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

Abstract

Background: Previous 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. Methods:We 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. Results:We 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. Conclusions:Across numerous causal simulation scenarios, we demonstrate that hJAM is unbiased, maintains correct type-I error and has increased power. Key Messages:• Mendelian 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 multivariateMendelian 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.(3) assuming there is no direct effect from the genetic variants to the outcome (i.e.The estimate of ߨ from Eq. 3 is equivalent to the result from the two-stage least square (2SLS) regression, which is employed by PrediXcan 15 and others 16 . The prior information ‫ܣ‬ መ is the association estimates between the genetic variants and the intermediate and can be applied to impute the intermediate with the genetic variants:Similar to above, we then fit a hierarchical model by incorporating the second-stage model (Eq.2) into Eq.5 and construct the hJAM model as

Statistical methods for cis‐Mendelian randomization with two‐sample summary‐level data

“…Outside of the context of cis -MR, JAM has been extended to handle violations of the no-pleiotropy assumption when working with multiple independent genetic variants, by augmenting its variable selection with a heterogeneity loss function to penalize and downweight pleiotropic variants ( Gkatzionis et al, 2021 ). Furthermore, a hierarchical version of the algorithm that is useful for multivariable MR, as well as transcriptome-wide association studies, was recently developed by Jiang et al (2020 ).…”

Statistical Methods for cis-Mendelian Randomization

“…Outside of the context of cis-MR, Gkatzionis et al (2020) extended JAM to handle violations of the no-pleiotropy assumption when working with multiple independent genetic variants, by augmenting its variable selection with a heterogeneity loss function to penalize and downweight pleiotropic variants. Furthermore, Jiang et al (2020) proposed a hierarchical version of the algorithm that is useful for multivariable MR, as well as transcriptome-wide association studies.…”