R: Quantiles from a survfit object

quantile.survfit {survival} | R Documentation

## Quantiles from a survfit object

### Description

Retrieve quantiles and confidence intervals for them from a survfit object.

### Usage

    ## S3 method for class 'survfit'
    quantile(x, probs = c(0.25, 0.5, 0.75), conf.int = TRUE,
      tolerance= sqrt(.Machine$double.eps), ...)
    ## S3 method for class 'survfitms'
    quantile(x, probs = c(0.25, 0.5, 0.75), conf.int = TRUE,
      tolerance= sqrt(.Machine$double.eps), ...)

### Arguments

`x` | a result of the survfit function
`probs` | numeric vector of probabilities with values in [0,1]
`conf.int` | should lower and upper confidence limits be returned?
`tolerance` | tolerance for checking that the survival curve exactly equals one of the quantiles
`...` | optional arguments for other methods

### Details

The kth quantile for a survival curve S(t) is the location at which a horizontal line at height p= 1-k intersects the plot of S(t). Since S(t) is a step function, it is possible for the curve to have a horizontal segment at exactly 1-k, in which case the midpoint of the horizontal segment is returned. This mirrors the standard behavior of the median when data is uncensored. If the survival curve does not fall to 1-k, then that quantile is undefined.

In order to be consistent with other quantile functions, the argument `prob` of this function applies to the cumulative distribution function F(t) = 1-S(t).

Confidence limits for the values are based on the intersection of the horizontal line at 1-k with the upper and lower limits for the survival curve. Hence confidence limits use the same p-value as was in effect when the curve was created, and will differ depending on the `conf.type` option of `survfit`. If the survival curves have no confidence bands, confidence limits for the quantiles are not available.

When a horizontal segment of the survival curve exactly matches one of the requested quantiles the returned value will be the midpoint of the horizontal segment; this agrees with the usual definition of a median for uncensored data. Since the survival curve is computed as a series of products, however, there may be round off error. Assume for instance a sample of size 20 with no tied times and no censoring. The survival curve after the 10th death is (19/20)(18/19)(17/18) ... (10/11) = 10/20, but the computed result will not be exactly 0.5. Any horizontal segment whose absolute difference with a requested percentile is less than `tolerance` is considered to be an exact match.

### Value

The quantiles will be a vector if the `survfit` object contains only a single curve, otherwise it will be a matrix or array. In this case the last dimension will index the quantiles.

If confidence limits are requested, then result will be a list with components `quantile`, `lower`, and `upper`, otherwise it is the vector or matrix of quantiles.

### Author(s)

Terry Therneau

### See Also

`survfit`, `print.survfit`, `qsurvreg`

### Examples

    fit <- survfit(Surv(time, status) ~ ph.ecog, data=lung)
    quantile(fit)

    cfit <- coxph(Surv(time, status) ~ age + strata(ph.ecog), data=lung)
    csurv<- survfit(cfit, newdata=data.frame(age=c(40, 60, 80)),
                      conf.type ="none")
    temp <- quantile(csurv, 1:5/10)
    temp[2,3,]  # quantiles for second level of ph.ecog, age=80
    quantile(csurv[2,3], 1:5/10)  # quantiles of a single curve, same result

[Package survival version 3.2-7 Index]