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I've gone through the various questions relating to Kaplan-Meier plots and survival estimates, but I haven't really been able to find anything to help with this specific scenario.

Sometimes, when reading medical publications you realise that the authors haven't reported median survival times of subgroups, but have simply plotted them in Kaplan-Meier curves. Drawing a line at 0.5 on the y-axis and dropping a vertical line to the x-axis when said line intersects with the Kaplan-Meier curve will give you a rough estimate of the median survival time and help you interpret the potential "difference", if the paper otherwise isn't too enlightening.

However, how do you estimate the median survival time, if say one subgroup never reaches the 0.5 mark during the analysis period?

Attached is such a situation taken from this paper:

Epidermal Growth Factor Receptor, p53 Mutation, and Pathological Response Predict Survival in Patients with Locally Advanced Esophageal Cancer Treated with Preoperative Chemoradiotherapy, Michael K Gibson et al., Clin Cancer Res 2003;9:6461-6468

a plot

I mean regardless of if the cohort with "no mutation" reaches 0.5 or not, you could still calculate a median survival time for that cohort if you had the raw data!
I appreciate that the method of "drawing a line" and eyeballing isn't exact science is it, but sometimes its the best you can do.

Any pointers helping with this issue would be great and any ideas for a work around would be great.

Many thanks in advance,

Oliver

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  • $\begingroup$ The data might show you that 16 out of 29 of the "mutation present" cases survived more than 4000 days (or whatever the numbers are), which is over 10 years. How would you work out the median from this? $\endgroup$ – Henry Jun 12 '15 at 6:40
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The time at which the Kaplan-Meier survival curve crosses the 50% line is the non-parametric estimate of the median survival time. If the Kaplan-Meier curve does not cross the 50% line, then the non-parametric estimate is not defined. At this stage, I can see two simple options:

  • use another quantile (e.g. 0.75) to compare the two groups;
  • approximate the survival curve by means of a parametric fit and derive the median survival time using the model.

As a side note, the typical underlying assumption in survival analysis is that any subject will eventually experience the event of interest if he is observed for a sufficient long period of time. In other words, the survival curve will reach zero (and in particular cross the 50% line) if the observation period lasts a sufficient long time. In contrast, cure modelling deals with situations where the survival curve eventually reaches a plateau. In that case, it is not correct to use a parametric model to extrapolate the survival curve below the plateau.

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  • $\begingroup$ Thanks ocram, in simple terms I guess this just means that there are different ways at estimating/calculating the median. Intuitively I find it odd to say that based on the survival curve the median is not defined, but if you had the data, you could easily define it. I will think about using a different quantile, but as I'm estimating these type of data from multiple studies, it would be suboptimatl to use different quantile estimates across different studies. Point b is something I personally am not too sure how to do honestly. $\endgroup$ – OFish Jun 12 '15 at 6:34
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    $\begingroup$ "based on the survival curve the median is not defined, but if you had the data, you could easily define it". Well, you can define it from a theoretical point of view, but in practice you won't be able to compute the Kaplan-Meier estimate of the median from the data because the observation period was too short... $\endgroup$ – ocram Jun 12 '15 at 6:40
  • $\begingroup$ agreed, but if you had the survival times themselves, couldn't you simply compute (in R) it by typing median(survivaltimes) of that subgroup to obtain a median of that cohort. Or is this incorrect, because we're dealing with censored data...? $\endgroup$ – OFish Jun 12 '15 at 6:42
  • $\begingroup$ Exactly, this is incorrect because of censoring $\endgroup$ – ocram Jun 12 '15 at 6:46
  • $\begingroup$ Thanks, this was an error of thought on my end then. Stupid me. Appreciate your help on getting my sleep-deprived brain back on top of its game :). +1 of course. $\endgroup$ – OFish Jun 12 '15 at 6:47

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