coxinterval (version 1.2)

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

Description

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

Usage

coxaalen(formula, data = parent.frame(), subset, init = NULL,
         formula.timereg = NULL, init.timereg = FALSE, control, ...)

Arguments

formula

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

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

an optional formula object specifying a model to fit with the timereg package's cox.aalen function using right-censored observations. Here the shorthand ~ .

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.

control

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

...

additional arguments to be passed to coxaalen.control.

Value

• An object of the class "coxinterval" and "coxaalen", which is a list with the following components.
• call
  the matched call to coxaalen.
• 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 right endpoints of the maximal intersections among the censoring intervals.
• init
  list of initial values used in the model fit.
• loglik
  a vector giving the log-likelihood at initiation and each iteration.
• iter
  number of iterations needed to meet the stopping criteria.
• 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
  the cox.aalen fit to any models specified by the formula.timereg argument. If formula.timereg is a list of formula objects, fit.timereg is an unnamed list following the same order.
• na.action
  the "na.action" attribute of the model frame.
• censor.rate
  a vector giving the rates of exact, left-censored, interval-censored and right-censored observations used in the model fit.
• control
  a named list of arguments passed to coxaalen.control.
• data
  a list containing the maximal intersections among the censoring intervals and model matrices for the multiplicative and additive terms in formula. This component is returned only if the coxaalen.control argument data is true.

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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 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.

coxaalen depends on libraries that are loaded only if coxinterval is installed from source on a system with http://www-03.ibm.com/software/products/en/ibmilogcpleoptistud/{ IBM ILOG CPLEX Optimization Studio}. Refer to the package's INSTALL file for detailed instructions.

References

Boruvka, A. and Cook, R. J. (2015) http://dx.doi.org/10.1111/sjos.12113{ A Cox-Aalen model for interval-censored data}. Scandinavian Journal of Statistics 42, 414--426.

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("coxaalen", "coxinterval")) {
  fit <- coxaalen(Surv(left, right, type = "interval2") ~ prop(treat),
                  data = cosmesis, init.timereg = TRUE,
                  formula.timereg = list(Surv(pmax(left, right, na.rm = TRUE),
                  !is.na(right)) ~ .))
  summary(fit)
}