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# Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

Hello all,

Usually for Kaplan-Meier estimates, the client is interested of having the 25%, 50% and 75% quartiles for survival estimates.  Now the client would like to have also the 10% percentile, since we don’t have enough events.

In proc lifetest, we can easily retrieve the 25%, 50% and 75% quartiles with the associated Confidence Interval (CI).

Does anyone know how to get the CI for another percentile, let’s say 10%?  From outsurv dataset, we can easily pull out the 10th percentile but not the associated CI to that value.  I do not want the CI for the curve, but the CI associated to the 10th percentile value.

OBSDUR_CENSOR_SURVIVALSDF_LCLSDF_UCL
10.1.0000001.000001.00000
2800.9200000.716390.97937
31300.880000

0.67256

0.95964

41800.8400000.628060.93673
52300.8000000.584450.91146
65200.7600000.542050.88428
76300.6800000.460930.82527
87000.6400000.422150.79378

So here's the 10th percentile is DUR=13 (using loglog).    So how do we get the CI associated to DUR=13?

Usually proc lifestest gives the 25%, 50% and 75% percentile automatically.

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Solution
2 weeks ago
Super Contributor
Posts: 301

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

I dont think you can get a CI of the percentile that is estimated by a non-parametric method like the KM-curve. That method is aiming on giving estimates and CI in terms of an interval around the curve, not an interval on the time-axis.

A way to get an interval on the time axis is to use an accelarated failure model instead. Here you model the time to event by assuming some parametric distribution on the time-to-event. See the documentation for PROC LIFEREG. For example, if you assume a weibull distribution on the time-to event, you can then find an analytic expression for the 10th percent percentile. Then you can plug in the confidence limits of the parameters into that expression.

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Super User
Posts: 20,750

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

You only have estimates for time points that you have. Usually estimates are reported for specific time points, not percentiles.

That being said the usual protocol is to pick the time closes to the time of interest and use that as the estimate which is in line with the step curve nature of KM estimates.  Extending that to percentiles, pick the time point that's closest to 10th percentile and use that.

New Contributor
Posts: 4

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

Yes I am ok with getting the time point closest to 10th percentile.  In the above example, it will be DUR=13.

Now, I need to calculate the 95% CI of that DUR=13.

Another example from SAS (http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_lifetest_sec...).  On this link, you will find the Quartile Estimates,  The quartiles 25%, 50% and 75% are given in proc lifestest (see below on print screen).   But if I want the 10th percentile, how can I get the associated 95% CI?

Super User
Posts: 20,750

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

Try the outsurv dataset?

New Contributor
Posts: 4

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

The oursurv gives the CI of the curve, not the CI of the percentile.  For example, on this print screen below, the 10th percentile is AVAL=4.  The SDF_LCL and SDF_UCL is the CI of the survival estimate (here 0.8947368421) and not the CI of AVAL=4.

I'm looking for the CI of the percentile, not the curve.  Thanks

Super User
Posts: 20,750

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

Ok, you want a CI on the survival time, the 10th percentile of the time of survival.

Your first sentence says survival estimates but those are time points not survival function estimates therefore my confusion.

I think this is the description of what you're looking for and I *think* it has to be calculated manually

SAS/STAT(R) 9.2 User's Guide, Second Edition

Solution
2 weeks ago
Super Contributor
Posts: 301

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

I dont think you can get a CI of the percentile that is estimated by a non-parametric method like the KM-curve. That method is aiming on giving estimates and CI in terms of an interval around the curve, not an interval on the time-axis.

A way to get an interval on the time axis is to use an accelarated failure model instead. Here you model the time to event by assuming some parametric distribution on the time-to-event. See the documentation for PROC LIFEREG. For example, if you assume a weibull distribution on the time-to event, you can then find an analytic expression for the 10th percent percentile. Then you can plug in the confidence limits of the parameters into that expression.

New Contributor
Posts: 4

## Re: Proc Lifetest: Getting Confidence Interval (CI) for a specific percentile, not 25%, 50%, 75% quartiles

Correct.  Does anyone know how to calculate this manually?