# [R] R Kaplan-Meier plotting quirks?

rent0009 at umn.edu rent0009 at umn.edu
Wed Oct 17 17:38:51 CEST 2012

```Thank you Chris! That makes very good sense, I was just so in the weeds I
could not see it. I will mess with survreg after I am done teaching today.
Thank you for the fresh set of eyes and advice.

Mike.

On Oct 17 2012, Andrews, Chris wrote:

>Mike,
>
>My guess is that you have censored observations in the middle.
When using the minimum time, the events are happening prior to censorings.
Then the riskset is large and the curve decreases slightly.
When using the maximum time, the events are happening after the
censorings. Then the riskset is small and the curve decreases quickly.
>
For example, moving the first event from time 1 to time 5 causes the final
survival estimate to be lower when using max time (.375) than min time
(.533):
>
>library(survival)
df <- data.frame(mintime = c(1,2,3,4,6), maxtime = c(5,2,3,4,6), Delta=
c(1,0,1,0,0))
>plot(survfit(Surv(mintime,Delta)~1,data=df), conf=FALSE, xlim=c(0,7))
>lines(survfit(Surv(maxtime,Delta)~1,data=df), col=2)
>
>> summary(survfit(Surv(mintime,Delta)~1,data=df))
>Call: survfit(formula = Surv(mintime, Delta) ~ 1, data = df)
>
> time n.risk n.event survival std.err lower 95% CI upper 95% CI
>    1      5       1    0.800   0.179        0.516            1
>    3      3       1    0.533   0.248        0.214            1
>> summary(survfit(Surv(maxtime,Delta)~1,data=df))
>Call: survfit(formula = Surv(maxtime, Delta) ~ 1, data = df)
>
> time n.risk n.event survival std.err lower 95% CI upper 95% CI
>    3      4       1    0.750   0.217       0.4259            1
>    5      2       1    0.375   0.286       0.0839            1
>
Given that you have interval censored data, you can consider fitting the
survival curve with interval censoring techniques. For example survreg fits
a parametric curve.
>
>Chris
>
>-----Original Message-----
>From: Michael Rentz [mailto:rent0009 at umn.edu]
>Sent: Tuesday, October 16, 2012 12:36 PM
>To: r-help at r-project.org
>Subject: [R] R Kaplan-Meier plotting quirks?
>
Hello. I apologize in advance for the VERY lengthy e-mail. I endeavor to
include enough detail.
>
I have a question about survival curves I have been battling off and on
for a few months. No one local seems to be able to help, so I turn here.
The issue seems to either be how R calculates Kaplan-Meier Plots, or
something with the underlying statistic itself that I am misunderstanding.
Basically, longer survival times are yielding steeper drops in survival
than a set of shorter survival times but with the same number of loss and
retention events.
>
As a minor part of my research I have been comparing tag survival in
marked wild rodents. I am comparing a standard ear tag with a relatively
new technique. The newer tag clearly “wins” using survival tests, but
the resultant Kaplan-Meier plot does not seem to make sense. Since I am
dealing with a wild animal and only trapped a few days out of a month the
data is fairly messy, with gaps in capture history that require assumptions
of tag survival. An animal that is tagged and recaptured 2 days later with
a tag and 30 days later without one could have an assumed tag retention of
2 days (minimum confirmed) or 30 days (maximum possible).
>
Both are significant with a survtest, but the K-M plots differ. A plot of
minimum confirmed (overall harsher data, lots of 0 days and 1 or 2 days)
yields a curve with a steep initial drop in “survival”, but then a
leveling off and straight line thereafter at about 80% survival. Plotting
the maximum possible dates (same number of losses/retention, but retention
times are longer, the length to the next capture without a tag, typically
25-30 days or more) does not show as steep of a drop in the first few
days, but at about the point the minimum estimate levels off this one
begins dropping steeply. 400 days out the plot with minimum possible
estimates has tag survival of about 80%, whereas the plot with the same
loss rate but longer assumed survival times shows only a 20% assumed
survival at 400 days. Complicating this of course is the fact that the
great majority of the animals die before the tag is lost, survival of the
rodents is on the order of months.
>
I really am not sure what is going on, unless somehow the high number of
events in the first few days followed by few events thereafter leads to the
assumption that after the initial few days survival of the tag is high. The
plotting of maximum lengths has a more even distribution of events, rather
than a clumping in the first few days, so I guess the model assumes
relatively constant hazards? As an aside, a plot of the mean between the
minimum and maximum almost mirrors the maximum plot. Adding five days to
the minimum when the minimum plus 5 is less than the maximum returns a plot
with a steeper initial drop, but then constant thereafter, mimicking the
minimum plot, but at a lower final survival rate.
>
Basically, I am at a loss why surviving longer would *decrease* the
survival rate???
>
My co-author wants to drop the K-M graph given the confusion, but I think
it would be odd to publish a survival paper without one. I am not sure
which graph to use? They say very different things, while the actual
statistics do not differ that greatly.
>
I am more than happy to provide the data and code for anyone who would
like to help if the above is not explanation enough. Thank you in advance.
>
>Mike.
>
>
>--
>Michael S. Rentz
>PhD Candidate, Conservation Biology
>University of Minnesota
>5122 Idlewild Street
>Duluth, MN 55804
>(218) 525-3299
>rent0009 at umn.edu
>
>
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