icemelt (version 1.0)

imw1: Parameter Estimation in Linear Transformation Model with Interval-censored Data and Covariate Measurement Error

Description

This function should be used when only a single replication of the error-prone covariate is available. If multiple replications are available please see im() function. This function estimates the parameters of the semiparametric linear transformation model using imputation method when time-to-event is interval-censored and a covariate is measured with error. Estimated standard errors of the model parameters are also provided. A right censoring indicator must be available along with the measurement error variance.

Usage

imw1(datamat, wmat, rfix, gridlen, ntimp, nximp, sigma2u)

Arguments

datamat

A data matrix with as many rows as there are subjects (n) in the study. The first column contains left points of the intervals, second column contains right points of the intervals, third column is the right censoring indicator and the fourth (and final) column is the error-free covariate.

wmat

A matrix with only one column of surrogate measurements for the covariate with measurement error.

rfix

A value that characterizes the error density in the linear transformation model. The value 0 corresponds to the Cox PH model and 1 corresponds to Proportional Odds model.

gridlen

A non-negative value representing the desired grid length used to divide the observed failure-time intervals.

ntimp

Number of failure time imputations required.

nximp

Number of imputations desired for the error-prone covariate.

sigma2u

A known value for the measurement error variance.

Value

Parameter estimates of the semiparamteric linear transformation model and their corresponding standard errors.

References

Mandal, S., Wang, S. and Sinha, S. (2019+). Analysis of Linear Transformation Models with Covariate Measurement Error and Interval Censoring. (accepted, Statistics In Medicine)

Examples

# NOT RUN {
## this function is used in generating epsilon from its CDF
  rsep= function(u,r)
        {
          if(r==0)
            return(  log(-log(1-u))  )
          else
            return(  log((exp(-r*log(1-u))-1)/r)  )
        }


  n= 30 #200     # sample size; small number used for quick demonstration only
  rfix= 1.0
  
  
  m= 3 #10       # imputed datasets for failure time; small number used for quick demonstration only
  
  nrep= 1        # number of repeated measurement of error prone covariate

  gridlen= 0.1
  sigma2u= 0.5

  result= NULL
  ah=1

  set.seed(ah)

#  z1= rnorm(n, mean= 0, sd=1)
  z1= (rgamma(n,shape=2,scale=2)-4)/sqrt(8)
  z2= rbinom(n,1,0.5)

  ugen= runif(n)
  ep= rsep(ugen,rfix)

  truebeta= c(-1,1)

  logt= -truebeta[1]*z1 -truebeta[2]*z2 + ep + 3
  ttime= exp(logt)

  cen= runif(n,0,0.0001)

## creating tau matrix to locate the actual times in each rows and form the corresponding intervals
  len= 0.15
  taumat= matrix(0,n,10)
  taumat[,10]= 9000000000             # if you're changing this, change rcpos below
  taumat[,2]= cen
  for(i1 in 3:9)
    taumat[,i1]= taumat[,2]+(i1-1)*len

## now forming the intervals
  right1= rep(0,n)
  left= rep(0,n)
  for(i2 in 1:n)
  {
    lenleft= length(which(taumat[i2,2:9]<ttime[i2]))
    leftpot= rep(0,8)
    leftpot[1:lenleft]= 1
    missvec1= c(rbinom(4,1,0.7),rbinom(4,1,0.5))
    left[i2]= max(leftpot*missvec1*taumat[i2,2:9])
    
    if(left[i2]==0)
      left[i2]= taumat[i2,2]
    
    lenright= length(which(taumat[i2,2:10]>ttime[i2]))
    rightpot= rep(0,9)
    rightpot[(9-lenright+1):9]= 1
    missvec2= c(rbinom(4,1,0.7),rbinom(4,1,0.5),1)    
    right1temp= rightpot*missvec2*taumat[i2,2:10]
    right1[i2]= min(right1temp[right1temp!=0])    
  }

  rcpos= which(right1==9000000000)
  lrcpos= length(rcpos)
  notrcpos= (1:n)[-rcpos]
  
  delta_temp= rep(1,n) # del=1 are uncensored observations
  delta_temp[rcpos]= 0
  k= sum(delta_temp)   # number of data points that are not right censored
  
## measurement error generation
  umat= matrix((rgamma(n*nrep,shape=2,scale=2)-4)*0.5/sqrt(8),n,nrep)

  wmat= z1+umat


  datamat= cbind(left,right1,delta_temp,z2)
  ntimp= m
  nximp= 5 #20    # number of x imputations; small number used for quick demonstration only

  library(icemelt)
  out_imw1= imw1(datamat, wmat, rfix, gridlen, ntimp, nximp, sigma2u)
  out_imw1

# }