randomForestSRC (version 2.8.0)

plot.survival: Plot of Survival Estimates

Description

Plot various survival estimates.

Usage

# S3 method for rfsrc
plot.survival(x, plots.one.page = TRUE, 
  show.plots = TRUE, subset, collapse = FALSE,
  haz.model = c("spline", "ggamma", "nonpar", "none"),
  k = 25, span = "cv", cens.model = c("km", "rfsrc"), ...)

Arguments

x

An object of class (rfsrc, grow) or (rfsrc, predict).

plots.one.page

Should plots be placed on one page?

show.plots

Should plots be displayed?

subset

Vector indicating which individuals we want estimates for. All individuals are used if not specified.

collapse

Collapse the survival and cumulative hazard function across the individuals specified by subset? Only applies when subset is specified.

haz.model

Method for estimating the hazard. See details below. Applies only when subset is specified.

k

The number of natural cubic spline knots used for estimating the hazard function. Applies only when subset is specified.

span

The fraction of the observations in the span of Friedman's super-smoother used for estimating the hazard function. Applies only when subset is specified.

cens.model

Method for estimating the censoring distribution used in the inverse probability of censoring weights (IPCW) for the Brier score:

km:

Uses the Kaplan-Meier estimator.

rfscr:

Uses random survival forests.

...

Further arguments passed to or from other methods.

Value

Invisibly, the conditional and unconditional Brier scores, and the integrated Brier score (if they are available).

Details

If subset is not specified, generates the following three plots (going from top to bottom, left to right):

1. Forest estimated survival function for each individual (thick red line is overall ensemble survival, thick green line is Nelson-Aalen estimator).

2. Brier score (0=perfect, 1=poor, and 0.25=guessing) stratified by ensemble mortality. Based on the IPCW method described in Gerds et al. (2006). Stratification is into 4 groups corresponding to the 0-25, 25-50, 50-75 and 75-100 percentile values of mortality. Red line is the overall (non-stratified) Brier score.

3. Plot of mortality of each individual versus observed time. Points in blue correspond to events, black points are censored observations.

When subset is specified, then for each individual in subset, the following three plots are generated:

1. Forest estimated survival function.

2. Forest estimated cumulative hazard function (CHF) (displayed using black lines). Blue lines are the CHF from the estimated hazard function. See the next item.

3. A smoothed hazard function derived from the forest estimated CHF (or survival function). The default method, haz.model="spline", models the log CHF using natural cubic splines as described in Royston and Parmar (2002). The lasso is used for model selection, implemented using the glmnet package (this package must be installed for this option to work). If haz.model="ggamma", a three-parameter generalized gamma distribution (using the parameterization described in Cox et al, 2007) is fit to the smoothed forest survival function, where smoothing is imposed using Friedman's supersmoother (implemented by supsmu). If haz.model="nonpar", Friedman's supersmoother is applied to the forest estimated hazard function (obtained by taking the crude derivative of the smoothed forest CHF). Finally, setting haz.model="none" suppresses hazard estimation and no hazard estimate is provided.

   At this time, please note that all hazard estimates are considered experimental and users should interpret the results with caution.

Note that when the object x is of class (rfsrc, predict) not all plots will be produced. In particular, Brier scores are not calculated.

Only applies to survival families. In particular, fails for competing risk analyses. Use plot.competing.risk in such cases.

Whenever possible, out-of-bag (OOB) values are used.

References

Cox C., Chu, H., Schneider, M. F. and Munoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374.

Gerds T.A and Schumacher M. (2006). Consistent estimation of the expected Brier score in general survival models with right-censored event times, Biometrical J., 6:1029-1040.

Graf E., Schmoor C., Sauerbrei W. and Schumacher M. (1999). Assessment and comparison of prognostic classification schemes for survival data, Statist. in Medicine, 18:2529-2545.

Ishwaran H. and Kogalur U.B. (2007). Random survival forests for R, Rnews, 7(2):25-31.

Royston P. and Parmar M.K.B. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects, Statist. in Medicine, 21::2175-2197.

See Also

plot.competing.risk, predict.rfsrc, rfsrc

Examples

# NOT RUN {
## veteran data
data(veteran, package = "randomForestSRC") 
plot.survival(rfsrc(Surv(time, status)~ ., veteran), cens.model = "rfsrc")

## pbc data
data(pbc, package = "randomForestSRC") 
pbc.obj <- rfsrc(Surv(days, status) ~ ., pbc)

# default spline approach
plot.survival(pbc.obj, subset = 3)
plot.survival(pbc.obj, subset = 3, k = 100)

# three-parameter generalized gamma is approximately the same
# but notice that its CHF estimate (blue line) is not as accurate
plot.survival(pbc.obj, subset = 3, haz.model = "ggamma")

# nonparametric method is too wiggly or undersmooths
plot.survival(pbc.obj, subset = 3, haz.model = "nonpar", span = 0.1)
plot.survival(pbc.obj, subset = 3, haz.model = "nonpar", span = 0.8)

# }