In this and the next few entries, we expand upon support in R and SAS for survival (time-to-event) models. We'll start with a small, artificial dataset of 19 subjects. Each subject contributes a pair of variables: the time and an indicator of whether the time is when the event occurred (event=TRUE) or when the subject was censored (event=FALSE).

time event 0.5 FALSE 1 TRUE 1 TRUE 2 TRUE 2 FALSE 3 TRUE 4 TRUE 5 FALSE 6 TRUE 7 FALSE 8 TRUE 9 TRUE 10 FALSE 12 TRUE 14 FALSE 14 TRUE 17 FALSE 20 TRUE 21 FALSE

Until an instant before time=1, no events were observed (only the censored observation), so the survival estimate is 1. At time=1, 2 subjects out of the 18 still at risk observed the event, so the survival function S(.) at time 1 is S(1) = 16/18 = 0.8889. The next failure occurs at time=2, with 16 still at risk, so S(2)=15/16 * 16/18 = 0.8333. Note that in addition to the event at time=2, there is a subject censored then, so the number at risk at time=3 is just 13 (so S(3) = 13/14 * 15*16 * 16/18 = 0.7738). The calculations continue until the final event is observed.

**R**

In R, we use the

`survfit()`function (section 5.1.19) within the

`survival`library to calculate the survival function across time.

library(survival) time = c(0.5, 1,1,2,2,3,4,5,6,7,8,9,10,12,14,14,17,20, 21) event = c(FALSE, TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE, TRUE, FALSE, TRUE, TRUE, FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, FALSE)

ds = data.frame(time, event) fit = survfit(Surv(time, event) ~ 1, data=ds)

The returned survival object includes a number of attributes, such as the survival estimates at each timepoint, the standard error of those estimates, and the number of subjects at risk.

> names(fit) [1] "n" "time" "n.risk" "n.event" "n.censor" "surv" "type" "std.err" [9] "upper" "lower" "conf.type" "conf.int" "call" > summary(fit) Call: survfit(formula = Surv(time, event) ~ 1, data = ds) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 18 2 0.889 0.0741 0.7549 1.000 2 16 1 0.833 0.0878 0.6778 1.000 3 14 1 0.774 0.0997 0.6011 0.996 4 13 1 0.714 0.1084 0.5306 0.962 6 11 1 0.649 0.1164 0.4570 0.923 8 9 1 0.577 0.1238 0.3791 0.879 9 8 1 0.505 0.1276 0.3078 0.829 12 6 1 0.421 0.1312 0.2285 0.775 14 5 1 0.337 0.1292 0.1587 0.714 20 2 1 0.168 0.1354 0.0348 0.815

**SAS**

We can read in the artificial data using an

`input`statement (section 1.1.8).

data ds; input time event; cards; 0.5 0 1 1 1 1 2 1 2 0 3 1 4 1 5 0 6 1 7 0 8 1 9 1 10 0 12 1 14 0 14 1 17 0 20 1 21 0 run;

proc lifetest data=ds; time time*event(0); run;

Here we denote censoring as being values where event is equal to 0. If we had a censoring indicator coded in reverse (1 = censoring), the second line might read

`time time*censored(1);`.

The survival function can be estimated in

`proc lifetest`(as shown in section 5.1.19). In a break from our usual practice, we'll include all of the output generated by

`proc lifetest`.

The LIFETEST Procedure Product-Limit Survival Estimates Survival Standard Number Number time Survival Failure Error Failed Left 0.0000 1.0000 0 0 0 19 0.5000* . . . 0 18 1.0000 . . . 1 17 1.0000 0.8889 0.1111 0.0741 2 16 2.0000 0.8333 0.1667 0.0878 3 15 2.0000* . . . 3 14 3.0000 0.7738 0.2262 0.0997 4 13 4.0000 0.7143 0.2857 0.1084 5 12 5.0000* . . . 5 11 6.0000 0.6494 0.3506 0.1164 6 10 7.0000* . . . 6 9 8.0000 0.5772 0.4228 0.1238 7 8 9.0000 0.5051 0.4949 0.1276 8 7 10.0000* . . . 8 6 12.0000 0.4209 0.5791 0.1312 9 5 14.0000 0.3367 0.6633 0.1292 10 4 14.0000* . . . 10 3 17.0000* . . . 10 2 20.0000 0.1684 0.8316 0.1354 11 1 21.0000* . . . 11 0 NOTE: The marked survival times are censored observations. Summary Statistics for Time Variable time Quartile Estimates Point 95% Confidence Interval Percent Estimate [Lower Upper) 75 20.0000 12.0000 . 50 12.0000 6.0000 20.0000 25 4.0000 1.0000 12.0000 Mean Standard Error 11.1776 1.9241 NOTE: The mean survival time and its standard error were underestimated because the largest observation was censored and the estimation was restricted to the largest event time. Summary of the Number of Censored and Uncensored Values Percent Total Failed Censored Censored 19 11 8 42.11

## 7 comments:

awesome thanks!!

Thank you! You made this so easy to get started.

Kudos to Giles Crane for pointing out that R can also compute quantiles, and confidence limits, of survival curves.

The quantile function has a method for survfit objects of the survival package:

quantile( survfit( fit), c(0.25, 0.50, 0.75) )

Nick

Great, much easier to understand. thanks!

Thanks for that. If you compare the n.risk at a particular time from the R output to the number left at a particular time from SAS, the two do not match. I am currently validating similar output from SAS using R, is there any way to make the R n.risk match the SAS number left, from within the survfit function in R? Thanks.

in the R example you forgot to define the data.frame "ds" before to use survfit(...)

Fixed! Thanks for pointing this out.

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