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The survival package function survfit() calculates a confidence interval for the estimated median survival time. It seems clear that this interval is calculated as the set of timepoints for which the 95% CI for S_hat(t) contains 0.5, and as such the interval will vary depending on which transformation is used to construct the pointwise 95% CIs.

My question is: I have seen this referred to on various message boards as the Brookmeyer-Crowley method - is this correct?

My thoughts: It seems that the Brookmeyer-Crowley method is related to the above method in that it constructs the interval as the set of points for which we do not reject the null hypothesis that S_hat(t) = 0.5, but that test is a sign test, and so stricly speaking, while related, the method survfit() uses is not the Brookmeyer-Crowley method, but rather a pseudo-Brookmeyer-Crowley method.

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The 'generalised sign test' in Brookmeyer & Crowley's paper rejects if $\hat S-1/2$ is greater than a specified multiple of the Greenwood standard error estimate. That's what the construction in survfit does.

It's a 'generalised sign test' in the sense that it generalises the sign test for the median, not in the sense that it uses signs and does some different thing with them.

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  • $\begingroup$ So the survfit default method can be correctly called the Brookmeyer & Crowley method? $\endgroup$
    – fair21comic
    Commented Jun 27, 2023 at 10:27
  • $\begingroup$ Yes, it's the same method. $\endgroup$
    – Thomas Lumley
    Commented Jun 27, 2023 at 21:13
  • $\begingroup$ Having looked into it further, I don't think this is correct. It's similar, in that that it builds intervals for median survival as the set of timepoints that fail to reject a null hypothesis that survival = 0.5, but the test is different. My reason for thinking this is that I used the quantileKM() function from the biostatUZH and the results it gives are different to those from survfit(). The biostatUZH package documentation states "Computation of confidence intervals is done according to Brookmeyer, R. and Crowley, J. (1982)" $\endgroup$
    – fair21comic
    Commented Jun 28, 2023 at 22:18
  • $\begingroup$ Furthermore, the median survival CI in survfit() changes as you alter the confidence interval type (for suvival estimates), whereas the B-C method, which is based on a single test (modified sign test), would not vary. $\endgroup$
    – fair21comic
    Commented Jun 28, 2023 at 22:18
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    $\begingroup$ @fair21comic the Brookmeyer-Crowley method is for using the set of point-wise confidence intervals (CIs) for survival fractions to estimate CI for the median (or other quantile) survival time. If the method for estimating the original survival-fraction CI changes, then the Brookmeyer-Crowley estimates will change, too. The default survival-fraction CI type for survfit() is "log"; that for quantileKM() is "log-log". I recall that the original Brookmeyer-Crowley paper might have used even a different survival-fraction CI type. I suspect that explains the differences you found. $\endgroup$
    – EdM
    Commented Jun 29, 2023 at 15:35

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