Miss.boosting {GEInter}

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

G

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

E

Input matrix of q environmental 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.

im_time

Number of imputation for accommodating missingness in E variables.

loop_time

Number of iterations of the sparse boosting.

num.knots

Numbers of knots for the B spline basis.

Boundary.knots

The boundary of knots for the B spline basis.

degree

Degree for the B spline basis.

v

The step size used in the sparse boosting process. Default is 0.1.

tau

Threshold used in the stability selection at the third step.

family

Response type of Y (see above).

knots

List of knots for the B spline basis. Default is NULL and knots can be generated with the given num.knots, degree and Boundary.knots.

E_type

A vector indicating the type of each E factor, with "ED" representing discrete E factor, and "EC" representing continuous E factor.

Value

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

call

The call that produced this object.

alpha0

A vector with each element indicating whether the corresponding E factor is selected.

beta0

A vector with each element indicating whether the corresponding G factor or G-E interaction is selected. The first element is the first G effect and the second to (q+1) elements are the interactions for the first G factor, and so on.

intercept

The intercept estimate.

unique_variable

A matrix with two columns that represents the variables that are selected for the model after removing the duplicates, since the loop_time iterations of the method may produce variables that are repeatedly selected into the model. Here, the first and second columns correspond to the indexes of E factors and G factors. For example, (1, 0) represents that this variable is the first E factor, and (1,2) represents that the variable is the interaction between the first E factor and second G factor.

unique_coef

Coefficients corresponding to unique_variable. Here, the coefficients are simple regression coefficients for the linear effect (discrete E factor, G factor, and their interaction), and B spline coefficients for the nonlinear effect (continuous E factor, and corresponding G-E interaction).

unique_knots

A list of knots corresponding to unique_variable. Here, when the type of unique_variable is discrete E factor, G factor or their interaction, knot will be NULL, and knots will be B spline otherwise.

unique_Boundary.knots

A list of boundary knots corresponding to unique_variable.

unique_vtype

A vector representing the variable type of unique_variable. Here, "EC" stands for continuous E effect, "ED" for discrete E effect, "G" for genetic factor variable, "EC-G" for the interaction between "EC" and "G", and "ED-G" for the interaction between "ED" and "G".

degree

Degree for the B spline basis.

NorM

The values of B spline basis.

E_type

The type of E effects.

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)