topic Re: Brookmeyer and Crowley Confidence Intervals? in Statistical Procedures

Brookmeyer and Crowley Confidence Intervals?

daveconifer1 — Sun, 03 Nov 2019 03:00:52 GMT

Does anybody know how to generate 95% Confidence Intervals "based on the Brookmeyer and Crowley method" ? I'm programming a table that contains stats that come from PROC LIFETEST, so I was assuming (or maybe just hoping) that there's an ODS data set containing these. I've never heard of Brookmeyer and Crowley CI's before, unfortunately.

Thanks!!!

...dave

Re: Brookmeyer and Crowley Confidence Intervals?

unison — Sun, 03 Nov 2019 14:11:20 GMT

According to: (page 33 of the PDF) https://support.sas.com/documentation/onlinedoc/stat/142/lifetest.pdf,

"Brookmeyer and Crowley constructed the confidence interval for the median survival time based on the confidence interval for S(t)..."
This method is then extended to estimate any pth percentile. There are numerous options in the LIFETEST procedure but it looks like the confidence intervals for the quartile estimates use the extended Brookmeyer and Crowley method. The ODS table is called Quartiles. Below is a sample from the sas documentation:

ods output Quartiles;
proc lifetest 
	data=sashelp.BMT 
	conftype=linear;

	time T * Status(0);

	strata Group / 
		test=logrank 
		adjust=sidak;
run;

I just added the option CONFTYPE=LINEAR to see if this code would correspond to what was shown in the linked PDF above. If you run this code and compare observation 3 in the output to the table at the bottom of page 34 of the PDF, you'll see that the LIFETEST procedure uses the described methodology by default. It's up to you to determine which g-transformation (i.e. linear, logit, etc.) to use in generating these estimates.

best,

-unison

Re: Brookmeyer and Crowley Confidence Intervals?

daveconifer1 — Sun, 03 Nov 2019 14:10:59 GMT

I found a macro online which actually calculates these things when passed a standard TTE data set.

Written by Xiao Chen, it ran flawlessly. I passed the results to the statistician on my project and will report his comments back here.

https://stats.idre.ucla.edu/sas/examples/asa2/applied-survival-analysis-by-hosmer-lemeshow-and-maychapter-5-model-development/

Brookmeyer-Crowley 95% Confidence Interval

Lower Upper
newgroup total Estimate Limit Limit bc_lower bc_upper

1 88 155.000 154.000 156.000 154
2 175 120.000 115.000 121.000 115
3 70 99.000 75.000 155.000 75 130
4 194 121.000 117.000 121.000 117

Re: Brookmeyer and Crowley Confidence Intervals?

daveconifer1 — Sun, 03 Nov 2019 14:12:15 GMT

Thanks, Unison! I will look into that as well!

Re: Brookmeyer and Crowley Confidence Intervals?

unison — Sun, 03 Nov 2019 14:12:43 GMT

That's great, Dave. Looking forward to it.

Best of luck!

Re: Brookmeyer and Crowley Confidence Intervals?

FreelanceReinh — Sun, 03 Nov 2019 14:36:08 GMT

Hello @daveconifer1 and welcome to the SAS Support Communities!

I've just seen that @unison was faster in answering your question (while I was writing the text below), so this is rather a confirmation of what he has written ...

As far as I know, this refers to the 1982 article by R. Brookmeyer and J. Crowley "A Confidence Interval for the Median Survival Time" in Biometrics (see the reference in the PROC LIFETEST documentation). This confidence interval (and the corresponding CIs for the other two quartiles) are available in ODS table Quartiles of PROC LIFETEST.

I think for the original CI as per Brookmeyer and Crowley you need to specify the option CONFTYPE=LINEAR in the PROC LIFETEST statement because the default has been changed to CONFTYPE=LOGLOG in SAS version 9.1, but this is rather based on a generalization of the original CI. The formula and more details can be found in section "Breslow, Fleming-Harrington, and Kaplan-Meier Methods" of the PROC LIFETEST documentation.

Note (in the procedure output "Quartile Estimates") that the upper confidence limit is not included in the interval, which can be easily overlooked when only the ODS output dataset is used.