cureph {curephEM}

NPMLE for Logistic-CoxPH Cure-Rate Model

Description

Fit NPMLE for Logistic-CoxPH Cure-Rate Model

Usage

cureph (formula, formula2 , data,  subset, na.action, init, control,
                 method = c("EM"), singular.ok = TRUE,
                  var = c("Louis"),...)

Arguments

formula

a formula object for cure logistic model,with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv.cure function.

formula2

a formula object for event time CoxPH model The Response can be suppressed.

data

a data.frame in which to interpret the variables named in the formula and formula2, or in the subset and the weights argument.

subset

expression indicating which subset of the rows of data should be used in the fit. All observations are included by default.

na.action

a missing-data filter function. This is applied to the model.frame after any subset argument has been used. Default is options()$na.action.

init

a list of length 3, initial values of the iteration. Its compoenents are: a vector of formula coefficients,a vector offormula2 coefficients and a step.fun step function of baseline cummulative hazard function. Default initial value is the estimate from naive separate glm and coxph models.

control

Object of class cureph.control specifying iteration limit and other control options. Default is cureph.control(...).

method

a character string specifying the method for estimation. The default method is the EM algorithm.

singular.ok

logical value indicating how to handle collinearity in the model matrix. If TRUE, the program will automatically skip over columns of the X matrix that are linear combinations of earlier columns. In this case the coefficients for such columns will be NA, and the variance matrix will contain zeros. For ancillary calculations, such as the linear predictor, the missing coefficients are treated as zeros.

var

a character string specifying the method for variance estimation. The default method is derived from the Louis formula.

...

other parameters passed to cureph.control.

Details

The function can handle left truncation.

"BFGS-Newton" method optimizes the discretized nonparametric likelihood directly. It has 3 steps. First, it roughly search for a local maximal by BFGS method with default setup. Second, it rescales the parameters proportional to the reciprocal of current gradient in another BFGS optimization. Finally, it searches for a solution to the score equations through a Newton's method with Armijo line search.

The "EM" method uses a “ghost copy” algorithm to accomodate left-truncation.

Both variance estimation methods are asymptotically correct, but they have undercoverage issue in case of a small event number. "Louis" is recommended among the two.

See Hou et al. (2016) for detail.

Author(s)

Jue (Marquis) Hou

References

Hou, J., Chambers, C. and Xu, R. (2016). "A nonparametric maximum likelihood approach for partially observed cured data with left truncation and right-censoring". To be submitted.

See Also

cureph.object, summary.cureph, survpred.cureph

Examples

# A simulated data set
data('sim.cureph.data')
# Or you may generate another one
sim.cureph.data = cureph.simgen()

# Check out the true coefficients and baseline survival
attributes(sim.cureph.data)

# Fit logistic-CoxPH cure-rate model
fit=cureph(Surv.cure(time,time2,event,origin=0,end=20)~Z1+Z2+Z3+Z4,data=sim.cureph.data)

# Check out the summary
summary(fit)

# Baseline cummulative hazard
basehaz.cureph(fit)