# GSMUT: Generalized Multi-SNP Mediation Intersection-Union Test In SMUT: Multi-SNP Mediation Intersection-Union Test

## Description

Testing the mediation effect of multiple SNPs on an outcome following an exponential family distribution or a survival outcome through a continuous mediator.

## Usage

 ```1 2``` ```GSMUT(G,mediator,outcome,covariates=NULL,outcome_type, approxi=TRUE,verbose=FALSE) ```

## Arguments

 `G` n by p matrix (n rows and p columns). Each row is one individual; each column is one SNP. `mediator` a vector length of n. It is the mediator variable. `outcome` a vector length of n. It is the outcome variable. `covariates` n by r matrix (n rows and r columns). Each row is one individual; each column is one covariate. `outcome_type` Type of the outcome variable. "continuous" for a continuous outcome; "binary" for a binary outcome; "count" for a count outcome; "survival" for a survival outcome. `approxi` a boolean value. This is an indicator whether the approximation of computing derivatives is applied to save computing time. Default is TRUE. `verbose` a boolean value. If TRUE a lot of computing details is printed. Default is FALSE.

## Value

 `p_value_IUT` The p value for testing the mediation effect (theta*beta) based on intersection-union test. `p_value_theta` The p value for testing theta in the outcome model. The outcome model is the following. outcome ~ intercept + covariates*iota + G*gamma + mediator*theta `theta_hat` The point estimate of theta (coefficient of mediator) in the outcome model. `p_value_beta` The p value for testing beta in the mediator model. The mediator model is the following. mediator ~ intercept + covariates*iota + G*beta + error

Wujuan Zhong

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72``` ```library(SMUT) # load the Genotype data included in this R package data("Genotype_data") ##### for a binary outcome ##### set.seed(1) # generate two covariates covariate_1=rnorm(nrow(Genotype_data),0,1) covariate_2=sample(c(0,1),size=nrow(Genotype_data),replace = TRUE) covariates=cbind(covariate_1,covariate_2) # generate a mediator beta=rnorm(ncol(Genotype_data),0,0.5) tau_M=c(-0.3,0.2) e1 = rnorm(nrow(Genotype_data), 0, 1) mediator = 1 + eigenMapMatMult(Genotype_data,beta) + eigenMapMatMult(covariates, tau_M) + e1 #### generate a binary outcome #### theta=1 gamma=rnorm(ncol(Genotype_data),0,0.5) tau=c(-0.2,0.2) eta=1 + eigenMapMatMult(Genotype_data, gamma) + eigenMapMatMult(covariates, tau) + theta * mediator pi=1/(1+exp( -(eta ) )) outcome=rbinom(length(pi),size=1,prob=pi) result=GSMUT(G=Genotype_data,mediator=mediator,outcome=outcome, covariates=covariates,outcome_type="binary") print(result) # p_value_IUT is the p value for the mediation effect. ## Not run: ##### generate a count outcome ##### theta=1 gamma=rnorm(ncol(Genotype_data),0,0.5) tau=c(-0.2,0.2) eta=1 + eigenMapMatMult(Genotype_data, gamma) + eigenMapMatMult(covariates, tau) + theta * mediator mu_param=exp(eta) # the mean parameter phi_param=10 # the shape parameter outcome=rnbinom(length(mu_param),size=phi_param,mu=mu_param) result=GSMUT(G=Genotype_data,mediator=mediator,outcome=outcome, covariates=covariates,outcome_type="count") print(result) # p_value_IUT is the p value for the mediation effect. ##### generate a survival outcome ##### theta=2 gamma=rnorm(ncol(Genotype_data),0,0.5) tau=c(-0.2,0.2) eta=1 + eigenMapMatMult(Genotype_data, gamma) + eigenMapMatMult(covariates, tau) + theta * mediator v=runif(nrow(Genotype_data)) lambda=0.01; rho=1; rateC=0.001 Tlat=(- log(v) / (lambda * exp( eta )))^(1 / rho) # censoring times C= rexp(nrow(Genotype_data), rate=rateC) # follow-up times and event indicators time= pmin(Tlat, C) status= as.numeric(Tlat <= C) outcome=cbind(time,status) colnames(outcome)=c("time","status") result=GSMUT(G=Genotype_data,mediator=mediator,outcome=outcome, covariates=covariates,outcome_type="survival") print(result) # p_value_IUT is the p value for the mediation effect. ## End(Not run) ```

SMUT documentation built on Sept. 24, 2019, 9:05 a.m.