coxseiInt {coxsei}

Calculate the estimator of the cumulative baseline intensity function in the CoxSEI model.

Description

It takes the paramter of the parametric part (or its theorized value) and calculate the values of the estimator at the jump times; it also gives the values of the estimator for the variance of the intensity estimator.

Usage

coxseiInt(dat, parest, hessian=NULL, vcovmat=solve(hessian), m = 2,
          gfun = function(x, pa) {
            ifelse(x <= 0, 0, pa[1] * pa[2] * exp(-pa[2] * x))
          },
          gfungrd = function(x, pa){
            if(length(x)==0)return(matrix(0,2,0));
            rbind(pa[2]*exp(-pa[2]*x),
                  pa[1]*exp(-pa[2]*x)*(1-pa[2]*x)
                 )
          })

Arguments

dat

a data frame containing the right-censored counting process data

parest

the estimate of parameter of the parametric part of the CoxSEI model

hessian

the hessian matrix returned by the optimization procedure in the estimation of the parametric part based on partial likelihood

vcovmat

the variance-covariance matrix of the estimator of the the parametric components; defaulted to the inverse of the hessian matrix

m

autoregressive order in the excitation part of the intensity

gfun

the excitation function; defaults to the exponential decay function

gfungrd

derivative/gradient function of the excitation function

Value

a list giving the jump times and values at these of the estimator of the cumulative baseline intensity function.

x

the ordered death/event times

y

the value of the estimator of the intensity function at the observed death/event times

varest

the value of the estimator of the variance of the estimator of the intensity function, at the jump times

The step function can be obtained using stepfun, and plotted by setting type="s" in the plot function.

Note

Currently doesn't compute the standard error or variance estimator of the baseline cumulative intensity estimator.

Author(s)

Feng Chen <[e-mail]>

Examples

data("dat")
est <- coxseiest3(dat,c(0.2,0.4,0.6,log(0.06),log(5)))
pe <- est$par; pe[4:5] <- exp(pe[4:5]);
ve <- diag(pe) %*% solve(est$hessian, diag(pe));
cintest <- coxseiInt(dat,pe,vcovmat=ve)
plot(cintest,type="s")