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Computes an estimate of a survival curve for censored data using the Aalen-Johansen estimator. For ordinary (single event) survival this reduces to the Kaplan-Meier estimate.
# S3 method for formula
survfit(formula, data, weights, subset, na.action,
stype=1, ctype=1, id, cluster, robust, istate, timefix=TRUE,
etype, error, ...)an object of class "survfit".
See survfit.object for
details. Methods defined for survfit objects are
print, plot,
lines, and points.
a formula object, which must have a
Surv object as the
response on the left of the ~ operator and, if desired, terms
separated by + operators on the right.
One of the terms may be a strata object.
For a single survival curve the right hand side should be ~ 1.
a data frame in which to interpret the variables named in the formula,
subset and weights arguments.
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.
expression saying that only a subset of the rows of the data should be used in the fit.
a missing-data filter function, applied to the model frame, after any
subset argument has been used.
Default is options()$na.action.
the method to be used estimation of the survival curve: 1 = direct, 2 = exp(cumulative hazard).
the method to be used for estimation of the cumulative hazard: 1 = Nelson-Aalen formula, 2 = Fleming-Harrington correction for tied events.
identifies individual subjects, when a given person can have multiple lines of data.
used to group observations for the infinitesimal jackknife variance estimate, defaults to the value of id.
logical, should the function compute a robust variance. For multi-state survival curves this is true by default. For single state data see details, below.
for multi-state models, identifies the initial state of each subject or observation
process times through the aeqSurv function to
eliminate potential roundoff issues.
a variable giving the type of event. This has been superseded by multi-state Surv objects and is deprecated; see example below.
this argument is no longer used
The following additional arguments are passed to internal functions
called by survfit.
logical value, default is TRUE. If FALSE then standard error computations are omitted.
One of "none", "plain", "log" (the default),
"log-log", "logit" or "arcsin". Only
enough of the string to uniquely identify it is necessary.
The first option causes confidence intervals not to be
generated. The second causes the standard intervals
curve +- k *se(curve), where k is determined from
conf.int. The log option calculates intervals based on the
cumulative hazard or log(survival). The log-log option bases the
intervals on the log hazard or log(-log(survival)), the
logit option on log(survival/(1-survival))
and arcsin on arcsin(survival).
a character string to specify modified lower limits to the curve, the
upper limit remains unchanged.
Possible values are "usual" (unmodified),
"peto",
and "modified". The modified lower limit
is based on an "effective n" argument. The confidence
bands will agree with the usual calculation at each death time, but unlike
the usual bands the confidence interval becomes wider at each censored
observation. The extra width is obtained by multiplying the usual
variance by a factor m/n, where n is the number currently at risk and
m is the number at risk at the last death time. (The bands thus agree
with the un-modified bands at each death time.)
This is especially useful for survival curves with a long flat tail.
The Peto lower limit is based on the same "effective n" argument as the modified limit, but also replaces the usual Greenwood variance term with a simple approximation. It is known to be conservative.
numeric value specifying a time to start calculating survival
information.
The resulting curve is the survival conditional on surviving to
start.time.
the level for a two-sided confidence interval on the survival curve(s). Default is 0.95.
a logical value indicating whether standard errors should be
computed. Default is TRUE.
a logical value indicating whether to return the
infinitesimal jackknife (influence) values for each subject.
These contain the values of the derivative of each value
with respect to the case weights of each subject i:
influence.surv and influence.chaz
components. Alternatively, options of influence=1 or
influence=2 will return values for only the
survival or hazard curves, respectively.
this applies only to multi-state curves.
An optional vector giving the initial probability across
the states. If this is missing, then p0 is estimated using the
frequency of the starting states of all observations at risk
at start.time, or if that is not specified, at
the time of the first event.
an older argument that combined stype and
ctype, now deprecated. Legal values were "kaplan-meier"
which is equivalent to stype=1, ctype=1, "fleming-harrington"
which is equivalent to stype=2, ctype=1, and "fh2" which
is equivalent to stype=2, ctype=2.
If there is a data argument, then variables in the formula,
codeweights, subset, id, cluster and
istate arguments will be searched for in that data set.
The routine returns both an estimated probability in state and an
estimated cumulative hazard estimate.
The cumulative hazard estimate is the Nelson-Aalen (NA) estimate or the
Fleming-Harrington (FH) estimate, the latter includes a correction for
tied event times. The estimated probability in state can estimated
either using the exponential of the cumulative hazard, or as a direct
estimate using the Aalen-Johansen approach.
For single state data the AJ estimate reduces to the Kaplan-Meier and
the probability in state to the survival curve;
for competing risks data the AJ reduces to the cumulative incidence (CI)
estimator.
For backward compatability the type argument can be used instead.
When the data set includes left censored or interval censored data (or both), then the EM approach of Turnbull is used to compute the overall curve. Currently this algorithm is very slow, only a survival curve is produced, and it does not support a robust variance.
Robust variance:
If a robust is TRUE, or for multi-state
curves, then the standard
errors of the results will be based on an infinitesimal jackknife (IJ)
estimate, otherwise the standard model based estimate will be used.
For single state curves, the default for robust will be TRUE
if one of: there is a cluster argument, there
are non-integer weights, or there is a id statement
and at least one of the id values has multiple events, and FALSE otherwise.
The default represents our best guess about when one would most
often desire a robust variance.
When there are non-integer case weights and (time1, time2) survival
data the routine is at an impasse: a robust variance likely is called
for, but requires either id or cluster information to be
done correctly; it will default to robust=FALSE.
One unanticipated side effect of defaulting to a robust variance when
there are non integer case weights is that a fit using
interval censored data, which iterates an underlying KM using an
updated weight vector, now returns a robust variance by default.
Based on Sun (2001) this may be preferred, as the naive estimate
ignores the estimation of the weights. The prior behavior can be
obtained with robust= FALSE.
With the IJ estimate, the leverage values themselves can be returned
as arrays with dimensions: number of subjects, number of unique times,
and for a multi-state model, the number of unique states.
Be forwarned that these arrays can be huge. If there is a
cluster argument this first dimension will be the number of
clusters and the variance will be a grouped IJ estimate; this can be
an important tool for reducing the size.
A numeric value for the influence argument allows finer
control: 0= return neither (same as FALSE), 1= return the influence
array for probability in state, 2= return the influence array for the
cumulative hazard, 3= return both (same as TRUE).
Dorey, F. J. and Korn, E. L. (1987). Effective sample sizes for confidence intervals for survival probabilities. Statistics in Medicine 6, 679-87.
Fleming, T. H. and Harrington, D. P. (1984). Nonparametric estimation of the survival distribution in censored data. Comm. in Statistics 13, 2469-86.
Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. New York:Wiley.
Kyle, R. A. (1997). Moncolonal gammopathy of undetermined significance and solitary plasmacytoma. Implications for progression to overt multiple myeloma}, Hematology/Oncology Clinics N. Amer. 11, 71-87.
Link, C. L. (1984). Confidence intervals for the survival function using Cox's proportional hazards model with covariates. Biometrics 40, 601-610.
Sun, J. (2001). Variance estimation of a survival function for interval-censored data. Stat Med 20, 1949-1957.
Turnbull, B. W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. J Am Stat Assoc, 69, 169-173.
survfit.coxph for survival curves from Cox models,
survfit.object for a description of the components of a
survfit object,
print.survfit,
plot.survfit,
lines.survfit,
coxph,
Surv.
#fit a Kaplan-Meier and plot it
fit <- survfit(Surv(time, status) ~ x, data = aml)
plot(fit, lty = 2:3)
legend(100, .8, c("Maintained", "Nonmaintained"), lty = 2:3)
#fit a Cox proportional hazards model and plot the
#predicted survival for a 60 year old
fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian)
plot(survfit(fit, newdata=data.frame(age=60)),
xscale=365.25, xlab = "Years", ylab="Survival")
# Here is the data set from Turnbull
# There are no interval censored subjects, only left-censored (status=3),
# right-censored (status 0) and observed events (status 1)
#
# Time
# 1 2 3 4
# Type of observation
# death 12 6 2 3
# losses 3 2 0 3
# late entry 2 4 2 5
#
tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4),
status=rep(c(1,0,2),4),
n =c(12,3,2,6,2,4,2,0,2,3,3,5))
fit <- survfit(Surv(time, time, status, type='interval') ~1,
data=tdata, weight=n)
#
# Three curves for patients with monoclonal gammopathy.
# 1. KM of time to PCM, ignoring death (statistically incorrect)
# 2. Competing risk curves (also known as "cumulative incidence")
# 3. Multi-state, showing Pr(in each state, at time t)
#
fitKM <- survfit(Surv(stop, event=='pcm') ~1, data=mgus1,
subset=(start==0))
fitCR <- survfit(Surv(stop, event) ~1,
data=mgus1, subset=(start==0))
fitMS <- survfit(Surv(start, stop, event) ~ 1, id=id, data=mgus1)
if (FALSE) {
# CR curves show the competing risks
plot(fitCR, xscale=365.25, xmax=7300, mark.time=FALSE,
col=2:3, xlab="Years post diagnosis of MGUS",
ylab="P(state)")
lines(fitKM, fun='event', xmax=7300, mark.time=FALSE,
conf.int=FALSE)
text(3652, .4, "Competing risk: death", col=3)
text(5840, .15,"Competing risk: progression", col=2)
text(5480, .30,"KM:prog")
}
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