coxinterval (version 1.0)

coxaalenic: Cox-Aalen model for interval-censored survival data

Description

Fit a Cox-Aalen model to interval-censored survival data with fixed covariates.

Usage

coxaalenic(formula, data = parent.frame(), subset, init = NULL,
           formula.timereg = NULL, init.timereg = FALSE,
           close.cplex = TRUE, control, ...)

Arguments

formula

an expression of the form response ~ terms, where response is a survival object returned by the Surv function and terms contains at least one multipli

data

an optional data frame in which to interpret the variables named in the arguments formula and formula.timereg.

subset

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

init

a list with elements named coef and basehaz. The coef element should be a scalar or vector specifying the initial values of the multiplicative regression coefficient. If init = NULL or

formula.timereg

a list of formula objects specifying models to fit with the timereg package's cox.aalen function using right-censored observations in data. Here the sho

init.timereg

a logical value indicating that init should be overrided by estimates based on the cox.aalen fit to the first model in formula.timereg.

close.cplex

a logical value indicating that CPLEX data structures should be freed when coxaalenic exits.

control

a named list of parameters controlling the model fit, as returned by the function coxaalenic.control. This defaults to coxaalenic.control().

...

additional arguments to be passed to coxaalenic.control.

Value

• An object of the class "coxinterval" and "coxaalenic", which is a list with the following components.
• call
  the matched call to coxic.
• n
  size of the sample used in the model fit.
• p
  number of (multiplicative) regression coefficients.
• coef
  a named p vector of regression coefficients.
• var
  a named p by p covariance matrix of the regression coefficients.
• basehaz
  a data frame giving the cumulative regression functions evaluated at time points given by the maximal intersections of the censoring intervals.
• init
  list of initial values used in the model fit.
• loglik
  a vector giving the initial and final log-likelihood values.
• iter
  number of iterations needed to achieve the model fit.
• maxnorm
  the maximum norm of the difference between the penultimate and final parameter values.
• gradnorm
  the inner product between the final parameter value and the score function.
• cputime
  the processing time for parameter and variance estimation.
• fit.timereg
  an unnamed list whose components give the cox.aalen fit to any models specified by the formula.timereg argument.
• na.action
  the "na.action" attribute of the model frame.
• censor.rate
  a vector giving the rates of left-, interval- and right-censoring among the observations used in the model fit.
• control
  a named list of arguments passed to coxic.control.

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Details

A valid response in the formula argument can be expressed as Surv(, , type = "interval2") where (, ] is the censoring interval for the survival time. Following the survival package's type = "interval2" censoring for the Surv function, we use the convention that any right-censoring times are provided in the variable and is set to the NA value.

Terms in the formula have either time-varying additive effects on the survival hazard as in Aalen's additive regression model, or fixed multiplicative effects as in the Cox model. Multiplicative terms are distinguished by applying timereg's prop function to each corresponding variable.

coxaalenic requires C functions, which are loaded only if coxinterval is installed from source on a system with (http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/){ CPLEX}. Refer to the package's README for detailed instructions.

References

Boruvka, A. and Cook, R. J. (2014a) A Cox-Aalen model for interval-censored data.

Martinussen, T. and Scheike, T. H. (2006) Dynamic Regression Models for Survival Data. New York: Springer.

Scheike, T. H. and Zhang, M.-J. (2002) http://dx.doi.org/10.1111/1467-9469.00065{ An additive-multiplicative Cox-Aalen regression model}. Scandinavian Journal of Statistics 29, 75--88.

See Also

cox.aalen, prop, Surv

Examples

# Fit a Cox model to the breast cosmesis dataset
if (is.loaded("coxaalenic", "coxinterval")) {
  fit <- coxaalenic(Surv(left, right, type = "interval2") ~ prop(treat),
                    data = cosmesis)
  fit
  plot(fit$basehaz, type = "s")
}