survCOX {adjSURVCI}

Stratified Marginal Proportional Hazards Model For Clustered Survival Data

Description

Stratified marginal proportional hazards model for clustered survival data. The estimates of the cumulative baseline hazard along with their standard errors are provided at the pre-specified time points. Furthermore, the estimated adjusted survival probabilities along with their standard errors are calculated at pre-specified time points. The standard errors of the difference in estimated adjusted survival probabilities between the groups are also provided. Finally, the estimates of survival probabilities 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

survCOX(
  times,
  deltas,
  covariates,
  treatment = NULL,
  clusters = 1:length(times),
  stratified.model = TRUE,
  est.t = FALSE,
  pre.t = sort(times[deltas == 1]),
  Z0 = NULL
)

Arguments

times

Vector of failure/censored times.

deltas

Event indicator with 1 as an event and 0 as censoring.

covariates

Matrix of covariates. For categorical covariates, dummy variable must be created.

treatment

Vector of treatment variable. This is also the strata variable. It is a vector with numeric code for each group or stratum.

clusters

Vector of clustering variable. Independent data are assumed if not provided.

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.

est.t

TRUE or FALSE. By default this is FALSE. If TRUE then estimates of cumulative baseline hazard, adjusted survival probabilities and predicted survival probabilities are calculated.

pre.t

Vector of pre-specified time points at which the standard errors of the cumulative baseline hazard, adjusted survival probabilities and predicted survival probabilities are calculated. By default these are the time points where main event occurs.

Z0

Vector of covariates at which predicted survival probabilities are calculated. By default this vector is a zero vector.

Value

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

$coef

Parameter estimates

$p.value

p-value of regression coefficients

$var

Covariance matrix of parameter estimates calculated based on sandwich type variance

$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

$CumBaseHaz.t

Cumlative baseline hazard estimates and their standard errors

$Spredict.t

Predicted survival probabilities and their standard errors

$AdjustedS.t

Adjusted survival probabilities and their standard errors

$Adjusted.se.diff

Standard error of the difference of adjusted survival probabilities between the treatment groups

Examples

#Simulated data 
alpha = 0.5
d = simulate_surv_data(N=100,alpha=alpha,beta1=0.5*1/alpha,beta2=-0.5*1/alpha,
beta3=1/alpha,rateC=1.3,lambda0=1,lambda1=2,stratified = TRUE)

#Stratified Model with est.t=TRUE
model1 <- survCOX(times=d$times,deltas=d$delta,covariates=d[,5:7],treatment=d[,8],
clusters=d$cluster,est.t=TRUE,pre.t=sort(d$times[d$delta==1]),Z0=c(1,0.5,1) )

#Unstratified Model with est.t=TRUE
model2 <- survCOX(times=d$times,deltas=d$delta,covariates=d[,5:7],treatment=d[,8],
clusters=d$cluster,est.t=TRUE,pre.t=sort(d$times[d$delta==1]),stratified.model=FALSE,
Z0=c(1,0.5,1) )

#Stratified Model with est.t=FALSE
model3 <- survCOX(times=d$times,deltas=d$delta,covariates=d[,5:7],treatment=d[,8],
clusters=d$cluster,est.t=FALSE,pre.t=sort(d$times[d$delta==1]),Z0=c(1,0.5,1) )

#Unstratified Model with est.t=FALSE
model4 <- survCOX(times=d$times,deltas=d$delta,covariates=cbind(d[,5:7],d[,8]),
clusters=d$cluster,est.t=FALSE,pre.t=sort(d$times[d$delta==1]),
stratified.model=FALSE,Z0=c(1,0.5,1) )

#Only continuous covariates are available
model5 <- survCOX(times=d$times,deltas=d$delta,covariates=d[,5:7],
clusters=d$cluster,est.t=FALSE,pre.t=sort(d$times[d$delta==1]),
stratified.model=FALSE,Z0=c(1,0.5,1) )