Charles M. Rowland
2010-Jul-15 20:45 UTC
[R] Standard Error for individual patient survival with survfit and summary.survfit
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.fitCall: 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 [[alternative HTML version deleted]]
Terry Therneau
2010-Jul-16 13:15 UTC
[R] Standard Error for individual patient survival with survfit and summary.survfit
> 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?help(survfit.object) will give you the answer. The std in the object is for the cumulative hazard, the printout uses a Taylor series argument to compute the se of the survival. (The are several reasons for this choice, including that se(survival) is not well defined by the standard formulas when S=0). Terry Therneau