Survival Curve Object

This class of objects is returned by the survfit class of functions to represent a fitted survival curve. For a multi-state model the object has class c('survfitms', 'survfit').

Objects of this class have methods for the functions print, summary, plot, points and lines. The print.survfit method does more computation than is typical for a print method and is documented on a separate page.

Structure

The following components must be included in a legitimate survfit or survfitms object.

Arguments

n

total number of observations in each curve.

time

the time points at which the curve has a step.

n.risk

the number of subjects at risk at t.

n.event

the number of events that occur at time t.

n.enter

for counting process data only, and only if there was an id argument, the number of subjects that enter the risk set during the current interval. If there are event/censoring times at 1, 3, 5 for instance, someone who enters at time 1 is counted in the (1, 3] interval, i.e., appears in the row for time 3.

n.censor

for counting process data only, the number of subjects who exit the risk set, without an event, at time t. (For right censored data, this number can be computed from the successive values of the number at risk).

surv

the estimate of survival at time t+0. This may be a vector or a matrix. The latter occurs when a set of survival curves is created from a single Cox model, in which case there is one column for each covariate set.

pstate

a multi-state survival will have the pstate component instead of surv. It will be a matrix containing the estimated probability of each state at each time, one column per state.

std.err

for a survival curve this contains standard error of the cumulative hazard or -log(survival), for a multi-state curve it contains the standard error of prev. This difference is a reflection of the fact that each is the natural calculation for that case.

cumhaz

optional. Contains the cumulative hazard for each possible transition.

counts

optional. If weights were used, the n.risk etc elements contain weighted sums; the counts matrix will contain unweighted values. Weighted values are normally more useful for further computation, unweighted may be preferred for labeling or printout.

strata

if there are multiple curves, this component gives the number of elements of the time vector corresponding to the first curve, the second curve, and so on. The names of the elements are labels for the curves.

upper

optional upper (2-sided) confidence limit for the survival curve or probability in state

lower

optional lower (2-sidedconfidence limit for the survival curve or probability in state

t0

optional, the starting time for the curve

p0, sp0

for a multistate object, the distribution of starting states. If the curve has a strata dimension, this will be a matrix one row per stratum. The sp0 element has the standard error of p0, if p0 was estimated.

newdata

for survival curves from a fitted model, this contains the covariate values for the curves

n.id

the total number of unique id values that contributed to the curve. This is only available if the original call used the id option.

conf.type

the approximation used to compute the confidence limits.

conf.int

the level of the confidence limits, e.g. 90 or 95%.

transitions

for multi-state data, the total number of transitions of each type.

na.action

the returned value from the na.action function, if any. It will be used in the printout of the curve, e.g., the number of observations deleted due to missing values.

call

an image of the call that produced the object.

type

type of survival censoring.

influence.p, influence.c

optional influence matrices for the pstate (or surv) and for the cumhaz estimates. A list with one element per stratum, each element of the list is an array indexed by subject, time, state.

version

the version of the object. Will be missing, 2, or 3

Subscripts

Survfit objects can be subscripted. This is often used to plot a subset of the curves, for instance. From the user's point of view the survfit object appears to be a vector, matrix, or array of curves. The first dimension is always the underlying number of curves or “strata”; for multi-state models the state is always the last dimension. Predicted curves from a Cox model can have a second dimension which is the number of different covariate prediction vectors.

Details

The survfit object has evolved over time: when first created there was no thought of multi-state models for instance. This evolution has almost entirely been accomplished by the addition of new elements.

For both plots of the curves and computation of the restricted mean time in state (RMTS) we need the concept of a starting point t0 and starting prevalence of the states p0 for each curve. (Sojourn time, area under the curve and restricted mean survival time are other labels for the RMTS). Time 0 is not, by default, included as part of the standard tableau of results, i.e., time, number at risk, number of events, etc. For simple survival with a 0/1 status variable, the starting state p0 is the obvious default of "everyone alive", and t0 is formally not discernable from the data and so was left out. (A design decision made in 1986, and now far too late to change.) However, for plots t0 is assumed to be the minimum of 0 and all observed times. Negative survival times are unusual but not invalid. Multi-state survival curves include t0 and p0 as a part of the returned object. The first is a single value for all curves, the second is per curve.

The survfit0 routine can be used to add these values to the main curve data, this is done by the default print, plot, and summary methods for survfit objects. The methods vignette has discussion of the rationale of how t0 and p0 are chosen in the multi-state case. Notice that if there is an event at time t0, e.g., a death on day 0 for competing risks, then p0 will contain the prevalence just before that event occured.

See also

plot.survfit, summary.survfit, print.survfit, survfit, survfit0