coxseiest: Function to estimate the parametric part of the Cox...
In coxsei: Fitting a CoxSEI Model

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Estimate the parametric part of the CoxSEI model using (conditionally) right-censored counting process data.

coxseiest(dat, par.init, m = 2, mit = 1000, tr = TRUE,
          method = "L-BFGS-B", lower=c(rep(-Inf,ncol(dat)-3),-Inf,0),
          upper=rep(Inf,ncol(dat)-3 + 2),
          gfun = function(x, pa) {
           ifelse(x <= 0, rep(0, length(x)), pa[1] * exp(-pa[2] * x))
          })
coxseiest2(dat, par.init, m = 2, mit = 1000, tr = TRUE,
           method = "L-BFGS-B", lower=c(rep(-Inf,ncol(dat)-3),-Inf,0),
           upper=rep(Inf,ncol(dat)-3 + 2),
           gfun = function(x, pa) {
             ifelse(x <= 0, rep(0, length(x)), pa[1] * exp(-pa[2] * x))
           })
coxseiest3(dat, par.init, m = 2, mit = 1000, tr = TRUE,
           method = "L-BFGS-B", lower=c(rep(-Inf,ncol(dat)-3),-Inf,0),
           upper=rep(Inf,ncol(dat)-3 + 2))

`dat`	a data frame with columns `Y` containing the censored event times of each individual process arranged in ascending order with the last time always being the the censoring time, `delta` containing the event time indicator with value indicator an event time and 0 a censoring time, `id` specifying the id (process number) of each event time recorded, and the others giving the value of the associated covariate process at the corresponding event times.
`par.init`	init guess of the value of the parameters to start the optimization iteration with.
`m`	order of "autoregression" of the excitation term.
`mit`	maximum number of iteration in the optimization routine
`tr`	if set to `TRUE`, print some summary information while the optimization routine is running.
`method`	method of optimization
`lower`	vector of lower boundary values of the parameter space
`upper`	vector of upper boundary of the parameter space
`gfun`	the excitation function. Defaults to the exponential decay function g(t;γ)=γ_1 γ_2 \exp (-γ_2 t)

coxseiest uses only R code; coxseiest2 uses external C code, and is expected to be 3~4 times fasters than the former; coxseiest3 assumes the excitation function is the exponential function as defaulted by the former two, and hardwares it in the C side of the code, and therefore is much faster than the former two when the exponential excitation function is desired.

A list as that returned by the call to the optimizer routine. For instance,

`par`	gives the estimate of the parameters
`hessian`	gives the inverse of the estimate of the variance-covariance matrix

the excitation function has to contain exactly two parameters; a feature that does not seem desiable and might change later.

Feng Chen <feng.chen@unsw.edu.au>

Feng Chen and Kani Chen. (2014). Modeling Event Clustering Using the m-Memory Cox-Type Self-Exciting Intensity Model. International Journal of Statistics and Probability. 3(3): 126-137. doi:10.5539/ijsp.v3n3p126 URL: http://dx.doi.org/10.5539/ijsp.v3n3p126

Feng Chen and Kani Chen. (2014). Case-cohort analysis of clusters of recurrent events. 20(1): 1-15. doi: 10.1007/s10985-013-9275-3

See optim for the components of the returned value

data("dat")
## this takes over 15 minutes
##est0 <- coxseiest(dat,par.init=c(0.2,0.4,0.6,0.6,5))
## this one takes about 4 minutes
##est1 <- coxseiest2(dat,par.init=c(0.2,0.4,0.6,0.6,5))
## this one takes about 10 seconds
est2 <- coxseiest3(dat,par.init=c(0.2,0.4,0.6,0.6,5))