PTReg {GEInter}

Robust gene-environment interaction analysis using penalized trimmed regression

Description

Gene-environment interaction analysis using penalized trimmed regression, which is robust to outliers in both predictor and response spaces. The objective function is based on trimming technique, where the samples with extreme absolute residuals are trimmed. A decomposition framework is adopted for accommodating "main effects-interactions" hierarchy, and minimax concave penalty (MCP) is adopted for regularized estimation and interaction (and main genetic effect) selection.

Usage

PTReg(
  G,
  E,
  Y,
  lambda1,
  lambda2,
  gamma1 = 6,
  gamma2 = 6,
  max_init,
  h = NULL,
  tau = 0.4,
  mu = 2.5,
  family = c("continuous", "survival")
)

Arguments

G

Input matrix of p genetic (G) measurements consisting of n rows. Each row is an observation vector.

E

Input matrix of q environmental (E) risk factors. Each row is an observation vector.

Y

Response variable. A quantitative vector for family="continuous". For family="survival", Y should be a two-column matrix with the first column being the log(survival time) and the second column being the censoring indicator. The indicator is a binary variable, with "1" indicating dead, and "0" indicating right censored.

lambda1

A user supplied lambda for MCP accommodating main G effect selection.

lambda2

A user supplied lambda for MCP accommodating G-E interaction selecton.

gamma1

The regularization parameter of the MCP penalty corresponding to G effects.

gamma2

The regularization parameter of the MCP penalty corresponding to G-E interactions.

max_init

The number of initializations.

h

The number of the trimmed samples if the parameter mu is not given.

tau

The threshold value used in stability selection.

mu

The parameter for screening outliers with extreme absolute residuals if the number of the trimmed samples h is not given.

family

Response type of Y (see above).

Value

An object with S3 class "PTReg" is returned, which is a list with the following components.

call

The call that produced this object.

intercept

The intercept estimate.

alpha

The matrix of the coefficients for main E effects.

beta

The matrix of the regression coefficients for all main G effects (the first row) and interactions.

df

The number of nonzeros.

BIC

Bayesian Information Criterion.

select_sample

Selected samples where samples with extreme absolute residuals are trimmed.

family

The same as input family.

References

Yaqing Xu, Mengyun Wu, Shuangge Ma, and Syed Ejaz Ahmed. Robust gene-environment interaction analysis using penalized trimmed regression. Journal of Statistical Computation and Simulation, 88(18):3502-3528, 2018.

See Also

coef, predict, and plot methods, and bic.PTReg method.

Examples

sigmaG<-AR(rho=0.3,p=30)
sigmaE<-AR(rho=0.3,p=3)
set.seed(300)
G=MASS::mvrnorm(150,rep(0,30),sigmaG)
EC=MASS::mvrnorm(150,rep(0,2),sigmaE[1:2,1:2])
ED = matrix(rbinom((150),1,0.6),150,1)
E=cbind(EC,ED)
alpha=runif(3,0.8,1.5)
beta=matrix(0,4,30)
beta[1,1:4]=runif(4,1,1.5)
beta[2,c(1,2)]=runif(2,1,1.5)


#continuous response
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=c(rnorm(130),
rcauchy(20,0,5)),family="continuous")
fit1<-PTReg(G=G,E=E,y1,lambda1=0.3,lambda2=0.3,gamma1=6,gamma2=6,
max_init=50,h=NULL,tau=0.6,mu=2.5,family="continuous")
coef1=coef(fit1)
y_hat1=predict(fit1,E,G)
plot(fit1)

# survival response
y2=simulated_data(G,E,alpha,beta,rnorm(150,0,1),
family="survival",0.7,0.9)
fit2<-PTReg(G=G,E=E,y2,lambda1=0.3,lambda2=0.3,gamma1=6,gamma2=6,
max_init=50,h=NULL,tau=0.6,mu=2.5,family="survival")
coef2=coef(fit2)
y_hat2=predict(fit2,E,G)
plot(fit2)