 I am using the coxph, survfit and summary.survfit functions to calculate an estimate of predicted survival with confidence interval for future patients based on the survival distribution of an existing cohort of subjects.  I am trying to understand the calculation and interpretation of the std.err and confidence intervals printed by the summary.survfit function.

Using the default confidence interval type of "log", I would have expected the confidence intervals to be calculated as
                exp( log(surv) +,- Z*std.err )
where z is the appropriate quantile of the normal distribution.   This does seem to be the case but using the std.err found in the survfit object rather than the std.err that is printed by and returned with the summary.survfit function.

Can anyone tell me what is the difference between these two standard errors and how should I interpret the confidence intervals and std.err given these differences?

An example using R version 2.11.1 with survival package version 2.35-8 on Windows operating system is below

Thanks,

Charley Rowland
Celera, Corp.

Example:

> fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian)    # Fit cox model to existing data
> s.fit=survfit(fit,newdata=data.frame(age=60))                    # Calculate predicted survival for a new patient
> sum.s.fit=summary(s.fit)                                                                # Print summary of predicted survival estimates.
> sum.s.fit
Call: survfit(formula = fit, newdata = data.frame(age = 60))

 time n.risk n.event survival std.err lower 95% CI upper 95% CI
   59     26       1    0.978  0.0240        0.932        1.000
  115     25       1    0.952  0.0390        0.878        1.000
  156     24       1    0.917  0.0556        0.814        1.000
  268     23       1    0.880  0.0704        0.752        1.000
  329     22       1    0.818  0.0884        0.662        1.000
  353     21       1    0.760  0.0991        0.588        0.981
  365     20       1    0.698  0.1079        0.516        0.945
  431     17       1    0.623  0.1187        0.429        0.905
  464     15       1    0.549  0.1248        0.352        0.858
  475     14       1    0.480  0.1267        0.286        0.805
  563     12       1    0.382  0.1332        0.193        0.757
  638     11       1    0.297  0.1292        0.127        0.697

### The confidence intervals extracted from the survfit and summary.survfit objects are identical and agree with what is printed by summary
> s.fit$lower
 [1] 0.9318402 0.8784979 0.8144399 0.7522512 0.6616253 0.5881502 0.5159010 0.4287437 0.3519573 0.2857688 0.1932689 0.1267205
> sum.s.fit$lower
 [1] 0.9318402 0.8784979 0.8144399 0.7522512 0.6616253 0.5881502 0.5159010 0.4287437 0.3519573 0.2857688 0.1932689 0.1267205

###  However, the standard errors extracted from the survfit and summary.survfit objects are different
> s.fit$std.err               ###Note the std.err from survfit does not agree with what is printed by the summary.survfit function
 [1] 0.02459050 0.04099162 0.06065735 0.07997872 0.10806000 0.13052489 0.15448058 0.19052784 0.22719704 0.26416491 0.34826243 0.43480448
> sum.s.fit$std.err     ###Note the std.err from the summary object agrees with what is printed by summary.survfit
 [1] 0.02404586 0.03902366 0.05563833 0.07037450 0.08836045 0.09914814 0.10787837 0.11866803 0.12481970 0.12669151 0.13320179 0.12919546

###  The (lower) confidence interval printed by the summary.survfit function appears to be based on the stderr contained in the survfit object  (not std.err printed in summary)
> zval <- qnorm(1- (1-.95)/2, 0,1)
> exp( log(s.fit$surv) - zval*s.fit$std.err)
 [1] 0.9318402 0.8784979 0.8144399 0.7522512 0.6616253 0.5881502 0.5159010 0.4287437 0.3519573 0.2857688 0.1932689 0.1267205


> exp( log(s.fit$surv) - zval*sum.s.fit$std.err)
 [1] 0.9328355 0.8818930 0.8224912 0.7665456 0.6876705 0.6254552 0.5652418 0.4935883 0.4301637 0.3741385 0.2945926 0.2306651



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