The penalized inverse-variance weighted (pIVW) estimator is a Mendelian randomization method for estimating the causal effect of an exposure variable on an outcome of interest based on summary-level GWAS data. The pIVW estimator accounts for weak instruments and balanced horizontal pleiotropy simultaneously.
Use the following command in R to install the package (The latest version v0.1.3 updated on April 26, 2024):
library(devtools)
install_github("siqixu/mr.pivw",ref="main")
mr_pivw(Bx, Bxse, By, Byse, lambda = 1, over.dispersion = TRUE, delta = 0, sel.pval = NULL, Boot.Fieller = NULL, n.boot = 1000, alpha = 0.05)
Bx
: A numeric vector of beta-coefficient values for genetic associations with the exposure variable.
Bxse
: The standard errors associated with the beta-coefficients Bx
.
By
: A numeric vector of beta-coefficient values for genetic associations with the outcome variable.
Byse
: The standard errors associated with the beta-coefficients By
.
lambda
: The penalty parameter in the pIVW estimator. It plays a role in the bias-variance trade-off of the estimator. It is recommended to choose lambda=1
to achieve the smallest bias and valid inference. By default, lambda=1
.
over.dispersion
: Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE.
delta
: The z-score threshold for IV selection. delta
should be greater than or equal to zero. By default, delta=0
(i.e., no IV selection will be conducted).
sel.pval
: A numeric vector containing the P-values of the SNP effects on the exposure, which will be used for the IV selection. sel.pval
should be provided when delta
is not zero.
Boot.Fieller
:
If Boot.Fieller=TRUE
, then the P-value and the confidence interval of the causal effect will be calculated based on the bootstrapping Fieller method. Otherwise, the P-value and the confidence interval of the causal effect will be calculated from the normal distribution. By default, Boot.Fieller=TRUE
when Condition
is smaller than 10 (see 'Details' in R Help Documentation), and Boot.Fieller=FALSE
otherwise.
n.boot
:
The number of bootstrap samples used in the bootstrapping Fieller method. It will be used only when Boot.Fieller=TRUE
. By default, n.boot=1000
. A larger value of n.boot
should be provided when a more precise P-value is needed.
alpha
:
The significance level used to calculate the confidence intervals. The default value is 0.05.
Over.dispersion
: TRUE
if the method has considered balanced horizontal pleiotropy, FALSE
otherwise.
Boot.Fieller
: TRUE
if the bootstrapping Fieller method is used to calculate the P-value and the confidence interval of the causal effect, FALSE
otherwise.
N.boot
: The number of bootstrap samples used in the bootstrapping Fieller method.
Lambda
: The penalty parameter in the pIVW estimator.
Delta
: The z-score threshold for IV selection.
Estimate
: The causal point estimate from the pIVW estimator.
StdError
: The standard error associated with Estimate
.
CILower
: The lower bound of the confidence interval for Estimate
.
CIUpper
: The upper bound of the confidence interval for Estimate
.
Pvalue
: P-value associated with Estimate
.
Tau2
: The variance of the balanced horizontal pleiotropy. Tau2
is calculated by using all IVs in the data before conducting the IV selection.
SNPs
: The number of SNPs after IV selection.
Condition
: The estimated effective sample size. It is recommended to be greater than 5 for the pIVW estimator to achieve reliable asymptotic properties.
library(mr.pivw) # load the mr.pivw package
mr_pivw(Bx = Bx_exp, Bxse = Bxse_exp, By = By_exp, Byse = Byse_exp) # analyze the example data with the pIVW method.
# results
Penalized inverse-variance weighted method
Account for over-dispersion: TRUE
CI and P-value: Normal approximation
Penalty parameter (lambda): 1
IV selection threshold (delta): 0
Number of variants: 1000
-----------------------------------------------------------
Method Estimate Std Error 95% CI p-value Condition
pIVW 0.560 0.291 -0.011, 1.131 0.0545 10.071
-----------------------------------------------------------
Xu S., Wang P., Fung W.K. and Liu Z. (2022). A Novel Penalized Inverse-Variance Weighted Estimator for Mendelian Randomization with Applications to COVID-19 Outcomes. Biometrics. doi:10.1111/biom.13732