rsadd {relsurv}R Documentation

Fit an Additive model for Relative Survival

Description

The function fits an additive model to the data. The methods implemented are the maximum likelihood method, a glm model with a binomial error and a glm model with a poisson error.

Usage

rsadd(formula, data=parent.frame(), ratetable = survexp.us,
      int, na.action, method, init,bwin,centered,cause,control,...)

Arguments

formula a formula object, with the response on the left of a ~ operator, and the terms on the right. The terms consist of predictor variables separated by the + operator, along with a ratetable term. The ratetable term matches each subject to his/her expected cohort. If the variables are organized and named in the same way as in the population tables, the ratetable term can be omitted. The response must be a survival object as returned by the Surv function. The time must be in days.
data a data.frame in which to interpret the variables named in the formula.
ratetable a table of event rates, organized as a ratetable object, such as survexp.us.
int either a single value denoting the number of follow-up years or a vector specifying the intervals (in years) in which the hazard is constant (the times that are bigger than max(int) are censored. If missing, the intervals are set to be one year long and include the maximum observed follow-up time. The EM method does not need the intervals, only the maximum time can be specified.
na.action a missing-data filter function, applied to the model.frame, after any subset argument has been used. Default is options()$na.action.
method glm.bin or glm.poi for a glm model, EM for the EM algorithm and max.lik for the maximum likelihood model (default).
init vector of initial values of the iteration. Default initial value is zero for all variables.
bwin controls the bandwidth used for smoothing in the EM algorithm. The follow-up time is divided into quartiles and bwin specifies a factor by which the maximum between events time length on each interval is multiplied. The default bwin=-1 lets the function find an appropriate value. If bwin=0, no smoothing is applied.
centered if TRUE, all the variables are centered before fitting and the baseline excess hazard is calculated accordingly. Default is FALSE.
cause A vector of the same length as the number of cases. 0 for population deaths, 1 for disease specific deaths, 2 (default) for unknown. Can only be used with the EM method.
control a list of parameters for controlling the fitting process. See the documentation for glm.control for details.
... other arguments will be passed to glm.control.

Details

The methods using glm are methods for grouped data. The groups are formed according to the covariate values. This should be taken into account when fitting a model. The glm method returns life tables for groups specified by the covariates in groups.

The EM method output includes the smoothed baseline excess hazard lambda0, the cumulative baseline excess hazard Lambda0 and times at which they are estimated. The individual probabilites of dying due to the excess risk are returned as Nie. The default bwin=-1 value lets the function find an appropriate value for the smoothing band width. While this ensures an unbiased estimate, the procedure time is much longer. As the value found by the function is independent of the covariates in the model, the value can be read from the output (bwinfac) and used for refitting different models to the same data to save time.

Value

An object of class rsadd. In the case of method="glm.bin" and method="glm.poi" the class also inherits from glm which inherits from the class lm. Objects of this class have methods for the functions print and summary. An object of class rsadd is a list containing at least the following components:

data the data as used in the model, along with the variables defined in the rate table
ratetable the ratetable used.
int the maximum time (in years) used. All the events at and after this value are censored.
method the fitting method that was used.
linear.predictors the vector of linear predictors, one per subject.

References

Pohar M., Stare J. "Relative survival analysis in R." Computer Methods and Programs in Biomedicine, 81: 272-278, 2006.

See Also

rstrans, rsmul

Examples

data(slopop)
data(rdata)
fit <- rsadd(Surv(time,cens)~sex+as.factor(agegr)+ratetable(age=age*365,
           sex=sex,year=year), ratetable=slopop,data=rdata,int=5)

#check the goodness of fit
rs.br(fit)

#use the EM method and plot the smoothed baseline excess hazard
fit <- rsadd(Surv(time,cens)~sex+age+ratetable(age=age*365,
           sex=sex,year=year), ratetable=slopop,data=rdata,int=5,method="EM")
plot(lowess(fit$times,fit$lambda0,f=.2),type="l")

[Package relsurv version 1.4 Index]