mr.pivw {mr.pivw}

The penalized inverse-variance weighted estimator for Mendelian randomization

Description

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.

Usage

  mr.pivw(data,lambda=1,plei=TRUE,sel.pval=NULL,delta=0,Boot.Fieller=TRUE,sig=0.05)

Arguments

data

A matrix or data frame consists of four columns. The 1st and 2nd columns contain the SNP effects on the outcome and the exposure, respectively. The 3rd and 4th columns contain the standard errors of the SNP effects on the outcome and the exposure, respectively.

lambda

The penalty parameter in the pIVW estimator. The penalty parameter plays a role in the bias-variance trade-off of the estimator. It is recommended to choose lambda=1 to achieve smallest bias and valid inference. By default, lambda=1.

plei

If plei=TRUE, then the horizontal pleiotropy will be taken into account in the pIVW estimator. By default, plei=TRUE.

sel.pval

A 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.

delta

The z-score threshold for IV selection. By default, delta=0 (i.e., no IV selection will be conducted).

Boot.Fieller

If Boot.Fieller=TRUE, then the P value and the confidence interval of the causal effect based on the bootstrapping Fieller method will be calculated. By default, Boot.Fieller=TRUE.

sig

The 100(1-sig)% confidence interval of the causal effect is calculated. By default, sig=0.05.

Value

beta.hat

The estimated causal effect of the exposure on the outcome

beta.se

The estimated standard error of beta.hat

pval (Normal)

The P value for testing whether the causal effect is zero, which is based on the normal approximation.

CI (Normal)

The confidence interval of the causal effect based on the normal approximation.

pval (Bootstrap Fieller)

The P value for testing whether the causal effect is zero, which is based on the bootstrapping Fieller method.

CI (Bootstrap Fieller)

The confidence interval of the causal effect based on the bootstrapping Fieller method.

tau2

The variance of the horizontal pleiotropy. tau2 is calculated by using all IVs in the data before conducting the IV selection.

eta

The estimated effective sample size. It is recommended to be greater than 5 for pIVW to achieve reliable asymptotic properties.

References

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>

Examples

  mr.pivw(data=example)