Boot.HRandIndex.param: Bootstrap Estimation of Hazard Function and Index Parameters

In HQM: Superefficient Estimation of Future Conditional Hazards Based on Marker Information

Bootstrap Estimation of Hazard Function and Index Parameters

Description

Performs bootstrap estimation of hazard rates and corresponding index parameters for a given set of bootstrap samples. For each bootstrap replicate, the function re-estimates the index parameters via optimisation and computes hazard estimates using Boot.hqm. The output is used as input in functions Quantile.Index.CIs and Pivot.Index.CIs

Usage

Boot.hrandindex.param(B, Boot.samples, marker_name1, marker_name2,event_time_name, 
                             time_name, event_name, b, t, true.haz, v.param, n.est.points)

Arguments

B	Integer. Number of bootstrap iterations.
Boot.samples	A list of bootstrap datasets. Each element corresponds to one replicate.
marker_name1	Character string. Name of the first longitudinal marker.
marker_name2	Character string. Name of the second longitudinal marker.
event_time_name	Name of the event time variable in the data.
time_name	Name of the time variable for the longitudinal marker measurements.
event_name	Name of the event indicator variable.
b	Numeric. Bandwidth parameter used in hazard estimation.
t	Numeric. Evaluation point for the conditional hazard.
true.haz	Numeric vector. The true or reference hazard used in the optimisation criterion.
v.param	Numeric vector. Starting values of the indexing parameters for the optimisation of the index coefficients.
n.est.points	Integer. Number of estimation grid points for the hazard curve.

Details

For each bootstrap iteration k = 1, \dots, B, the function:

1. Extracts the bootstrap sample data.use.

2. Computes centred marker values at the subject and observation level.

3. Estimates index parameters by minimising index_optim using optim.

4. Computes the bootstrap hazard estimate via Boot.hqm.

The outputs are matrices collecting the hazard estimates and estimated index parameter vectors across bootstrap replicates.

Value

A matrix of dimension n.est.points × B containing the bootstrap hazard estimates.

See Also

Boot.hqm, index_optim, to_id

Examples

marker_name1 <- 'albumin'
marker_name2 <-  'serBilir'
event_time_name <- 'years' 
time_name <- 'year' 
event_name <- 'status2'
id<-'id'

par.x1  <- 0.0702  
par.x2 <- 0.0856  
t.x1 = 0 # refers to zero mean variables - slightly high
t.x2 = 1.9 # refers to zero mean variable - high
b = 0.42 
t = par.x1 * t.x1 + par.x2 *t.x2

# first simulate true HR function:
xin <- pbc2[,c(id, marker_name1, marker_name2, event_time_name, time_name, event_name)]
n <- length(xin$id)
nn<-max(  as.double(xin[,'id']) )
xin.id <- to_id(xin)


#  Create bootstrap samples by group:
set.seed(1)  
B<- 10 # 400 #50
Boot.samples<-list()
for(j in 1:B)
{
  i.use<-c()
  id.use<-c()
  index.nn <- sample (nn, replace = TRUE)  
  for(l in 1:nn)
  {
    i.use2<-which(xin[,id]==index.nn[l])
    i.use<-c(i.use, i.use2)
    id.use2<-rep(index.nn[l], times=length(i.use2))
    id.use<-c(id.use, id.use2)
  }
  xin.i<-xin[i.use,]
  xin.i<-xin[i.use,]
  Boot.samples[[j]]<- xin.i[order(xin.i$id),] #xin[i.use,]
}
true.hazard<- Sim.True.Hazard(Boot.samples, id='id', 100,  marker_name1=marker_name1,  
                    marker_name2= marker_name2, event_time_name = event_time_name, 
                    time_name = time_name,  event_name = event_name, 
                    in.par = c(par.x1,  par.x2), b)
                              
res <- Boot.hrandindex.param( B,  Boot.samples, marker_name1, marker_name2, 
          event_time_name,  time_name,  event_name ,  b = 0.4, t = 1.0,  
          true.haz = true.hazard, v.param = c(0.07, 0.08), n.est.points = 100)
          
#return bootstrap hazard rate estimators in marix format:
res

HQM documentation built on Jan. 8, 2026, 9:08 a.m.