emcc: Fits Cox's regression model for nested case-control data and...
In nccMLE: MLE for nested case cohort and case-cohort designs

Description Usage Arguments Value Author(s) References Examples

Z covariates observed only for cases and controls

X observed for all subjects in the study such as sex and age

The distribution of Z given X needs is specified non-parametrically on a number of strata specified by X through the stratum variable.

Intensity model

λ_{X,Z}(t)) = λ_S(X) \exp( β^T Z )

The baseline stratification based on S(X) is specified by baseline.stratum.

When fullobsX is given the baseline may be also on Cox form

λ_{X}(t)) = λ_{S(X_1)} \exp( β_X^T X_2 )

where a stratum is used for some covariates and other covariates are modelled as regression effects. This model is specified by fullobsX=X_2, and S(X_1)= baseline.stratum

When stratZ==1 the baseline is stratified by the Z components as specified by baseline.stratum=S(Z)

λ_{X,Z}(t)) = λ_S(Z) \exp( β^T X )

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em.ncc(Zobs,Tobs,status,tau,nno,Nit=1,beta=0,detail=0,
betait=2,em.dif=1,stratum=0,baseline=0,emvar=0,
fullobsZ=0,baseline.stratum=0,stratZ=0)

`Zobs`	covariates observed for cases and controls, fullobsX is also given it means that the first columns of Zobs is the Z from the above intensity and the second part is the covariates X.
`Tobs`	observed survival times for cases and controls.
`status`	censoring status for observed cases and controls.
`tau`	end of observation period. If tau has length equal to the number of subjects that are not cases and controls it is individual censoring times.
`nno`	number of subjects in the cohort that are not cases or controls.
`Nit`	number of itterations for EM algorithm.
`beta`	starting value for regression parameter.
`detail`	prints out iteration details.
`betait`	number of itterations for Cox regression score in EM, should be at least 2.
`em.dif`	constant used for EM aided differentation, default is (em.dif/number of subjects in cohort).
`stratum`	case specific strata for number of strata for specification of the distribution of Z given X.
`baseline`	starting value for baseline estimates.
`emvar`	computes EM based variance by EM aided differentation.
`fullobsZ`	The fully observed covariates if these are needed for a possible regression model for the baseline
`baseline.stratum`	stratum for the baseline, defined as the grouping given by S(X), a vector of length ntot=nno+nrow(Zobs).
`stratZ`	stratifies after the Z covariate that is only observed for cases and controls, stratification given by baseline.stratum

returns an object of type "em.ncc". With the following arguments:

`cum`	cumulative timevarying regression coefficient estimates are computed within the estimation interval.
`baseline`	the baseline estimates.
`beta`	estimate of parametric components of model.
`var.beta`	variance for beta.
`p`	the distribution of covariates.
`delta`	something about convergence.
`em.dif`	parameter used for EM aided differentation.
`covz`	the covariates realtes do p.
`konv`	something about convergence.

Thomas Scheike

Scheike and Juul, Biostatistics

Scheike and Maritnussen, SJS

###library(nccMLE)

# ud<-simNCC(3728,2,rate=1/0.004,win=1) realistic simulation

ud<-simNCC(500,2,rate=1/0.04,win=1)
Zobs<-ud$Xobs; Tobs<-ud$Tobs; status<-ud$status;
nno<-ud$nno;  tau<-15;

###################################################################
# Fits model with one common baseline and Z independent of X
# \lambda_0(t) \exp( Z^T \beta)
###################################################################
out<-em.ncc(Zobs,Tobs,status,tau,nno,Nit=100,beta=c(-.2,.2),
betait=20,detail=0,emvar=1)
print(c(out$beta,diag(out$var)^.5)); # estimates related to Z
plot(out$baseline,type="l")          # baseline estimates

#### using numDeriv for second derivative
out<-em.ncc(Zobs,Tobs,status,tau,nno,Nit=100,beta=c(-.2,.2),
betait=20,detail=0,emvar=2)
print(c(out$beta,diag(out$var)^.5)); # estimates related to Z


####################################################################
## slow way of fitting the same model, when censoring not the same 
####################################################################
out1<-em.ncc(Zobs,Tobs,status,rep(tau,nno),nno,Nit=100,beta=c(-.2,.2),
betait=20,detail=0,emvar=1)
print(c(out1$beta,diag(out1$var)^.5));     # estimates related to Z
lines(out$baseline,lty=2  )                # baseline estimates
#out$p                                     # distribution of Z

###################################################################
# Fits model : \lambda_S(X)(t) \exp( Z^T \beta)
#  Z | S(X) is equivalent gives conditional distribution of Z | X
###################################################################
strat<-rbinom(nrow(Zobs),1,0.5)
stratnoobs<-rbinom(500-nrow(Zobs),1,0.5)

out.strat<-em.ncc(Zobs,Tobs,status,tau,nno,Nit=100,beta=0,betait=20,
detail=0,stratum=c(strat,stratnoobs),emvar=1,
baseline.stratum=c(strat,stratnoobs))

print(cbind(out.strat$beta,diag(out.strat$var)^.5));
plot(out.strat$baseline[,1:2],type="l")     # baseline estimates
lines(out.strat$baseline[,c(1,3)],type="l") # baseline estimates
out.strat$p                                 # distribution of Z | S(X)