crrscCOX {adjSURVCI}

Stratified Competing Proportional Subdistribution Hazards Model For Clustered Competing Risks Data With Covariate-Dependent Censoring

Description

Stratified proportional subdistribution hazards model for clustered competing risks data. The stratified Cox proportional hazards model is fitted for the censoring distribution. The estimates of the cumulative baseline hazard along with their standard errors are provided at the pre-specified time points. Furthermore, the adjusted cumulative incidence rates along with their standard errors are calculated at pre-specified time points. The standard error of the the difference in adjusted cumulative incidence between the groups are also provided. Finally, the estimates of adjusted cumulative incidence rates given vector Z0 along with their standard errors are provided at pre-specified time points. Tied data are handled by adding a tiny random shift from a normal distribution with mean 0 and standard deviation 1e-09.

Usage

crrscCOX(
  times,
  causes,
  covariates,
  cencovariates,
  treatment = NULL,
  clusters = 1:length(times),
  cencode = 0,
  failcode = 1,
  treatmentC = NULL,
  stratified.model = TRUE,
  stratified.model.cens = TRUE,
  est.t = FALSE,
  pre.t = sort(times[causes == failcode]),
  Z0 = NULL
)

Arguments

times

Failure/censored times.

causes

Failure code for each failure type (1 or 2) and 0 for censoring.

covariates

Matrix of covariates. Dummy variables must be created for categorical covariates.

cencovariates

Matrix of covariates for censoring. Dummy variable must be created for categorical covariates.

treatment

Treatment variable.

clusters

Cluster variable. Independent data is assumed if this is not provided.

cencode

Code for censoring. By default it is 0.

failcode

Code for the failure type of interest. By default it is 1.

treatmentC

Treatment variable for censoring. Could also be stratification variable.

stratified.model

TRUE or FALSE. By default, it is TRUE for stratified model. The stratification variable is treatment. If this is FALSE and est.t=TRUE, then the treatment variable still needs to be provided and will be used as a covariate.

stratified.model.cens

TRUE or FALSE. By default, it is TRUE for stratified model for censoring. For unstratified model treatmentC does not need to be provided.

est.t

TRUE or FALSE. By default this is FALSE. If it is TRUE then estimates of cumulative baseline hazard, adjusted cumulative incidence and predicted cumulative incidence are provided along with their standard errors at pre-specified time points.

pre.t

Pre-specified time points. By default these are all main event times.

Z0

Covariate vector for prediction. By default this vector is a zero vector.

Value

Returns a list with the following components. If est.t=FALSE then only upto $nstrataC are provided.

$coef

Parameter estimates

$p.value

p-value of regression coefficients

$var

Covariance matrix of parameter estimates

$infor

Information matrix

$loglikelihood

Maximum log-likelihood value

$n

Total number of observations used

$nevents

Total number of events and censored observations

$nclusters

Total number of clusters

$nstrata

Total number of treatment groups

$nstrataC

Total number of treatment groups for censoring

$CumBaseHaz.t

Cumulative basline hazard estimates and their standard errors

$Fpredict.t

Predicted cumulative incidence and their standard errors

$AdjustedF.t

Adjusted cumulative incidence and their standard errors

$Adjusted.se.diff

Standard error of the difference of adjusted cumulative incidence between the treatment groups

Examples

#Simulated data
alpha = 0.5
d = simulate_CR_data(n=4,m=50,alpha=alpha,beta1=c(0.7,-0.7,-0.5)*1/alpha,
beta2=c(0.5,-0.5,1),betaC=c(2,-2,1)*1/alpha,lambdaC=0.59)

#Note: Since est.t=TRUE, model1 through model4 below will also output the 
#estimates of cumulative baseline hazard, adjusted probabilities and predicted 
#probabilities along with their standard errors.

#Stratified Model for the main cause and stratified model for censoring
model1 <- crrscCOX(times=d[,1],causes=d[,2],covariates=d[,4:5],cencovariates=d[,4:5],
treatment=d[,3],clusters=d[,6],treatmentC=d[,3],stratified.model=TRUE,
est.t=TRUE,stratified.model.cens=TRUE,pre.t=sort(d$time[d$cause==1]),Z0=c(0.5,0.5))

#Unstratified Model for the main cause and stratified model for censoring
model2 <- crrscCOX(times=d[,1],causes=d[,2],covariates=d[,4:5],cencovariates=d[,4:5],
treatment=d[,3],clusters=d[,6],treatmentC=d[,3],stratified.model=FALSE,
stratified.model.cens=TRUE,est.t=TRUE,pre.t=sort(d$time[d$cause==1]),Z0=c(0.5,0.5))

#Stratified Model for the main cause and unstratified model for censoring
model3 <- crrscCOX(times=d[,1],causes=d[,2],covariates=d[,4:5],cencovariates=d[,4:5],
treatment=d[,3],clusters=d[,6],stratified.model=TRUE,
est.t=TRUE,stratified.model.cens=FALSE,pre.t=sort(d$time[d$cause==1]),Z0=c(0.5,0.5))

#Unstratified Model for the main cause and unstratified model for censoring
model4 <- crrscCOX(times=d[,1],causes=d[,2],covariates=d[,4:5],cencovariates=d[,4:5],
treatment=d[,3],clusters=d[,6],stratified.model=FALSE,
stratified.model.cens=FALSE,est.t=TRUE,pre.t=sort(d$time[d$cause==1]),Z0=c(0.5,0.5))

#Now set est.t=FALSE which means the cumulative baseline hazard estimate, adjusted
#probabilities and predicted cumulative incidence are not returned.

#Assume only continuous covariates are available for main cause and censoring.
#In this case both stratified.model and stratified.model.cens need to be FALSE.
model5 <- crrscCOX(times=d[,1],causes=d[,2],covariates=d[,4:5],cencovariates=d[,4:5],
clusters=d[,6],stratified.model=FALSE,stratified.model.cens=FALSE,est.t=FALSE)