for potential causal effects of inflammation on increased risk of coronary artery disease, colorectal cancer and rheumatoid arthritis, while standard MR analysis for individual biomarkers often failed to detect consistent evidence for such effects.

scholarly journals Weak-Instrument Robust Tests in Two-Sample Summary-Data Mendelian Randomization

2019 ◽  
Author(s):  
Sheng Wang ◽  
Hyunseung Kang
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Likelihood Ratio Tests ◽  
Type I ◽  
Conditional Likelihood ◽  
Test Statistics ◽  
Weak Instruments ◽  
Robust Tests ◽  
Summary Data

AbstractMendelian randomization (MR) is a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two-sample summary-data MR being the most popular due to privacy. Unfortunately, many MR methods for two-sample summary data are not robust to weak instruments, a common phenomena with genetic instruments; many of these methods are biased and no existing MR method has Type I error control under weak instruments. In this work, we propose test statistics that are robust to weak instruments by extending Anderson-Rubin, Kleibergen, and conditional likelihood ratio tests in econometrics to the two-sample summary data setting. We conclude with a simulation and an empirical study and show that the proposed tests control size and have better power than current methods.

scholarly journals Improving the accuracy of two-sample summary data Mendelian randomization: moving beyond the NOME assumption

2017 ◽  
Author(s):  
Jack Bowden ◽  
Fabiola Del Greco M ◽  
Cosetta Minelli ◽  
Qingyuan Zhao ◽  
Debbie A Lawlor ◽  
...  
Keyword(s):  
Genetic Variants ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Disease Risk ◽  
Causal Effect ◽  
Meta Analysis ◽  
Type I ◽  
Weak Instruments ◽  
Using Data ◽  
Summary Data

AbstractBackgroundTwo-sample summary data Mendelian randomization (MR) incorporating multiple genetic variants within a meta-analysis framework is a popular technique for assessing causality in epidemiology. If all genetic variants satisfy the instrumental variable (IV) and necessary modelling assumptions, then their individual ratio estimates of causal effect should be homogeneous. Observed heterogeneity signals that one or more of these assumptions could have been violated.MethodsCausal estimation and heterogeneity assessment in MR requires an approximation for the variance, or equivalently the inverse-variance weight, of each ratio estimate. We show that the most popular ‘1st order’ weights can lead to an inflation in the chances of detecting heterogeneity when in fact it is not present. Conversely, ostensibly more accurate ‘2nd order’ weights can dramatically increase the chances of failing to detect heterogeneity, when it is truly present. We derive modified weights to mitigate both of these adverse effects.ResultsUsing Monte Carlo simulations, we show that the modified weights outperform 1st and 2nd order weights in terms of heterogeneity quantification. Modified weights are also shown to remove the phenomenon of regression dilution bias in MR estimates obtained from weak instruments, unlike those obtained using 1st and 2nd order weights. However, with small numbers of weak instruments, this comes at the cost of a reduction in estimate precision and power to detect a causal effect compared to 1st order weighting. Moreover, 1st order weights always furnish unbiased estimates and preserve the type I error rate under the causal null. We illustrate the utility of the new method using data from a recent two-sample summary data MR analysis to assess the causal role of systolic blood pressure on coronary heart disease risk.ConclusionsWe propose the use of modified weights within two-sample summary data MR studies for accurately quantifying heterogeneity and detecting outliers in the presence of weak instruments. Modified weights also have an important role to play in terms of causal estimation (in tandem with 1st order weights) but further research is required to understand their strengths and weaknesses in specific settings.

scholarly journals A Hierarchical Approach Using Marginal Summary Statistics for Multiple Intermediates in a Mendelian Randomization or Transcriptome Analysis

2020 ◽  
Author(s):  
Lai Jiang ◽  
Shujing Xu ◽  
Nicholas Mancuso ◽  
Paul J. Newcombe ◽  
David V. Conti
Keyword(s):  
Hierarchical Model ◽  
Prior Information ◽  
Type I Error ◽  
Mendelian Randomization ◽  
Association Studies ◽  
Joint Analysis ◽  
Type I ◽  
List Type ◽  
Summary Statistics ◽  
Single Nucleotide

AbstractBackgroundPrevious research has demonstrated the usefulness of hierarchical modeling for incorporating a flexible array of prior information in genetic association studies. When this prior information consists of effect estimates from association analyses of single nucleotide polymorphisms (SNP)-intermediate or SNP-gene expression, a hierarchical model is equivalent to a two-stage instrumental or transcriptome-wide association study (TWAS) analysis, respectively.MethodsWe propose to extend our previous approach for the joint analysis of marginal summary statistics (JAM) to incorporate prior information via a hierarchical model (hJAM). In this framework, the use of appropriate effect estimates as prior information yields an analysis similar to Mendelian Randomization (MR) and TWAS approaches such as FUSION and S-PrediXcan. However, hJAM is applicable to multiple correlated SNPs and multiple correlated intermediates to yield conditional estimates of effect for the intermediate on the outcome, thus providing advantages over alternative approaches.ResultsWe investigate the performance of hJAM in comparison to existing MR approaches (inverse-variance weighted MR and multivariate MR) and existing TWAS approaches (S-PrediXcan) for effect estimation, type-I error and empirical power. We apply hJAM to two examples: estimating the conditional effects of body mass index and type 2 diabetes on myocardial infarction and estimating the effects of the expressions of gene NUCKS1 and PM20D1 on the risk of prostate cancer.ConclusionsAcross numerous causal simulation scenarios, we demonstrate that hJAM is unbiased, maintains correct type-I error and has increased power.Key MessagesMendelian randomization and transcriptome-wide association studies (TWAS) can be viewed as similar approaches via a hierarchical model.The hierarchal joint analysis of marginal summary statistics (hJAM) is a multivariate Mendelian randomization approach which offers a simple way to address the pleiotropy bias that is introduced by genetic variants associated with multiple risk factors or expressions of genes.hJAM incorporates the linkage disequilibrium structure of the single nucleotide polymorphism (SNPs) in a reference population to account for the correlation between SNPs.In addition to Mendelian randomization and TWAS, hJAM offers flexibility to incorporate functional or genomic annotation or information from metabolomic studies.

Correction: “Influence of Selection Bias on the Test Decision – A Simulation Study”

2014 ◽  
Vol 53 (05) ◽  
pp. 343-343
Keyword(s):  
Selection Bias ◽  
Simulation Study ◽  
Error Rate ◽  
Type I Error ◽  
Block Size ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rate ◽  
Representation Error ◽  
Numeric Representation

We have to report marginal changes in the empirical type I error rates for the cut-offs 2/3 and 4/7 of Table 4, Table 5 and Table 6 of the paper “Influence of Selection Bias on the Test Decision – A Simulation Study” by M. Tamm, E. Cramer, L. N. Kennes, N. Heussen (Methods Inf Med 2012; 51: 138 –143). In a small number of cases the kind of representation of numeric values in SAS has resulted in wrong categorization due to a numeric representation error of differences. We corrected the simulation by using the round function of SAS in the calculation process with the same seeds as before. For Table 4 the value for the cut-off 2/3 changes from 0.180323 to 0.153494. For Table 5 the value for the cut-off 4/7 changes from 0.144729 to 0.139626 and the value for the cut-off 2/3 changes from 0.114885 to 0.101773. For Table 6 the value for the cut-off 4/7 changes from 0.125528 to 0.122144 and the value for the cut-off 2/3 changes from 0.099488 to 0.090828. The sentence on p. 141 “E.g. for block size 4 and q = 2/3 the type I error rate is 18% (Table 4).” has to be replaced by “E.g. for block size 4 and q = 2/3 the type I error rate is 15.3% (Table 4).”. There were only minor changes smaller than 0.03. These changes do not affect the interpretation of the results or our recommendations.

The Use of Theory of Linear Mixed-Effects Models to Detect Fraudulent Erasures at an Aggregate Level

2021 ◽  
pp. 001316442199489
Author(s):  
Luyao Peng ◽  
Sandip Sinharay
Keyword(s):  
Type I Error ◽  
Real Data ◽  
Mixed Effects ◽  
Error Rates ◽  
Mixed Effects Models ◽  
Type I ◽  
Aggregate Level ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
Best Linear Unbiased

Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs for detecting fraudulent erasures at the aggregate or group level. This article follows up on the research of Wollack and Eckerly (2017) and Sinharay (2018) and suggests a new aggregate-level EDI by incorporating the empirical best linear unbiased predictor from the literature of linear mixed-effects models (e.g., McCulloch et al., 2008). A simulation study shows that the new EDI has larger power than the indices of Wollack and Eckerly (2017) and Sinharay (2018). In addition, the new index has satisfactory Type I error rates. A real data example is also included.

The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

2001 ◽  
Vol 26 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Douglas A. Powell ◽  
William D. Schafer
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Type I Error ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Error Rates ◽  
Type I ◽  
Chi Square ◽  
Distribution Free ◽  
Projection Techniques

The robustness literature for the structural equation model was synthesized following the method of Harwell which employs meta-analysis as developed by Hedges and Vevea. The study focused on the explanation of empirical Type I error rates for six principal classes of estimators: two that assume multivariate normality (maximum likelihood and generalized least squares), elliptical estimators, two distribution-free estimators (asymptotic and others), and latent projection. Generally, the chi-square tests for overall model fit were found to be sensitive to non-normality and the size of the model for all estimators (with the possible exception of the elliptical estimators with respect to model size and the latent projection techniques with respect to non-normality). The asymptotic distribution-free (ADF) and latent projection techniques were also found to be sensitive to sample sizes. Distribution-free methods other than ADF showed, in general, much less sensitivity to all factors considered.

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