[R] confidence interval for survfit

Terry Therneau therneau at mayo.edu
Fri Mar 15 15:01:27 CET 2013

The first thing you are missing is the documentation -- try ?survfit.object.
      fit <- survfit(Surv(time,status)~1,data)
fit$std.err will contain the standard error of the cumulative hazard or -log(survival)

The standard error of the survival curve is approximately S(t) * std(hazard), by the delta 
method.  This is what is printed by the summary function, because it is what user's 
expect, but it has very poor performance for computing confidence intervals.  A much 
better one is exp(-1* confidence interval for the cumulative hazard), which is the 
default.  In fact there are lots of better ones whose relative ranking depends on the 
details of your simulation study.  About the only really consistent result is that 
anything thoughtful beats S(t) +- 1.96 se(S), easily.  The default in R is the one that 
was best in the most recent paper I had read at the time I set the default.  If I were to 
rank them today using an average over all the comparison papers it would be second or 
third, but the good methods are so close that in practical terms it hardly matters.

Terry Therneau

On 03/15/2013 06:00 AM, r-help-request at r-project.org wrote:
> Hi, I am wondering how the confidence interval for Kaplan-Meier estimator is calculated by survfit(). For example,?
>> >  summary(survfit(Surv(time,status)~1,data),times=10)
> Call: survfit(formula = Surv(rtime10, rstat10) ~ 1, data = mgi)
> ?time n.risk n.event survival std.err lower 95% CI upper 95% CI
> ?? 10 ?? 168????? 55??? 0.761? 0.0282??????? 0.707??????? 0.818
> I am trying to reproduce the upper and lower CI by using standard error. As far I understand, the default method for survfit() to calculate confidence interval is on the log survival scale, so:
> upper CI = exp(log(0.761)+qnorm(0.975)*0.0282) = 0.804
> lower CI = exp(log(0.761)-qnorm(0.975)*0.0282) = 0.720
> they are not the same as the output from survfit().
> Am I missing something?
> Thanks
> John

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