TPNPMLE: Penalized Non-Parametric Maximum-Likelihood Estimation...
In NPMLENCC: Non-Parametric Maximum Likelihood Estimate for Cohort Samplings

Description Usage Arguments Value Note References See Also Examples

The function utilizes a self-consistency iterative algorithm to calculate PNPMLEs by adding penalty function for cohort samplings with time matching under Cox's regression model. In addition to compute PNPMLEs, it can also estimate asymptotic varance, as described in Wang et al. (2019+). The Cox's regression model is

λ(t|z)=λ_{0}(t)\exp(z^Tβ).

1 2	TPNPMLE(data, iteration1, iteration2, converge, penalty, penaltytuning, fold, cut, seed)

`data`	The description is the same as the statement of `TNPMLE` function.
`iteration1`	The number of iteration for computing (P)NPMLEs.
`iteration2`	The number of iteration for computing profile likelihoods which are used to estimate asymptotic variance.
`converge`	The description is the same as the statement of `TNPMLE` function.
`penalty`	The choice of penalty, it can be SCAD, HARD or LASSO.
`penaltytuning`	The tuning parameter for penalty function, it is a sequence of numeric vector.
`fold`	The `fold` information for cross validation. Without loss of generality, we note that `fold` value have to be bigger than one (>1) and cohort size is divisible by `fold` value. However, if cohort size is not able to be divided, we are going to partition off cohort into several suitable parts according to `fold` value automaticly for cross-validation.
`cut`	The cut point. When \hat{β}_j is smaller than the cut point, we set \hat{β}_j be zero, i.e. remove the corresponding covariate from our model to do variable selection.
`seed`	The seed of the random number generator to obtain reproducible results.

Returns a list with components

`num`	The numbers of case and observed subjects.
`iloop`	The final number of iteration for computing PNPMLEs.
`diff`	The sup-norm distance between the last two iterations of the estimates of the relative risk coefficients.
`cvl`	The cross-validated profile log-likelihood.
`tuning`	The suitable tuning parameter, such that the maximum of cross-validated profile log-likelihood is attained.
`likelihood`	The log likelihood value of PNPMLEs.
`pnpmle`	The estimated regression coefficients with their corresponding estimated standard errors and p-values.
`Lpnpmle`	The estimated cumulative baseline hazards function.
`Ppnpmle`	The empirical distribution of covariates which are missing for unobserved subjects.
`elements`	The description is the same as the statement of `TNPMLE` function.
`Adata`	The description is the same as the statement of `TNPMLE` function.

The missing value (NA) in the DATA is not allowed in this version.

Wang JH, Pan CH, Chang IS*, and Hsiung CA (2019) Penalized full likelihood approach to variable selection for Cox's regression model under nested case-control sampling. published in Lifetime Data Analysis <doi:10.1007/s10985-019-09475-z>.

See TNPMLE.

set.seed(100)
library(splines)
library(survival)
library(MASS)
beta=c(1,0)
lambda=0.3
cohort=100
covariate=2+length(beta)
z=matrix(rnorm(cohort*length(beta)),nrow=cohort)
rate=1/(runif(cohort,1,3)*exp(z%*%beta))
c=rexp(cohort,rate)
u=-log(runif(cohort,0,1))/(lambda*exp(z%*%beta))
time=apply(cbind(u,c),1,min)
status=(u<=c)+0
casenum=sum(status)
odata=cbind(time,status,z)
odata=data.frame(odata)
a=order(status)
data=matrix(0,cohort,covariate)
data=data.frame(data)
for (i in 1:cohort){
data[i,]=odata[a[cohort-i+1],]
}
ncc=matrix(0,cohort,covariate)
ncc=data.frame(data)
aa=order(data[1:casenum,1])
for (i in 1:casenum){
ncc[i,]=data[aa[i],]
}
control=1
q=matrix(0,casenum,control)
for (i in 1:casenum){
k=c(1:cohort)
k=k[-(1:i)]
sumsc=sum(ncc[i,1]<ncc[,1][(i+1):cohort])
if (sumsc==0) {
			q[i,]=c(1)
} else {
			q[i,]=sample(k[ncc[i,1]<ncc[,1][(i+1):cohort]],control)
}
}
cacon=c(q,1:casenum)
k=c(1:cohort)
owf=k[-cacon]
wt=k[-owf]
owt=k[-wt]
ncct=matrix(0,cohort,covariate)
ncct=data.frame(ncct)
for (i in 1:length(wt)){
ncct[i,]=ncc[wt[i],]
}
for (i in 1:length(owt)){
ncct[length(wt)+i,]=ncc[owt[i],]
}
d=length(wt)+1
ncct[d:cohort,3:covariate]=-9
TPNPMLEtest=TPNPMLE(ncct,100,30,0,"SCAD",seq(0.10,0.13,0.005),2,1e-05,1)