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Does this mean you can't compute the median?

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The median is the data point which is greater than 50% of all data points. As soon as you have one or more data points, you always have a median. What does the phrase "doesn't reach 0.5" mean? Please clarify. – blubb Nov 30 '11 at 19:22
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Survival curves are typically used for censored data, Simon. It frequently happens that more than 50% of the data are censored and therefore the median is indeterminate. For example, five years after treatment for a cancer, 60% of the initial cohort of 100 patients were still alive. What is their median survival time? All you know is it's greater than five years. – whuber♦ Nov 30 '11 at 19:52
@whuber Shouldn't the question be phrased as: "Does this mean that you can't estimate the median?". – varty Nov 30 '11 at 20:11
As B_Miner points out, @varty, you can estimate the median by adopting some distributional assumptions. But, due to the censoring, the dataset itself has no median: we can only place a bound on it. Some people might claim that this dataset does have a median, but the median happens to be an interval rather than a number, but that's just another way of saying the same thing. – whuber♦ Nov 30 '11 at 20:14
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No, because survivorship can vary over time. A search of Google Images for "survival curve" will turn up plenty of plots of multiple survival curves that cross each other. Consider two populations of people at birth, one of which has high infant mortality but otherwise is very long-lived. The second population will start out with a higher survival rate, but eventually it will drop below the curve for the second population. – whuber♦ Nov 30 '11 at 21:44
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Yes, unless you use a parametric approach and are willing to extrapolate. See SAS Lifereg.

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+1 for this post. While non-parametric survival curves are far and away the most common, they are not the only method of constructing a survival curve. Caveats about extrapolation still apply however. – EpiGrad Nov 30 '11 at 22:53
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The median survival time is defined to be the time at which the survival curve crosses 50% survival. If the curve doesn't cross 50% (because survival is greater than 50% at the last time point), then median survival is simply undefined. More precisely, it is greater than the last time point on your survival curve. The only way around this, as B_Miner posted,is if you fit some kind of model so are willing to extrapolate beyond the time span you have data for.

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