robustAFT: This function implement the B-J estimator with lasso or group...

In muxuanliang/RobustAFT: Robust Estimation of AFT Model with High-dimensional Covariates

Description

This function implement the B-J estimator with lasso or group lasso penalty

Usage

robustAFT(
  surv_obj,
  covariate,
  loss = "square",
  penalty = TRUE,
  group_index = NULL,
  lambda_lasso = 60,
  lambda_group = NULL,
  standardize = TRUE,
  ...
)

Arguments

surv_obj	The output of the Survival Object created by survival::Surv. It includes the time and event status.
covariate	A p-dimensional covariate. Each row is an observation; each col represents a covariate.
loss	Type of the loss functions available. Include 'square' for square loss, 'absolute' for absolute loss, 'huber' for huber loss, 'tukey' for tukey loss.
penalty	A Bool variable. True represents a penalty will be added; FALSE represents no penalty. The type of the penalty depends on whether group_index is specified.
group_index	A p-dimensional Vector. The same index represents the same group. For example, group_index=c(1,1,2,2,2) represents that there are two groups.
lambda_lasso	A non-negative numeric. The parameter for the lasso penalty.
lambda_group	A non-negative numeric. The parameter for the grouped lasso penalty.
standardize	A Bool variable. if TRUE, the covariate will be standardized druing the calculation.
...	Other parameters related to the algorithm. For example, maxit determine the maximum iteration allowed.

Value

A list

penalty_type

Type of the penalty

intercept

Estimated intercept

coef

Estimated coefficients

nonZeroIndex

Indicators of non-zero coefficients

coef_path

Coefficients after convergence (including intercept)

coef_refit

Refitted coefficients wihtout penalty based on the selected non-zero coefficients (including intercept)

iter

Number of iterations until convergence

Examples

library(MASS)
library(survival)
library(RobustAFT)
###sample size
nobs <- 200

###regression parameters
p <- 30
alpha <- 1
beta <- c(1,1.5,2,2.5,3,array(0,10),1,-1,1,-1,1,array(0,10))

###group structure
index <- ceiling(1:p/5)

###covariance structure
pau <- 0.5
cov_x <- pau*matrix(1,p,p)
diag(cov_x) <- 1

###error distribution and signal to-noise ratio
error <- 4
snr <- 5
sigma <- as.numeric(sqrt(t(as.matrix(beta))%*%cov_x%*%as.matrix(beta)/snr/23.4))
m <- 100
set.seed(10*m)

###generate covariates
x <- mvrnorm(nobs, rep(0,p), cov_x)
if (error == 1){
 epsilon <- rnorm(nobs, 0, 1)
} else if (error == 2){
 epsilon <- rt(nobs, 3)
} else if (error == 3){
 epsilon <- rdoublex(nobs)
} else if (error == 4){
 epsilon <- NULL
 for (j in 1:nobs){
   z <- rbinom(1, 1, 0.9)
   if (z==1) {epsilon[j] <- rnorm(1, 0, 1)}
   else {epsilon[j] <- rnorm(1, 0, 15) }
 }
}
epsilon <- sigma * epsilon
tlogt.expect <- x %*% beta + alpha
tlogt <- tlogt.expect + epsilon
tau <- 950
tc <- runif(nobs, min = 0, max = tau)
tlogc <- log(tc)
censor <- sum(tlogc < tlogt)/nobs
logt <- pmin(tlogt, tlogc)
indi <- (tlogt <= tlogc)
y <- Surv(logt, indi)

###square loss
#oracle
olsfit1 <- robustAFT(covariate=x[,abs(beta) > 1e-5], surv_obj=y, loss="square", penalty=FALSE)
#lasso
fitlasso1 <- robustAFT(covariate=x, surv_obj=y, loss="square", lambda_lasso=60, standardize=TRUE)
#sgl
fitsgl1 <- robustAFT(covariate=x, surv_obj=y, group_index = index, lambda_lasso=30 , lambda_group=20, loss="square")

###huber loss
#oracle
olsfit3 <- robustAFT(covariate=x[,abs(beta) > 1e-5], surv_obj=y, loss="huber", penalty=FALSE)
#lasso
fitlasso3 <- robustAFT(covariate=x, surv_obj=y, loss="huber", lambda_lasso=25, standardize=TRUE)
#sgl
fitsgl3 <- robustAFT(covariate=x, surv_obj=y, group_index = index, lambda_lasso=20 , lambda_group=5, loss="huber")

###absolute loss
#oracle
olsfit2 <- robustAFT(covariate=x[,abs(beta) > 1e-5], surv_obj=y, loss="absolute", penalty=FALSE)
#lasso
fitlasso2 <- robustAFT(covariate=x, surv_obj=y, loss="absolute", lambda_lasso=20, standardize=TRUE)
#sgl
fitsgl2 <- robustAFT(covariate=x, surv_obj=y, group_index = index, lambda_lasso=20 , lambda_group=5, loss="absolute")

###tukey loss
#oracle
olsfit4 <- robustAFT(covariate=x[,abs(beta) > 1e-5], surv_obj=y, loss="tukey", penalty=FALSE)
#lasso
fitlasso4 <- robustAFT(covariate=x, surv_obj=y, loss="tukey", lambda_lasso=20, standardize=TRUE)
#sgl
fitsgl4 <- robustAFT(covariate=x, surv_obj=y, group_index = index, lambda_lasso=20 , lambda_group=5, loss="tukey")

muxuanliang/RobustAFT documentation built on April 12, 2021, 9:38 a.m.