trans_alasso {transmdl}

Adaptive LASSO for Semiparametric Transformation Models.

Description

Select the important variables in semiparametric transformation models for right censored data using adaptive lasso.

Usage

trans_alasso(Z, Y, delta_i, r, lamb_vec, solu = TRUE)

Arguments

Z

the baseline covariates

Y

observed event times

delta_i

censoring indicator. If Y is censored, delta_i=0. If not, delta_i=1.

r

parameter in transformation function

lamb_vec

the grad of the tuning parameter \lambda

solu

determines whether the solution path will be plotted. The default is TRUE.

Details

The initial value of the coefficient \beta used as the adapting weights is EM estimator, which is computed by the function EM_est. The tuning parameter \lambda is data-dependent and we select it using generalized crossvalidation. There may be some errors for small \lambda, in which case the \lambda and the number of adaptive lasso iteration are recorded in the skip_para.

Value

a list containing

beta_res			the estimated \beta with the selected tuning parameter \lambda
GCV_res			the value of GCV with the selected tuning parameter \lambda
lamb_res			the selected tuning parameter \lambda
beta_all			estimated \beta with all tuning parameters
CSV_all			value of GCV with all tuning parameters
skip_para			a list containing the \lambda and the number of adaptive lasso iteration when adaptive lasso doesn't work.

References

Xiaoxi, L. , & Donglin, Z. . (2013). Variable selection in semiparametric transformation models for right-censored data. Biometrika(4), 859-876.

Examples

 if(!requireNamespace("MASS", quietly = TRUE))
 {stop("package MASS needed for this example. Please install it.")}

 gen_lasdat = function(n,r,rho,beta_true,a,b,seed=66,std = FALSE)
{

  set.seed(seed)
  beta_len = length(beta_true)
  beta_len = beta_len
  sigm = matrix(0, nrow = beta_len, ncol = beta_len)
  for(i in 1:(beta_len-1))
  {
    diag(sigm[1:(beta_len+1-i),i:beta_len]) = rho^(i-1)
  }
  sigm[1,beta_len] = rho^(beta_len-1)
  sigm[lower.tri(sigm)] = t(sigm)[lower.tri(sigm)]

  Z = MASS::mvrnorm(n, mu = rep(0, beta_len), Sigma = sigm)
  beta_Z.true = c(Z %*% beta_true)
  U = runif(n)
  if(r>0)
  {
    t = ((U^(-r)-1)/(a*r*exp(beta_Z.true)))^(1/b)
  }else if(r == 0)
  {
    t = (-log(U)/(a*exp(beta_Z.true)))^(1/b)
    #t = (exp(-log(U)/(0.5 * exp(beta_Z.true))) - 1)
  }
  C = runif(n,0,8)
  Y = pmin(C,t)
  delta_i = ifelse( C >= t, 1, 0)
  if(std)
  {
    Z = apply(Z,2,normalize)
  }
  return(list(Z = Z, Y = Y, delta_i = delta_i,censor = mean(1-delta_i)))
}

now_rep=1
dat = gen_lasdat(100,1,0.5,c(0.3,0.5,0.7,0,0,0,0,0,0,0),2,5,seed= 6+60*now_rep,std = FALSE)
Z = dat$Z
Y = dat$Y
delta_i = dat$delta_i

tra_ala = trans_alasso(Z,Y,delta_i,lamb_vec = c(5,7),r=1)
tra_ala$GCV_res
tra_ala$beta_res
tra_ala$lamb_res