Fluorite | Level 6

## Brookmeyer and Crowley Confidence Intervals?

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

1 ACCEPTED SOLUTION

Accepted Solutions
Lapis Lazuli | Level 10

## Re: Brookmeyer and Crowley Confidence Intervals?

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
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

-unison
5 REPLIES 5
Lapis Lazuli | Level 10

## Re: Brookmeyer and Crowley Confidence Intervals?

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
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

-unison
Fluorite | Level 6

## Re: Brookmeyer and Crowley Confidence Intervals?

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

Fluorite | Level 6

## Re: Brookmeyer and Crowley Confidence Intervals?

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.

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

Lapis Lazuli | Level 10

## Re: Brookmeyer and Crowley Confidence Intervals?

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

Best of luck!

-unison

## Re: Brookmeyer and Crowley Confidence Intervals?

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.

Discussion stats
• 5 replies
• 20103 views
• 7 likes
• 3 in conversation