The covariance matrix with an autoregressive (AR) structure among variables

Description

The covariance matrix with an AR structure among variables, where the marginal variances are 1 and the jth and kth variables have correlation coefficient rho^abs(j-k).

Usage

AR(rho, p)

Arguments

Value

A covariance matrix.

Accommodating missingness in environmental measurements in gene-environment interaction analysis

Description

We consider the scenario with missingness in environmental (E) measurements. Our approach consists of two steps. We first develop a nonparametric kernel-based data augmentation approach to accommodate missingness. Then, we adopt a penalization approach BLMCP for regularized estimation and selection of important interactions and main genetic (G) effects, where the "main effects-interactions" hierarchical structure is respected. As E variables are usually preselected and have a low dimension, selection is not conducted on E variables. With a well-designed weighting scheme, a nice "byproduct" is that the proposed approach enjoys a certain robustness property.

Usage

Augmented.data(G, E, Y, h, family = c("continuous", "survival"), E_type)

Arguments

Value

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

Examples

set.seed(100)
sigmaG=AR(0.3,50)
G=MASS::mvrnorm(100,rep(0,50),sigmaG)
E=matrix(rnorm(100*5),100,5)
E[,2]=E[,2]>0
E[,3]=E[,3]>0
alpha=runif(5,2,3)
beta=matrix(0,5+1,50)
beta[1,1:7]=runif(7,2,3)
beta[2:4,1]=runif(3,2,3)
beta[2:3,2]=runif(2,2,3)
beta[5,3]=runif(1,2,3)

# continuous with Normal error N(0,4)
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=rnorm(100,0,4),family="continuous")

# survival with Normal error N(0,1)
y2=simulated_data(G,E,alpha,beta,rnorm(100,0,1),family="survival",0.7,0.9)

# generate E measurements with missingness
miss_label1=c(2,6,8,15)
miss_label2=c(4,6,8,16)
E1=E2=E;E1[miss_label1,1]=NA;E2[miss_label2,1]=NA

# continuous
data_new1<-Augmented.data(G,E1,y1,h=c(0.5,1), family="continuous",
E_type=c("EC","ED","ED","EC","EC"))
fit1<-BLMCP(data_new1$G_w, data_new1$E_w, data_new1$y_w, data_new1$weight,
lambda1=0.025,lambda2=0.06,gamma1=3,gamma2=3,max_iter=200)
coef1=coef(fit1)
y1_hat=predict(fit1,E[c(1,2),],G[c(1,2),])
plot(fit1)

## survival
data_new2<-Augmented.data(G,E2,y2, h=c(0.5,1), family="survival",
E_type=c("EC","ED","ED","EC","EC"))
fit2<-BLMCP(data_new2$G_w, data_new2$E_w, data_new2$y_w, data_new2$weight,
lambda1=0.04,lambda2=0.05,gamma1=3,gamma2=3,max_iter=200)
coef2=coef(fit2)
y2_hat=predict(fit2,E[c(1,2),],G[c(1,2),])
plot(fit2)

Accommodating missingness in environmental measurements in gene-environment interaction analysis: penalized estimation and selection

Description

The joint gene-environment (G-E) interaction analysis approach developed in Liu et al, 2013. To accommodate "main effects, interactions" hierarchy, two types of penalty, group minimax concave penalty (MCP) and MCP are adopted. Specifically, for each G factor, its main effect and corresponding G-E interactions are regarded as a group, where the group MCP is imposed to identify whether this G factor has any effect at all. In addition, the MCP is imposed on the interaction terms to further identify important interactions.

Usage

BLMCP(
  G,
  E,
  Y,
  weight = NULL,
  lambda1,
  lambda2,
  gamma1 = 6,
  gamma2 = 6,
  max_iter = 200
)

Arguments

Value

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

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

predict, and coef, and plot, and bic.BLMCP and Augmentated.data methods.

Examples

set.seed(100)
sigmaG=AR(0.3,100)
G=MASS::mvrnorm(250,rep(0,100),sigmaG)
E=matrix(rnorm(250*5),250,5)
E[,2]=E[,2]>0;E[,3]=E[,3]>0
alpha=runif(5,2,3)
beta=matrix(0,5+1,100);beta[1,1:8]=runif(8,2,3)
beta[2:4,1]=runif(3,2,3);beta[2:3,2]=runif(2,2,3);beta[5,3]=runif(1,2,3)

# continuous with Normal error
y1=simulated_data(G,E,alpha,beta,error=rnorm(250),family="continuous")
fit1<-BLMCP(G,E,y1,weight=NULL,lambda1=0.05,lambda2=0.06,gamma1=3,gamma2=3,max_iter=200)
coef1=coef(fit1)
y1_hat=predict(fit1,E,G)
plot(fit1)

# survival with Normal error
y2=simulated_data(G,E,alpha,beta,rnorm(250,0,1),family="survival",0.7,0.9)
fit2<-BLMCP(G,E,y2,weight=NULL,lambda1=0.05,lambda2=0.06,gamma1=3,gamma2=3,max_iter=200)
coef2=coef(fit2)
y2_hat=predict(fit2,E,G)
plot(fit2)

A data frame containing the TCGA head and neck squamous cell carcinoma (HNSCC) data.

Description

A data frame containing the 7 environmental (E) effects (the first 7 columns), 2000 genetic (G) effects (column 8 to column 2007), logarithm of survival time (column 2008), and censoring indicator (column 2009). All of them can be downloaded from TCGA Provisional using the R package cgdsr. See details.

Usage

data(HNSCC)

Format

A data frame with 484 rows and 2009 variables.

Details

There are seven E effects, namely alcohol consumption frequency (ACF), smoking pack years (SPY), age, gender, PN, PT, and ICD O3 site. For G effects, 2,000 gene expressions are considered. Among 484 subjects, 343 subjects have missingness in ACF and/or SPY. For G effects, we analyze mRNA gene expressions. A total of 18,409 gene expression measurements are available, then prescreening is conducted using marginal Cox models, finally, the top 2,000 genes with the smallest p-values are selected for downstream analysis.

Examples

data(HNSCC)
E=as.matrix(HNSCC[,1:7])
G=as.matrix(HNSCC[,8:2007])
Y=as.matrix(HNSCC[,2008:2009])

fit<-Miss.boosting(G,E,Y,im_time=10,loop_time=1000,v=0.25,num.knots=5,degree=3,tau=0.3,
family="survival",E_type=c(rep("EC",3),rep("ED",4)))
plot(fit)

Robust gene-environment interaction analysis approach via sparse boosting, where the missingness in environmental measurements is effectively accommodated using multiple imputation approach

Description

This gene-environment analysis approach includes three steps to accommodate both missingness in environmental (E) measurements and long-tailed or contaminated outcomes. At the first step, the multiple imputation approach based on sparse boosting method is developed to accommodate missingness in E measurements, where we use NA to represent those E measurments which are missing. Here a semiparametric model is assumed to accommodate nonlinear effects, where we model continuous E factors in a nonlinear way, and discrete E factors in a linear way. For estimating the nonlinear functions, the B spline expansion is adopted. At the second step, for each imputed data, we develop RobSBoosting approach for identifying important main E and genetic (G) effects, and G-E interactions, where the Huber loss function and Qn estimator are adopted to accommodate long-tailed distribution/data contamination (see RobSBoosting). At the third step, the identification results from Step 2 are combined based on stability selection technique.

Usage

Miss.boosting(
  G,
  E,
  Y,
  im_time = 10,
  loop_time = 500,
  num.knots = c(2),
  Boundary.knots,
  degree = c(2),
  v = 0.1,
  tau,
  family = c("continuous", "survival"),
  knots = NULL,
  E_type
)

Arguments

Value

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

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

Examples

data(Rob_data)
G=Rob_data[,1:20];E=Rob_data[,21:24]
Y=Rob_data[,25];Y_s=Rob_data[,26:27]
knots=list();Boundary.knots=matrix(0,(20+4),2)
for (i in 1:4){
  knots[[i]]=c(0,1)
  Boundary.knots[i,]=c(0,1)
}
E2=E1=E

##continuous
E1[7,1]=NA
fit1<-Miss.boosting(G,E1,Y,im_time=1,loop_time=100,num.knots=c(2),Boundary.knots,
degree=c(2),v=0.1,tau=0.3,family="continuous",knots=knots,E_type=c("EC","EC","ED","ED"))
y1_hat=predict(fit1,matrix(E1[1,],nrow=1),matrix(G[1,],nrow=1))
plot(fit1)


##survival
E2[4,1]=NA
fit2<-Miss.boosting(G,E2,Y_s,im_time=2,loop_time=200,num.knots=c(2),Boundary.knots,
degree=c(2),v=0.1,tau=0.3,family="survival",knots,E_type=c("EC","EC","ED","ED"))
y2_hat=predict(fit2,matrix(E1[1,],nrow=1),matrix(G[1,],nrow=1))
plot(fit2)

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

Value

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

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)

Robust identification of gene-environment interactions using a quantile partial correlation approach

Description

A robust gene-environment interaction identification approach using the quantile partial correlation technique. This approach is a marginal analysis approach built on the quantile regression technique, which can accommodate long-tailed or contaminated outcomes. For response with right censoring, Kaplan-Meier (KM) estimator-based weights are adopted to easily accommodate censoring. In addition, it adopts partial correlation to identify important interactions while properly controlling for the main genetic (G) and environmental (E) effects.

Usage

QPCorr.matrix(G, E, Y, tau, w = NULL, family = c("continuous", "survival"))

Arguments

Value

Matrix of (censored) quantile partial correlations for interactions.

References

Yaqing Xu, Mengyun Wu, Qingzhao Zhang, and Shuangge Ma. Robust identification of gene-environment interactions for prognosis using a quantile partial correlation approach. Genomics, 111(5):1115-1123, 2019.

See Also

QPCorr.pval method.

Examples

alpha=matrix(0,5,1)
alpha[1:2]=1
beta=matrix(0,6,100)
beta[1,1:5]=1
beta[2:3,1:5]=2
beta[4:6,6:7]=2
sigmaG<-AR(rho=0.3,100)
sigmaE<-AR(rho=0.3,5)
G<-MASS::mvrnorm(200,rep(0,100),sigmaG)
E<-MASS::mvrnorm(200,rep(0,5),sigmaE)
e1<-rnorm(200*.05,50,1);e2<-rnorm(200*.05,-50,1);e3<-rnorm(200*.9)
e<-c(e1,e2,e3)

# continuous
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=e,family="continuous")
cpqcorr_stat1<-QPCorr.matrix(G,E,y1,tau=0.5,w=NULL,family="continuous")

# survival
y2=simulated_data(G,E,alpha,beta,rnorm(200,0,1),family="survival",0.7,0.9)
cpqcorr_stat<-QPCorr.matrix(G,E,y2,tau=0.5,w=NULL,family="survival")

P-values of the "QPCorr.matrix" obtained using a permutation approach

Description

P-values of the "QPCorr.matrix " obtained using a permutation approach, the interactions with smaller p-values are regarded as more important.

Usage

QPCorr.pval(
  G,
  E,
  Y,
  tau,
  w = NULL,
  permutation_t = 1000,
  family = c("continuous", "survival")
)

Arguments

Value

Matrix of p-value, with the element in the ith row and the j column represents the p-value of the (censored) quantile partial correlation corresponding to the ith E and the jth G.

References

Yaqing Xu, Mengyun Wu, Qingzhao Zhang, and Shuangge Ma. Robust identification of gene-environment interactions for prognosis using a quantile partial correlation approach. Genomics, 111(5):1115-1123, 2019.

See Also

QPCorr.matrix method.

Examples

n=50
alpha=matrix(0,5,1)
alpha[1:2]=1
beta=matrix(0,6,20)
beta[1,1:4]=1
beta[2:3,1:4]=2
sigmaG<-AR(rho=0.3,20)
sigmaE<-AR(rho=0.3,5)
G<-MASS::mvrnorm(n,rep(0,20),sigmaG)
E<-MASS::mvrnorm(n,rep(0,5),sigmaE)
e1<-rnorm(n*.05,50,1);e2<-rnorm(n*.05,-50,1);e3<-rnorm((n-length(e1)-length(e2)))
e<-c(e1,e2,e3)


# continuous
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=e,family="continuous")
cpqcorr_pvalue1<-QPCorr.pval(G,E,y1,tau=0.5,permutation_t=500,family="continuous")

# survival
y2=simulated_data(G,E,alpha,beta,rnorm(n,0,1),family="survival",0.7,0.9)
cpqcorr_pvalue2<-QPCorr.pval(G,E,y2,tau=0.5,permutation_t=500,family="survival")

Robust semiparametric gene-environment interaction analysis using sparse boosting

Description

Robust semiparametric gene-environment interaction analysis using sparse boosting. Here a semiparametric model is assumed to accommodate nonlinear effects, where we model continuous environmental (E) factors in a nonlinear way, and discrete E factors and all genetic (G) factors in a linear way. For estimating the nonlinear functions, the B spline expansion is adopted. The Huber loss function and Qn estimator are adopted to accommodate long-tailed distribution/data contamination. For model estimation and selection of relevant variables, we adopt an effective sparse boosting approach, where the strong hierarchy is respected.

Usage

RobSBoosting(
  G,
  E,
  Y,
  loop_time,
  num.knots = NULL,
  Boundary.knots = NULL,
  degree = 1,
  v = 0.1,
  family = c("continuous", "survival"),
  knots = NULL,
  E_type
)

Arguments

Value

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

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

bs method for B spline expansion, coef, predict, and plot methods, and Miss.boosting method.

Examples

data(Rob_data)
G=Rob_data[,1:20];E=Rob_data[,21:24]
Y=Rob_data[,25];Y_s=Rob_data[,26:27]
knots = list();Boundary.knots = matrix(0, 24, 2)
for(i in 1:4) {
  knots[[i]] = c(0, 1)
  Boundary.knots[i, ] = c(0, 1)
  }

#continuous
fit1= RobSBoosting(G,E,Y,loop_time = 80,num.knots = 2,Boundary.knots=Boundary.knots,
degree = 2,family = "continuous",knots = knots,E_type=c("EC","EC","ED","ED"))
coef1 = coef(fit1)
predict1=predict(fit1,newE=E[1:2,],newG=G[1:2,])
plot(fit1)


#survival
fit2= RobSBoosting(G,E,Y_s,loop_time = 200, num.knots = 2, Boundary.knots=Boundary.knots,
family = "survival", knots = knots,E_type=c("EC","EC","ED","ED"))
coef2 = coef(fit2)
predict2=predict(fit2,newE=E[1:2,],newG=G[1:2,])
plot(fit2)

A matrix containing the simulated data for RobSBoosting and Miss.boosting methods

Description

A matrix containing the simulated genetic (G) effects (the first 20 columns), environmental (E) effects (column 21 to column 24), continuous response (column 25), logarithm of survival time (column 26), and censoring indicator (column 27).

Usage

data(Rob_data)

Format

A matrix with 100 rows and 27 variables.

Examples

data(Rob_data)

BIC for BLMCP

Description

Selects a point along the regularization path of a fitted BLMCP object according to the BIC.

Usage

bic.BLMCP(
  G,
  E,
  Y,
  weight = NULL,
  lambda1_set = NULL,
  lambda2_set = NULL,
  nlambda1 = 20,
  nlambda2 = 20,
  gamma1 = 6,
  gamma2 = 6,
  max_iter = 200
)

Arguments

Value

An object with S3 class "bic.BLMCP" is returned, which is a list with the ingredients of the BIC fit.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

predict, coef and plot methods, and the BLMCP function.

Examples

set.seed(100)
sigmaG=AR(0.3,50)
G=MASS::mvrnorm(150,rep(0,50),sigmaG)
E=matrix(rnorm(150*5),150,5)
E[,2]=E[,2]>0;E[,3]=E[,3]>0
alpha=runif(5,2,3)
beta=matrix(0,5+1,50);beta[1,1:8]=runif(8,2,3)
beta[2:4,1]=runif(3,2,3)
beta[2:3,2]=runif(2,2,3)
beta[5,3]=runif(1,2,3)

# continuous with Normal error
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=rnorm(150),family="continuous")

# survival with Normal error
y2=simulated_data(G,E,alpha,beta,rnorm(150,0,1),family="survival",0.8,1)

# continuous
fit1<-bic.BLMCP(G,E,y1,weight=NULL,lambda1_set=NULL,lambda2_set=NULL,
nlambda1=10,nlambda2=10,gamma1=6,gamma2=6,max_iter=200)
coef1=coef(fit1)
y1_hat=predict(fit1,E,G)
plot(fit1)


## survival
fit2<-bic.BLMCP(G,E,y2,weight=NULL,lambda1_set=NULL,lambda2_set=NULL,
nlambda1=20,nlambda2=20,gamma1=6,gamma2=6,max_iter=200)
coef2=coef(fit2)
y2_hat=predict(fit2,E,G)
plot(fit2)

BIC for PTReg

Description

Selects a point along the regularization path of a fitted PTReg object according to the BIC.

Usage

bic.PTReg(
  G,
  E,
  Y,
  lambda1_set,
  lambda2_set,
  gamma1,
  gamma2,
  max_init,
  h = NULL,
  tau = 0.4,
  mu = 2.5,
  family = c("continuous", "survival")
)

Arguments

Value

An object with S3 class "bic.PTReg" is returned, which is a list with the ingredients of the BIC fit.

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.

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)
lambda1_set=lambda2_set=c(0.2,0.25,0.3,0.35,0.4,0.5)


#continuous response with outliers/contaminations in response variable
y1=simulated_data(G,E,alpha,beta,error=c(rnorm(140),rcauchy(10,0,5)),family="continuous")
fit1<-bic.PTReg(G,E,y1,lambda1_set,lambda2_set,gamma1=6,gamma2=6,
max_init=50,tau=0.6,mu=2.5,family="continuous")
coefficients1=coefficients(fit1)
y_predict=predict(fit1,E,G)
plot(fit1)

# survival with Normal error
y2=simulated_data(G,E,alpha,beta,rnorm(150,0,1),family="survival",0.7,0.9)
fit2<-bic.PTReg(G,E,y2,lambda1_set,lambda2_set,gamma1=6,gamma2=6,
max_init=50,tau=0.6,mu=2.5,family="survival")
coefficients2=coefficients(fit2)
y_predict=predict(fit2,E,G)
plot(fit2)

Extract coefficients from a "BLMCP" object

Description

This function extracts the coefficients of main effects and interactions from a BLMCP model, using the stored "BLMCP" object.

Usage

## S3 method for class 'BLMCP'
coef(object, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the coef method for BLMCP objects.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

BLMCP, and predict, plot methods, and bic.BLMCP.

Extract coefficients from a "PTReg" object

Description

This function extracts main effect and interaction coefficients from a PTReg model, using the stored "PTReg" object.

Usage

## S3 method for class 'PTReg'
coef(object, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the coef method for PTReg objects.

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

PTReg, and predict methods, and bic.PTReg.

Extract coefficients from a "RobSBoosting" object

Description

This function extracts coefficients from a RobSBoosting model, using the stored "RobSBoosting" object.

Usage

## S3 method for class 'RobSBoosting'
coef(object, ...)

Arguments

Value

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

RobSBoosting, and predict, and plot methods.

Extract coefficients from a "bic.BLMCP" object

Description

This function extracts the coefficients of main effects and interactions from a BIC BLMCP model, using the stored "bic.BLMCP" object.

Usage

## S3 method for class 'bic.BLMCP'
coef(object, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the coef method for bic.BLMCP objects.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

bic.BLMCP, and predict, and plot methods, and the BLMCP function.

Extract coefficients from a "bic.PTReg" object

Description

This function extracts the coefficients of main effects and interactions from a BIC PTReg model, using the stored "bic.PTReg" object.

Usage

## S3 method for class 'bic.PTReg'
coef(object, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the coef method for bic.PTReg objects.

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

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

Plot coefficients from a "BLMCP" object

Description

Draw a heatmap for estimated coefficients in a fitted "BLMCP" object.

Usage

## S3 method for class 'BLMCP'
plot(x, ...)

Arguments

Value

A heatmap for estimated coefficients.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.

Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

BLMCP, and predict and coef methods.

Plot coefficients from a "Miss.boosting" object

Description

Draw plots for estimated parameters in a fitted "Miss.boosting" object, including a heatmap for discrete environmental (E) effects, and selected genetic (G) effects and G-E interactions, and plots for each of selected continuous E (EC) effect and interactions between EC and G.

Usage

## S3 method for class 'Miss.boosting'
plot(x, ...)

Arguments

Value

A heatmap for estimated coefficients.

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

Miss.boosting, and predict methods.

Plot coefficients from a "PTReg" object

Description

Draw a heatmap for estimated coefficients in a fitted "PTReg" object.

Usage

## S3 method for class 'PTReg'
plot(x, ...)

Arguments

Value

A heatmap for estimated coefficients.

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

PTReg, and predict, and coef methods.

Plot coefficients from a "RobSBoosting" object

Description

Draw plots for estimated parameters in a fitted "RobSBoosting" object, including a heatmap for discrete environmental (E) effects, and selected genetic (G) effects and G-E interactions, and plots for each of selected continuous E (EC) effect and interactions between EC and G.

Usage

## S3 method for class 'RobSBoosting'
plot(x, ...)

Arguments

Value

Plots for estimated coefficients.

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

RobSBoosting, predict and coef methods.

Plot coefficients from a "bic.BLMCP" object

Description

Draw a heatmap for estimated coefficients in a fitted "bic.BLMCP" object.

Usage

## S3 method for class 'bic.BLMCP'
plot(x, ...)

Arguments

Value

A heatmap for estimated coefficients.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

predict, coef and BLMCP methods.

Plot coefficients from a "bic.PTReg" object

Description

Draw a heatmap for estimated coefficients in a fitted "bic.PTReg" object.

Usage

## S3 method for class 'bic.PTReg'
plot(x, ...)

Arguments

Value

A heatmap for estimated coefficients.

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

bic.PTReg, and predict, and coef methods.

Make predictions from a "BLMCP" object

Description

This function makes predictions from a BLMCP model, using the stored "BLMCP" object.

Usage

## S3 method for class 'BLMCP'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for BLMCP objects.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

BLMCP, coef, and plot methods, and bic.BLMCP method.

Make predictions from a "Miss.boosting" object

Description

This function makes predictions from a Miss.boosting model, using the stored "Miss.boosting" object.

Usage

## S3 method for class 'Miss.boosting'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for Miss.boosting objects.

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

Miss.boosting, and plot methods.

Make predictions from a "PTReg" object

Description

This function makes predictions from a PTReg model, using the stored "PTReg" object.

Usage

## S3 method for class 'PTReg'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for PTReg objects.

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

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

Make predictions from a "RobSBoosting" object

Description

This function makes predictions from a RobSBoosting model, using the stored "RobSBoosting" object.

Usage

## S3 method for class 'RobSBoosting'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for RobSBoosting objects.

References

Mengyun Wu and Shuangge Ma. Robust semiparametric gene-environment interaction analysis using sparse boosting. Statistics in Medicine, 38(23):4625-4641, 2019.

See Also

RobSBoosting, coef, and plot methods.

Make predictions from a "bic.BLMCP" object.

Description

This function makes predictions from a BIC BLMCP model, using the stored "bic.BLMCP" object. This function makes it easier to use the results of BIC to make a prediction.

Usage

## S3 method for class 'bic.BLMCP'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for BLMCP objects.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.

Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.
http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC3869641&blobtype=pdf

See Also

coef, and plot and bic.BLMCP methods, and BLMCP.

Make predictions from a "bic.PTReg" object

Description

This function makes predictions from a BIC PTReg model, using the stored "bic.PTReg" object. This function makes it easier to use the results of BIC to make a prediction.

Usage

## S3 method for class 'bic.PTReg'
predict(object, newE, newG, ...)

Arguments

Value

The object returned depends on the ... argument which is passed on to the predict method for PTReg objects.

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

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

Simulated data for generating response

Description

Generate simulated response.

Usage

simulated_data(
  G,
  E,
  alpha,
  beta,
  error,
  family = c("continuous", "survival"),
  a1 = NULL,
  a2 = NULL
)

Arguments

Value

Response variable. A quantitative vector for family="continuous". For family="survival", it would 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.