0
$\begingroup$

I am doing survival analysis with KM estimates and one of my curve displays a survival drop to zero:

KM curve drops to zero

As I was explained here the drop is here because the last time is an observed event (death) and not a censor. In my case it is not a database error because I don't have a constant censoring time. In this case, how should I interpret the drop? What is counterintuitive is that I probably don't have zero survival at this time point...

Here is the data:

time event
0.1 0
0.1 0
0.6 1
1.3 0
1.8 0
1.9 0
3.2 0
3.5 0
4.3 0
4.5 1
Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ What do you mean by: "don't have a constant censoring time"? You say, "I probably don't have zero survival at this time point...{presumably 4.5)". What is that based on? At time 4.31, there is only one animal/object/participant left in the cohort (the rest either had the event or their data was censored). When that last one has the event at time 4.5, there is no one left so survival is 0. $\endgroup$
    – Harvey Motulsky
    Commented Jan 25, 2023 at 11:00
  • $\begingroup$ I think "constant censoring time" is when the censoring time is the same for everyone, like in this post. I don't have this in my data because some events (death) can happen after the last censoring time. In this case I will always have the survival drop to 0%. What is not obvious to me is why the 7 censored persons should be considered dead? In my case we lost the followup, and it is more probable they are still alive. $\endgroup$
    – lacb
    Commented Jan 25, 2023 at 14:35

1 Answer 1

Reset to default
3
$\begingroup$

The underlying population might not have zero survival at that time point, but the cases in your data sample do. Thus the drop at the last time point to zero survival is correct. It describes your data accurately.

You have a small number of cases and an even smaller number of events. The power of survival analysis is limited by the number of events; you only have 2. Your estimates of survival throughout most of the time period are thus very imprecise. If the shaded region on your plot represents 95% confidence intervals for the survival curve, then you can't distinguish whether median survival is reached at time = 0.6 or time = 4.5. If you can't get more data from the underlying population, the Kaplan-Meier curve is the best you can do with what you have in a non-parametric model.

The prediction from a parametric survival model might look more intuitively pleasing without a sudden drop. A parametric model, however, means assuming a particular form for the survival curve and would be very unreliable with only 2 events.

Improve this answer
$\endgroup$
4
  • $\begingroup$ What I don't understand is why the 7 censored persons should be considered "dead"? In my case we lost the followup, and it is more probable they are still alive, thus it does not look like an accurate representation. $\endgroup$
    – lacb
    Commented Jan 25, 2023 at 14:37
  • 2
    $\begingroup$ @lacb individuals with censored observations provide no information about survival after they are no longer observed. In principle, each of them might have experienced the event immediately after the corresponding censoring time, or they might all have survived beyond your final observation time. But you can't tell either way from these data. You might consider a parametric model, as indicated in my edited answer, but with only 2 events that would be risky. $\endgroup$
    – EdM
    Commented Jan 25, 2023 at 14:54
  • $\begingroup$ OK I understand better what the KM curve represents. Also, I was wondering if in my case, low number of events could be interpreted as information about the survival process. For example, if I have a category of persons with many events occurring (death) and another one with only 2, then I tend to conclude that the second category has better survival. But it looks harder to have statistical significance or model fitting on such series of data. Maybe I should use a parametric model as you say. $\endgroup$
    – lacb
    Commented Jan 26, 2023 at 8:12
  • $\begingroup$ @lacb if you want to compare survival across different "categories of persons" then you should consider a semi-parametric Cox regression model (which includes a traditional "log-rank test" as a special case) that evaluates all persons together. Unlike a fully parametric model, that doesn't require an assumption about the overall shape of the survival curve. It still lets you evaluate how different characteristics are associated with survival. See the vignettes of the R survival package, starting with "The survival package." $\endgroup$
    – EdM
    Commented Jan 26, 2023 at 13:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.