genius_mulY: MR GENIUS under multiplicative outcome model
In bluosun/MR-GENIUS: G-Estimation under No-Interaction with Unmeasured Selection

Description Usage Arguments Details Value References Examples

View source: R/MAIN.R

Implements MR GENIUS under a multiplicative outcome model.

1 2	genius_mulY(Y, A, G, formula = A ~ G, alpha = 0.05, lower = -10, upper = 10)

`Y`	A numeric vector of outcomes.
`A`	A numeric vector of exposures (binary values should be coded in 0/1).
`G`	A numeric matrix of instruments; each column stores values for one instrument (a numeric vector if only a single instrument is available).
`formula`	An object of class "formula" describing the linear predictor of the model for E(A\|G) (default A~G, main effects of all available instruments).
`alpha`	Significance level for confidence interval (default value=0.05).
`lower`	The lower end point of the causal effect interval to be searched (default value=-10).
`upper`	The upper end point of the causal effect interval to be searched (default value=10).

This function implements MR GENIUS as the solution to the empirical version of equation (14) in Tchetgen Tchetgen et al (2017). The term E(A|G) is modelled under the logit and identity links for binary and continuous exposure respectively, with a default linear predictor consisting of the main effects of all available instruments.

A "genius" object containing the following items:

`beta.est`	The point estimate of the causal effect (on the multiplicative scale) of the exposure on the outcome.
`beta.var`	The corresponding estimated variance.
`ci`	The corresponding Wald-type confidence interval at specified significance level.
`pval`	The p-value for two-sided Wald test of null causal effect (on the multiplicative scale) of the exposure on the outcome.

Tchetgen Tchetgen, E., Sun, B. and Walter, S. (2017). The GENIUS Approach to Robust Mendelian Randomization Inference. arXiv e-prints.

#the following packages are needed to simulate data
library("msm")
library("MASS")

### examples under multiplicative outcome model, all instruments invalid ###
# true causal effect, beta = 1.5
# Number of instruments, nIV = 10
# Y: vector of outcomes
# A: vector of exposures
# G: matrix of instruments, one column per instrument

### binary exposure
nIV=10; N=2000; beta=1.5;
phi=rep(-0.02,nIV); gamma=rep(-0.15,nIV); alpha=rep(-0.5,nIV);
Gn = mvrnorm(N,rep(0,nIV),diag(rep(1,nIV)))
G  = (Gn>0)*1;
U= as.vector(phi%*%t(G))+ rtnorm(n=N,mean=0.35,lower=0.2,upper=0.5);
A = rbinom(N,1,expit(as.vector(gamma%*%t(G)))+U-0.35-as.vector(phi%*%t(G)));
Y = exp(beta*A)*(as.vector(alpha%*%t(G)) + U) + rnorm(N);

genius_mulY(Y,A,G);

### specify a more richly parameterized linear predictor for the model of E[A|G] 
### containing all main effects and pairwise interactions of instruments                                                       

colnames(G)=paste("g",1:10,sep="")

genius_mulY(Y,A,G,A~(g1+g2+g3+g4+g5+g6+g7+g8+g9+g10)^2);

### continuous exposure
nIV=10; N=2000; beta=0.25; 
phi=rep(0.2,nIV); gamma=rep(0.5,nIV); alpha=rep(0.5,nIV);
lambda0=0.5; lambda1=rep(0.5,nIV);
Gn = mvrnorm(N,rep(0,nIV),diag(rep(1,nIV)))
G  = (Gn>0)*1;
U = as.vector(phi%*%t(G))+rnorm(N);
A = as.vector(gamma%*%t(G)) +U + rnorm(N,mean=0,sd=abs(lambda0+as.vector(lambda1%*%t(G))));
Y = exp(beta*A)*(as.vector(alpha%*%t(G)) + U) + rnorm(N);

genius_mulY(Y,A,G);