coxaalen {coxinterval}R Documentation

Cox-Aalen model for interval-censored survival data


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


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



an expression of the form response ~ terms, where response is an object returned by the Surv function and terms contains at least one multiplicative term identified by the prop function from the timereg package.


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


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


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 coef = NULL, this coefficient will be initialized to zero. The element basehaz should be a matrix or data frame whose columns represent time and the corresponding value for the cumulative baseline hazard function and any remaining additive cumulative coefficients. Initial values are obtained by linear interpolation or extrapolation at observation times relevant in the data. If init = NULL or basehaz = NULL, the cumulative baseline hazard function is initialized to a linear function of time and any cumulative coefficients are started at zero.


an optional formula object specifying a model to fit with the timereg package's cox.aalen function using right-censored observations. Here the shorthand ~ . refers to the same terms given in formula. Multiple formula objects can be provided as a list.


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


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.


A valid response in the formula argument can be expressed as

Surv(<left>, <right>, type = "interval2")

where (<left>, <right>] 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 <left> and <right> 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 IBM ILOG CPLEX Optimization Studio. Refer to the package's INSTALL file for detailed instructions.


An object of the class "coxinterval" and "coxaalen", which is a list with the following components.


the matched call to coxaalen.


size of the sample used in the model fit.


number of (multiplicative) regression coefficients.


a named p vector of regression coefficients.


a named p by p covariance matrix of the regression coefficients.


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.


list of initial values used in the model fit.


a vector giving the log-likelihood at initiation and each iteration.


number of iterations needed to meet the stopping criteria.


the maximum norm of the difference between the penultimate and final parameter values.


the inner product between the final parameter value and the score function.


the processing time for parameter and variance estimation.


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.


the "na.action" attribute of the model frame.


a vector giving the rates of exact, left-censored, interval-censored and right-censored observations used in the model fit.


a named list of arguments passed to coxaalen.control.


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.


Boruvka, A. and Cook, R. J. (2015) 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) An additive-multiplicative Cox-Aalen regression model. Scandinavian Journal of Statistics 29, 75–88.

See Also

cox.aalen, prop, Surv


# 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),
                  ! ~ .))

[Package coxinterval version 1.2 Index]