Cox Survival Estimates

Compute survival probabilities and optional confidence limits for Cox survival models. If x=TRUE, y=TRUE were specified to cph, confidence limits use the correct formula for any combination of predictors. Otherwise, if surv=TRUE was specified to cph, confidence limits are based only on standard errors of log(S(t)) at the mean value of \(X\beta\). If the model contained only stratification factors, or if predictions are being requested near the mean of each covariable, this approximation will be accurate. Unless times is given, at most one observation may be predicted.

Usage

survest(fit, ...)
# S3 method for class 'cph'
survest(fit, newdata, linear.predictors, x, times, 
        fun, loglog=FALSE, conf.int=0.95, type, vartype,
        conf.type=c("log", "log-log", "plain", "none"), se.fit=TRUE,
        what=c('survival','parallel'),
        individual=FALSE, ...)

Arguments

fit: a model fit from cph
newdata: a data frame containing predictor variable combinations for which predictions are desired
linear.predictors: a vector of linear predictor values (centered) for which predictions are desired. If the model is stratified, the "strata" attribute must be attached to this vector (see example).
x: a design matrix at which to compute estimates, with any strata attached as a "strata" attribute. Only one of newdata, linear.predictors, or x may be specified. If none is specified, but times is specified, you will get survival predictions at all subjects' linear predictor and strata values.
times: a vector of times at which to get predictions. If omitted, predictions are made at all unique failure times in the original input data.
loglog: set to TRUE to make the log-log transformation of survival estimates and confidence limits.
fun: any function to transform the estimates and confidence limits (loglog is a special case)
conf.int: set to FALSE or 0 to suppress confidence limits, or e.g. .95 to cause 0.95 confidence limits to be computed
type: see survfit.coxph
vartype: see survfit.coxph
conf.type: specifies the basis for computing confidence limits. "log" is the default as in the survival package.
se.fit: set to TRUE to get standard errors of log predicted survival (no matter what conf.type is). If FALSE, confidence limits are suppressed.
individual: set to TRUE to have survfit interpret newdata as specifying a covariable path for a single individual (represented by multiple records).
what: Normally use what="survival" to estimate survival probabilities at times that may not correspond to the subjects' own times. what="parallel" assumes that the length of times is the number of subjects (or one), and causes survest to estimate the ith subject's survival probability at the ith value of times (or at the scalar value of times). what="parallel" is used by val.surv for example.
...: unused

Value

If times is omitted, returns a list with the elements time, n.risk, n.event, surv, call (calling statement), and optionally std.err, upper, lower, conf.type, conf.int. The estimates in this case correspond to one subject. If times is specified, the returned list has possible components time, surv, std.err, lower, and upper. These will be matrices (except for time) if more than one subject is being predicted, with rows representing subjects and columns representing times. If times has only one time, these are reduced to vectors with the number of elements equal to the number of subjects.

Details

The result is passed through naresid if newdata, linear.predictors, and x are not specified, to restore placeholders for NAs.

Author

Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com

Examples

# Simulate data from a population model in which the log hazard
# function is linear in age and there is no age x sex interaction
# Proportional hazards holds for both variables but we
# unnecessarily stratify on sex to see what happens
require(survival)
n <- 1000
set.seed(731)
age <- 50 + 12*rnorm(n)
label(age) <- "Age"
sex <- factor(sample(c('Male','Female'), n, TRUE))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
dt <- -log(runif(n))/h
label(dt) <- 'Follow-up Time'
e <- ifelse(dt <= cens,1,0)
dt <- pmin(dt, cens)
units(dt) <- "Year"
dd <- datadist(age, sex)
options(datadist='dd')
Srv <- Surv(dt,e)


f <- cph(Srv ~ age*strat(sex), x=TRUE, y=TRUE) #or surv=T
#> Error in Design(data, formula, specials = c("strat", "strata")): dataset dd not found for options(datadist=)
survest(f, expand.grid(age=c(20,40,60),sex=c("Male","Female")),
      times=c(2,4,6), conf.int=.9)
#> Error: object 'f' not found
f <- update(f, surv=TRUE)
#> Error: object 'f' not found
lp <- c(0, .5, 1)
f$strata   # check strata names
#> Error: object 'f' not found
attr(lp,'strata') <- rep(1,3)  # or rep('sex=Female',3)
survest(f, linear.predictors=lp, times=c(2,4,6))
#> Error: object 'f' not found

# Test survest by comparing to survfit.coxph for a more complex model
f <- cph(Srv ~ pol(age,2)*strat(sex), x=TRUE, y=TRUE)
#> Error in Design(data, formula, specials = c("strat", "strata")): dataset dd not found for options(datadist=)
survest(f, data.frame(age=median(age), sex=levels(sex)), times=6)
#> Error: object 'f' not found

age2 <- age^2
f2 <- coxph(Srv ~ (age + age2)*strata(sex))
new <- data.frame(age=median(age), age2=median(age)^2, sex='Male')
summary(survfit(f2, new), times=6)
#> Call: survfit(formula = f2, newdata = new)
#> 
#>                 1 
#>         time       n.risk      n.event     survival      std.err lower 95% CI 
#>       6.0000     285.0000      56.0000       0.8839       0.0178       0.8497 
#> upper 95% CI 
#>       0.9196 
#> 
new$sex <- 'Female'
summary(survfit(f2, new), times=6)
#> Call: survfit(formula = f2, newdata = new)
#> 
#>                 1 
#>         time       n.risk      n.event     survival      std.err lower 95% CI 
#>       6.0000     206.0000      90.0000       0.7731       0.0246       0.7264 
#> upper 95% CI 
#>       0.8228 
#> 

options(datadist=NULL)