使用R生存软件包计算proc寿命测试95％CI的中位生存时间

Question

I have been trying to replicate the results of proc lifetest in SAS using R ( survival package and survifit function) -and especially calculate the 95%Confidence interval for the median survival time.

I know that SAS is using the following formula to calculate the confidence interval for the median:

*abs(g(S(t))-g(1-0.5)/g'(S(t))σ(S(t)))<=1.96*

with g'(x) being the first derivative of g(x) and σ(S(t)) is the standard error of the Survival curve, and the default transformation of g in SAS is the g(x)=log(-log(x))

So the formula inside the absolute becomes:

(log(-log(S(t)))-log(-log(0.5)))*S(t)*log(S(t))/σ(S(t))

Here is an example using the kidney data from the survival package:

fit1 = survfit(Surv(kidney$time,kidney$status)~kidney$sex, data=kidney)
print(fit1)
BCinds<-abs((log(-log(fit1$surv))-log(-log(0.5)))*fit1$surv*log(fit1$surv)/fit1$std.err)<=1.96

when I run the code I got from the print(fit1) :

                n events median 0.95LCL 0.95UCL
kidney$sex=1 20     18     22      12      63
kidney$sex=2 56     40    130      66     190

However when I calculate it through the BCinds I get a very different and wider CI of (9, 154) for sex=1 and for sex=2 the CI is (39, 511).

sex=1 95%CI: (9, 154)  sex=2 95%CI: (39, 511)

SAS code also produces different confidence intervals for the median survival time for the same dataset:

    ods graphics on;
proc lifetest data=work.test
    plots=survival(nocensor cb=hw cl strata=panel);
    strata sex/group=sex;
    time time*status(0);
    run;
ods graphics off;

Results in the following:

 sex=1: median=22 and 95%CI: (12, 30)
 sex=2: median=130 and 95%CI: (58,185)

Any ideas on why I get so different results? Also could you suggest how I could automate the final step of the method? At the moment I do it visually but I would like to put it in a loop so I need to do it automatically.

Thanks!

Answer 1

Update

So after "randomly" typing arguments in the R code I managed to solve part of my problem.

So survfit calculates the median time confidence interval using the log transformation of the formula given above and that is why there is a disagreement between the intervals of R and SAS (which uses by default the log-log transformation).

So by adding an argument in the R code we can force R to calculate the Confidence intervals the same way SAS does. So for the example I gave above with the kidney data we have:

    `survfit(Surv(kidney$time,kidney$status)~kidney$sex, conf.type="log-log"
    + )
    Call: survfit(formula = Surv(kidney$time, kidney$status) ~ kidney$sex, 
        conf.type = "log-log")

              n events median 0.95LCL 0.95UCL
kidney$sex=1 20     18     22      12      30
kidney$sex=2 56     40    130      58     185`

other confidence interval types that we can get from the survfit are: “log”, “log-log”, “plain”, “none”

I still haven't figured out though what is wrong with the code I used to get the confidence interval so if anyone has any idea what is wrong with it I would appreciate any feedback.

Answer 2

I guess it's because of the fit1$std.err part in BCinds . Here you are supposed to fit in the standard error of S(t) -- but fit1$std.err (according to the R documentation of survfit.object ) gives you the standard error of the cumulative hazard or -log(survival). Try using summary(fit1)$std.err instead.