Regression Model for Censored Data

DESCRIPTION:

Computes a parametric survival model for censored data.

USAGE:

censorReg(formula=formula(data), data=sys.parent(),
     weights=rep(1,n), truncation, subset, na.action,
     distribution="weibull", threshold=0, initial,
     fixed=list(), control=NULL, model=F, x=F, y=F, ...) 

REQUIRED ARGUMENTS:

formula
a formula expression as for other regression models. The response is usually a an object of class "censor" as computed by the censor function. See the documentation for censor, lm, and formula for details. Two special variable types are handled on the right-hand-side. These are: strata() - indicates that the sample is to be split into sub-samples, and as separate model fit in each subsample. See strata for additional details. offset() - the offset for each observation is subtracted from the (transformed if one of the logged distribution is used) response and truncation times prior to fitting the model.

OPTIONAL ARGUMENTS:

data
a data frame in which to interpret the variables named in the formula, subset and weights argument.
weights
vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the likelihood contribution for each observation. In this way, and in the computation of degrees of freedom, the weights behave like frequencies. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous, compared to use of the subset argument.
truncation
a class censor object that is used to indicate a truncation distribution. The usual arguments to censor are used in creating the truncation object, but notice that right truncation means that the failure (or censoring) must occur between zero and the truncation point, left truncation means that the failure (or censoring) must occur between the truncation point and infinity, and interval truncation means that the failure (or censoring) must occur within the truncation interval. In particular, this implies that an observation that is right censored cannot also come from a right- or interval-truncation distribution, and similarly for other combinations of censoring and truncation types.
subset
expression saying that only a subset of the rows of the data should be used in the fit.
na.action
a missing-data filter function, applied to the model.frame, after any subset argument has been used. Default is options()$na.action.
distribution
assumed distribution for the (possibly censored) response variable. There are ten basic distributions - minimum extreme value, weibull, gaussian (or normal), lognormal, logistic, loglogistic, exponential, logexponential, rayleigh and lograyleigh. All ten distributions have a scale parameter. The rayleigh distribution is the minimum extreme value distribution with the scale parameter fixed at 0.5. The exponential distribution is the minimum extreme value distribution with the scale parameter fixed at 1.
threshold
A value to be subtracted from each of the failure and censoring times (and the truncation intervals as well). This is the time during which no observation can fail. If not specified, this defaults to 0.0. If a logical value T is input, threshold is computed as the smallest failure time minus 10% of its absolute value. An alternate estimate of threshold is obtained by specifying threshold="Linearized-qq" which computes an optimization to minimize the curvature of a quantile-quantile plot of the quantiles of the response versus the quantiles obtained from a Kaplan-Meier estimate of survival.
initial
optional vector of initial values for the model parameters. If used, the linear model parameters are first, followed by the scale parameter (not the Log(scale), and providing that the scale parameter is not fixed).
fixed
a list of fixed parameters. The names in the list must be valid names of variables in the model.
control
a list of options for controlling the iterations. These may include: maxiter - the maximum number of iterations. This defaults to 500. rel.tolerance - the convergence criterion. When the scaled change in the all parameter estimates is less than rel.tolerance, convergence is assumed. This defaults to 0.0001. escale - a vector of scale factors, one for each parameter. By default, these all equal 10000. If a scalar is input, it is applied to all elements.
model
a logical value, if TRUE then the model frame is included as component model in the object returned by the function.
x
a logical value, if TRUE then the model matrix is included as component x in the object returned by the function.
y
a logical value, if TRUE then the response is included as component y in the object returned by the function.

VALUE:

If there are no stratification variables, or if there is only a single strata, then an object of class "censorReg" is returned. See censorReg.object for details. If there are stratification variables, than a list of objects of class "censorReg" is produced. This is a class "censorRegList" object.

COMPUTATION:

A Fletcher-Powell algorithm is used in model fitting. The basic estimation code comes from W. Q. Meeker and is described in Meeker and Duke (1981) which details a program named CENSOR. Recently, W. Q. Meeker has refined the estimation algorithms, making them more general and stable.

REFERENCES::

Meeker, W. Q. and Duke, S. D. (1981). CENSOR - A User-Oriented Computer Program for Life Data Analysis. The American Statistician, 35, 112.

SEE ALSO:

, , , , , .

EXAMPLES:

# Fit an exponential model 
censorReg(censor(futime,fustat) ~ ecog.ps + rx, data=ovarian, 
        distribution="exponential", fixed=list(scale=1)) 
censorReg(censor(days, event)~voltage, data=capacitor2,
         weights=weights, fixed=list(voltage=-0.30))