Inverse estimation for Kaplan-Meier survival curves

Inverts a Kaplan-Meier estimate of the survival function: given a survival probability y0, these methods estimate the survival time \(t\) at which \(S(t) = y_0\), along with a confidence interval obtained by inverting the pointwise confidence band for the survival curve (the same inversion idea used by invest() for regression models). For example, the default y0 = 0.5 gives the median survival time.

Usage

# S3 method for class 'survfit'
invest(object, y0 = 0.5, level = object$conf.int, ...)

# S3 method for class 'Surv'
invest(object, y0 = 0.5, level = 0.95, ...)

Arguments

object

An object that inherits from class "survfit" (a fitted Kaplan-Meier curve from survival::survfit()) or class "Surv" (a censored response object from survival::Surv(), for which a Kaplan-Meier curve is fit internally).

y0

A numeric scalar in (0, 1) giving the survival probability at which to invert the curve. Default is 0.5 (i.e., the median survival time).

level

A numeric scalar between 0 and 1 giving the confidence level for the interval. For "survfit" objects, this must match the conf.int level the curve was fit with (the default); refit with survival::survfit(..., conf.int = level) for a different level. For "Surv" objects, the internal fit uses level directly.

...

Additional optional arguments. At present, no optional arguments are used.

Value

An object of class "invest" containing the components estimate, lower, upper, and interval (always "inversion"). Components are NA whenever the survival curve (or a confidence limit) never drops below y0; in particular, upper is frequently NA in small samples, meaning the upper confidence limit is indeterminate (infinite).

Note

These methods only support a single survival curve; for a "survfit" object with multiple strata, invert each stratum's curve separately (e.g., via survfit[i] subscripting).

See also

The quantile.survfit method in the survival package, which these methods use for the inversion and which expresses the same calculation in terms of quantiles of the event-time distribution (i.e., probs = 1 - y0).

Examples

if (requireNamespace("survival", quietly = TRUE)) {

  # Median survival time (with 95% confidence limits) for the acute
  # myelogenous leukemia data
  km <- survival::survfit(survival::Surv(time, status) ~ 1,
                          data = survival::aml)
  invest(km)  # y0 = 0.5 is the median

  # Same, but fitting the curve internally from a censored response
  invest(survival::Surv(survival::aml$time, survival::aml$status))

  # Time at which 75% survival is reached
  invest(km, y0 = 0.75)

}
#> estimate    lower    upper 
#>       12        8       30