# median survival time

#### noob

##### New Member
Hello,

I'm trying to plot a survival curve and I also need median survival time and 95%CI.
I specifically need the 95% CI which is not easy to calculate for a median.
So that's why i'm using spss, though i don't have experience with it.
(I do have some experience with statistica, it plots the survival curve but it doesn't calulate the median 95% CI, so that why I'm using SPSS 17.0 for the first time.)

When use kaplan-meier, the resulting median survival time doesn't correspond with the median when calculated with excel???
Should'nt they be the same?

Tnx

#### noob

##### New Member
Perhaps I should be more to the point.

708, 288, 180, 228, 856, 344, 89, 78, 78, 600, 88, 26, 202, 100 75
12, 235, 25, 156, 76, 223, 7, 64

Mediaan is 100 right. Which formula would u use to calculate 95% confidence interval for the median?

100 (95% CI: ?,? )

#### Dason

In general it depends on the underlying distribution. I don't work with survival data much but I'm guessing there's a specific way to do it for this type of data.

##### Ninja say what!?!
In general it depends on the underlying distribution. I don't work with survival data much but I'm guessing there's a specific way to do it for this type of data.
There is. noob, I can show you how to do it parametrically. However, I'll have to look at some references to show you how to do it non-parametric, which appears like what you are asking.

#### gianmarco

##### TS Contributor
Hi.

You can calculate CI for the median in, two ways:

1) you can attach some sort of error range by bootstrapping the median and using the percentile method (or BCa) for assessing the CI;

2) you can use the method developed by:

D. Bonett, R.M. Price, “Statistical Inference for a Linear Function of Medians: Confidence Intervals, Hypothesis Testing, and Sample Size Requirement,” Psychological Methods 7 [2003] 370-83

I have implemented this latter method in my free Excel Template for Robust Statistics (see my previous post: http://talkstats.com/showthread.php?t=9486).

See attached image for a screen-shot of the statistics reported by my Template for your data. 95% CI and its lower and upper bound are displayed.

Hope this helps,
regards
Gm

#### fed1

##### TS Contributor
Before you get out the super computer, consider using confidence limit based on order statistics. Consider bracketing with say the ith and jth smallest observation (count from the smallest).

$$Pr( X_{i} < median < X_{j} ) = \sum_{i}^{j - 1} Binomial(n,0.5,x)$$

#### noob

##### New Member
Hello, tnx everyone for your replies. I really appreciate it.

708, 288, 180, 228, 856, 344, 89, 78, 78, 600, 88, 26, 202, 100 75
12, 235, 25, 156, 76, 223, 7, 64

I gave it a try with SPSS. By the way all data are uncensored.
Analyse --> survival --> Kaplan-meier

median estimate : 100 (Std Error 54,301)
95% CI : 0 - 206,4

lower bound is 0 ??? This can't be correct?

#### noob

##### New Member
100 (95% CI: 0 - 206,4)
Maybe lower bound could be 0? upper bound is also high I guess. What do you think?

Hi Gianmarco, when comparing with your results: 100 (95% CI: 29,5 - 170,5) I see a big difference
Maybe when using Kaplan-meier this is calculated differently?

When surfing on the net I see there are several methods for calculating confidence interval for the median survival time. I don't know which one SPSS uses, but it's not so relevant for me. I'm not an expert, just hoping for easy result via software I'm using SPSS and I hope it gives me a good and reliable result.

Furthermore when I use a smaller dataset, doing everyhing (survival --> kaplan- meier) the same I noticed the estimate for the median according SPSS didn't correspond with the conventional median (via excel).

This is strange I thought they would be the same?

#### gianmarco

##### TS Contributor
Hi!

Sorry for having lead you astray with my reply: I was only talking about CI for the median, with not specific reference to time series.

Best Regards,
Gm